[{"data":1,"prerenderedAt":20926},["ShallowReactive",2],{"lesson:\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture":3,"course-wordcounts":15146,"ref-card-index":16058,"nav:deep-learning":20740,"tikz:d6ce671c97176b2b643ad7955b2ca46fd4e1dbf2599996eaa1c0995765addaec":20917,"tikz:9246ea2730ba777edb7cc9c149081657e223097713af609d24b4c6f8cefae95d":20918,"tikz:7cacdfcad2b10ed197c265b5330e0fbcf7c1f572e5e269b398b3def3e55b39f5":20919,"tikz:0e9b89062c79a5c37cdd4f177fc8bd439a35bcf110e9a6cfe596ef67b45c56b9":20920,"tikz:f15e98a0903dca7a539173f9fdedc5ae5795eb2cef9a9c789da04c8bce4ac7e7":20921,"tikz:0059ea8284efc4aadd7974cc24538e4d5f228170f7667a0b2dd57d4959a5a141":20922,"tikz:b25d3e058486111736ec5a3f07ac94e34c428ecad378919f94f609c6203ee565":20923,"tikz:272e623b47105a0ccce820783ca7f87425ae84725cf3a114befa4e199f3ab22f":20924,"tikz:38040bac6fd1de2d5f8ae650fb1326d4806fae00522338df1a790bff3914a4ac":20925},{"id":4,"title":5,"blurb":6,"body":7,"brief":15118,"category":15119,"description":15120,"draft":15121,"extension":15122,"meta":15123,"module":15125,"navigation":15126,"path":15127,"practice":15128,"rawbody":15129,"readingTime":15130,"seo":15135,"sources":15136,"status":15141,"stem":15142,"summary":15143,"topics":15144,"__hash__":15145},"course\u002F06.deep-learning\u002F05.architectures\u002F06.the-transformer-architecture.md","The Transformer Architecture","",{"type":8,"value":9,"toc":15105},"minimark",[10,44,82,87,118,884,1067,1146,2043,2181,2273,3042,3336,3343,3508,3517,4046,4929,4952,4956,4960,4978,5791,6004,6007,6010,6121,6351,6355,6373,6552,6563,6906,7691,7799,7802,7805,7809,7816,8022,8080,8084,8123,8126,8129,8133,8427,8783,8937,9428,9814,9817,9875,9879,9882,9955,9989,9992,9996,10027,10617,10620,10623,10627,10637,11401,12064,12067,12317,13180,13326,13402,13547,14215,14472,14475,14486,14490,15009,15101],[11,12,13,14,19,20,24,25,28,29,33,34],"p",{},"The previous lesson built the\n",[15,16,18],"a",{"href":17},"\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers","attention mechanism",":\nscaled dot-product attention, multi-head projection, and the positional\nencoding that restores order to a permutation-equivariant operation. That is the\n",[21,22,23],"em",{},"operation",". This lesson assembles the ",[21,26,27],{},"architecture",": how those operations\nstack into the encoder–decoder of ",[30,31,32],"q",{},"Attention Is All You Need,"," how the stack\nsplits into the three families that dominate modern practice, and where its\nparameters and its quadratic cost actually live.",[35,36,37],"sup",{},[15,38,43],{"href":39,"ariaDescribedBy":40,"dataFootnoteRef":6,"id":42},"#user-content-fn-chollet-transformer",[41],"footnote-label","user-content-fnref-chollet-transformer","1",[45,46,48],"callout",{"type":47},"definition",[11,49,50,54,55,81],{},[51,52,53],"strong",{},"Definition (Transformer)."," A sequence model built entirely from attention\nand position-wise feed-forward layers, with no recurrence or convolution.\nToken embeddings plus positional encodings feed a stack of ",[56,57,60],"span",{"className":58},[59],"katex",[56,61,65],{"className":62,"ariaHidden":64},[63],"katex-html","true",[56,66,69,74],{"className":67},[68],"base",[56,70],{"className":71,"style":73},[72],"strut","height:0.6833em;",[56,75,80],{"className":76,"style":79},[77,78],"mord","mathnormal","margin-right:0.109em;","N"," identical\nlayers; each layer interleaves multi-head attention with a position-wise MLP,\nand wraps every sublayer in a residual connection followed by layer\nnormalization. A linear projection and softmax read the top of the stack out\nto a distribution over the vocabulary.",[83,84,86],"h2",{"id":85},"the-sublayer-wrapper","The sublayer wrapper",[11,88,89,90,93,94,112,113,117],{},"The atom of the architecture is not a layer but a ",[51,91,92],{},"sublayer wrapper",": a\nresidual skip around a function ",[56,95,97],{"className":96},[59],[56,98,100],{"className":99,"ariaHidden":64},[63],[56,101,103,107],{"className":102},[68],[56,104],{"className":105,"style":106},[72],"height:0.8889em;vertical-align:-0.1944em;",[56,108,111],{"className":109,"style":110},[77,78],"margin-right:0.1076em;","f",", followed by\n",[15,114,116],{"href":115},"\u002Fdeep-learning\u002Fregularization\u002Fnormalization","layer normalization",". Every\nattention block and every feed-forward block in the entire model is wrapped this\nway, so we fix the convention before stacking anything.",[45,119,120,144,755],{"type":47},[11,121,122,125,126,143],{},[51,123,124],{},"Definition (Position-wise feed-forward network)."," A two-layer MLP applied\nindependently and identically to every position, with an expansion factor of\ntypically ",[56,127,129],{"className":128},[59],[56,130,132],{"className":131,"ariaHidden":64},[63],[56,133,135,139],{"className":134},[68],[56,136],{"className":137,"style":138},[72],"height:0.6444em;",[56,140,142],{"className":141},[77],"4",":",[56,145,148],{"className":146},[147],"katex-display",[56,149,151],{"className":150},[59],[56,152,154,197,397,505,665],{"className":153,"ariaHidden":64},[63],[56,155,157,161,170,175,179,184,189,194],{"className":156},[68],[56,158],{"className":159,"style":160},[72],"height:1em;vertical-align:-0.25em;",[56,162,165],{"className":163},[164],"mop",[56,166,169],{"className":167},[77,168],"mathrm","FFN",[56,171,174],{"className":172},[173],"mopen","(",[56,176,178],{"className":177},[77,78],"x",[56,180,183],{"className":181},[182],"mclose",")",[56,185],{"className":186,"style":188},[187],"mspace","margin-right:0.2778em;",[56,190,193],{"className":191},[192],"mrel","=",[56,195],{"className":196,"style":188},[187],[56,198,200,203,343,347,388,391,394],{"className":199},[68],[56,201],{"className":202,"style":160},[72],[56,204,207,212,219,222,225,283,287,292,295,337,340],{"className":205},[206],"minner",[56,208,174],{"className":209,"style":211},[173,210],"delimcenter","top:0em;",[56,213,215],{"className":214},[164],[56,216,218],{"className":217},[77,168],"ReLU",[56,220,174],{"className":221},[173],[56,223,178],{"className":224},[77,78],[56,226,228,233],{"className":227},[77],[56,229,232],{"className":230,"style":231},[77,78],"margin-right:0.1389em;","W",[56,234,237],{"className":235},[236],"msupsub",[56,238,242,274],{"className":239},[240,241],"vlist-t","vlist-t2",[56,243,246,269],{"className":244},[245],"vlist-r",[56,247,251],{"className":248,"style":250},[249],"vlist","height:0.3011em;",[56,252,254,259],{"style":253},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[56,255],{"className":256,"style":258},[257],"pstrut","height:2.7em;",[56,260,266],{"className":261},[262,263,264,265],"sizing","reset-size6","size3","mtight",[56,267,43],{"className":268},[77,265],[56,270,273],{"className":271},[272],"vlist-s","​",[56,275,277],{"className":276},[245],[56,278,281],{"className":279,"style":280},[249],"height:0.15em;",[56,282],{},[56,284],{"className":285,"style":286},[187],"margin-right:0.2222em;",[56,288,291],{"className":289},[290],"mbin","+",[56,293],{"className":294,"style":286},[187],[56,296,298,302],{"className":297},[77],[56,299,301],{"className":300},[77,78],"b",[56,303,305],{"className":304},[236],[56,306,308,329],{"className":307},[240,241],[56,309,311,326],{"className":310},[245],[56,312,314],{"className":313,"style":250},[249],[56,315,317,320],{"style":316},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[56,318],{"className":319,"style":258},[257],[56,321,323],{"className":322},[262,263,264,265],[56,324,43],{"className":325},[77,265],[56,327,273],{"className":328},[272],[56,330,332],{"className":331},[245],[56,333,335],{"className":334,"style":280},[249],[56,336],{},[56,338,183],{"className":339},[182],[56,341,183],{"className":342,"style":211},[182,210],[56,344],{"className":345,"style":346},[187],"margin-right:0.1667em;",[56,348,350,353],{"className":349},[77],[56,351,232],{"className":352,"style":231},[77,78],[56,354,356],{"className":355},[236],[56,357,359,380],{"className":358},[240,241],[56,360,362,377],{"className":361},[245],[56,363,365],{"className":364,"style":250},[249],[56,366,367,370],{"style":253},[56,368],{"className":369,"style":258},[257],[56,371,373],{"className":372},[262,263,264,265],[56,374,376],{"className":375},[77,265],"2",[56,378,273],{"className":379},[272],[56,381,383],{"className":382},[245],[56,384,386],{"className":385,"style":280},[249],[56,387],{},[56,389],{"className":390,"style":286},[187],[56,392,291],{"className":393},[290],[56,395],{"className":396,"style":286},[187],[56,398,400,403,443,448,452,455,495,498,502],{"className":399},[68],[56,401],{"className":402,"style":106},[72],[56,404,406,409],{"className":405},[77],[56,407,301],{"className":408},[77,78],[56,410,412],{"className":411},[236],[56,413,415,435],{"className":414},[240,241],[56,416,418,432],{"className":417},[245],[56,419,421],{"className":420,"style":250},[249],[56,422,423,426],{"style":316},[56,424],{"className":425,"style":258},[257],[56,427,429],{"className":428},[262,263,264,265],[56,430,376],{"className":431},[77,265],[56,433,273],{"className":434},[272],[56,436,438],{"className":437},[245],[56,439,441],{"className":440,"style":280},[249],[56,442],{},[56,444,447],{"className":445},[446],"mpunct",",",[56,449],{"className":450,"style":451},[187],"margin-right:2em;",[56,453],{"className":454,"style":346},[187],[56,456,458,461],{"className":457},[77],[56,459,232],{"className":460,"style":231},[77,78],[56,462,464],{"className":463},[236],[56,465,467,487],{"className":466},[240,241],[56,468,470,484],{"className":469},[245],[56,471,473],{"className":472,"style":250},[249],[56,474,475,478],{"style":253},[56,476],{"className":477,"style":258},[257],[56,479,481],{"className":480},[262,263,264,265],[56,482,43],{"className":483},[77,265],[56,485,273],{"className":486},[272],[56,488,490],{"className":489},[245],[56,491,493],{"className":492,"style":280},[249],[56,494],{},[56,496],{"className":497,"style":188},[187],[56,499,501],{"className":500},[192],"∈",[56,503],{"className":504,"style":188},[187],[56,506,508,512,607,610,613,616,656,659,662],{"className":507},[68],[56,509],{"className":510,"style":511},[72],"height:1.0935em;vertical-align:-0.1944em;",[56,513,515,520],{"className":514},[77],[56,516,519],{"className":517},[77,518],"mathbb","R",[56,521,523],{"className":522},[236],[56,524,526],{"className":525},[240],[56,527,529],{"className":528},[245],[56,530,533],{"className":531,"style":532},[249],"height:0.8991em;",[56,534,536,539],{"style":535},"top:-3.113em;margin-right:0.05em;",[56,537],{"className":538,"style":258},[257],[56,540,542],{"className":541},[262,263,264,265],[56,543,545,549,553],{"className":544},[77,265],[56,546,548],{"className":547},[77,78,265],"d",[56,550,552],{"className":551},[290,265],"×",[56,554,556,559],{"className":555},[77,265],[56,557,548],{"className":558},[77,78,265],[56,560,562],{"className":561},[236],[56,563,565,598],{"className":564},[240,241],[56,566,568,595],{"className":567},[245],[56,569,572],{"className":570,"style":571},[249],"height:0.3448em;",[56,573,575,579],{"style":574},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[56,576],{"className":577,"style":578},[257],"height:2.5em;",[56,580,584],{"className":581},[262,582,583,265],"reset-size3","size1",[56,585,587],{"className":586},[77,265],[56,588,591],{"className":589},[77,590,265],"text",[56,592,594],{"className":593},[77,265],"ff",[56,596,273],{"className":597},[272],[56,599,601],{"className":600},[245],[56,602,605],{"className":603,"style":604},[249],"height:0.1512em;",[56,606],{},[56,608,447],{"className":609},[446],[56,611],{"className":612,"style":188},[187],[56,614],{"className":615,"style":346},[187],[56,617,619,622],{"className":618},[77],[56,620,232],{"className":621,"style":231},[77,78],[56,623,625],{"className":624},[236],[56,626,628,648],{"className":627},[240,241],[56,629,631,645],{"className":630},[245],[56,632,634],{"className":633,"style":250},[249],[56,635,636,639],{"style":253},[56,637],{"className":638,"style":258},[257],[56,640,642],{"className":641},[262,263,264,265],[56,643,376],{"className":644},[77,265],[56,646,273],{"className":647},[272],[56,649,651],{"className":650},[245],[56,652,654],{"className":653,"style":280},[249],[56,655],{},[56,657],{"className":658,"style":188},[187],[56,660,501],{"className":661},[192],[56,663],{"className":664,"style":188},[187],[56,666,668,671,752],{"className":667},[68],[56,669],{"className":670,"style":511},[72],[56,672,674,677],{"className":673},[77],[56,675,519],{"className":676},[77,518],[56,678,680],{"className":679},[236],[56,681,683],{"className":682},[240],[56,684,686],{"className":685},[245],[56,687,689],{"className":688,"style":532},[249],[56,690,691,694],{"style":535},[56,692],{"className":693,"style":258},[257],[56,695,697],{"className":696},[262,263,264,265],[56,698,700,746,749],{"className":699},[77,265],[56,701,703,706],{"className":702},[77,265],[56,704,548],{"className":705},[77,78,265],[56,707,709],{"className":708},[236],[56,710,712,738],{"className":711},[240,241],[56,713,715,735],{"className":714},[245],[56,716,718],{"className":717,"style":571},[249],[56,719,720,723],{"style":574},[56,721],{"className":722,"style":578},[257],[56,724,726],{"className":725},[262,582,583,265],[56,727,729],{"className":728},[77,265],[56,730,732],{"className":731},[77,590,265],[56,733,594],{"className":734},[77,265],[56,736,273],{"className":737},[272],[56,739,741],{"className":740},[245],[56,742,744],{"className":743,"style":604},[249],[56,745],{},[56,747,552],{"className":748},[290,265],[56,750,548],{"className":751},[77,78,265],[56,753,447],{"className":754},[446],[11,756,757,758,840,841,844,845,848,849,883],{},"with ",[56,759,761],{"className":760},[59],[56,762,764,827],{"className":763,"ariaHidden":64},[63],[56,765,767,771,818,821,824],{"className":766},[68],[56,768],{"className":769,"style":770},[72],"height:0.8444em;vertical-align:-0.15em;",[56,772,774,777],{"className":773},[77],[56,775,548],{"className":776},[77,78],[56,778,780],{"className":779},[236],[56,781,783,810],{"className":782},[240,241],[56,784,786,807],{"className":785},[245],[56,787,790],{"className":788,"style":789},[249],"height:0.3361em;",[56,791,792,795],{"style":316},[56,793],{"className":794,"style":258},[257],[56,796,798],{"className":797},[262,263,264,265],[56,799,801],{"className":800},[77,265],[56,802,804],{"className":803},[77,590,265],[56,805,594],{"className":806},[77,265],[56,808,273],{"className":809},[272],[56,811,813],{"className":812},[245],[56,814,816],{"className":815,"style":280},[249],[56,817],{},[56,819],{"className":820,"style":188},[187],[56,822,193],{"className":823},[192],[56,825],{"className":826,"style":188},[187],[56,828,830,834,837],{"className":829},[68],[56,831],{"className":832,"style":833},[72],"height:0.6944em;",[56,835,142],{"className":836},[77],[56,838,548],{"className":839},[77,78]," the standard inner width. Attention mixes\n",[21,842,843],{},"across"," positions; the FFN is the only nonlinearity acting ",[21,846,847],{},"within"," a\nposition. Because its weights are shared across positions, it amounts to a\n",[56,850,852],{"className":851},[59],[56,853,855,874],{"className":854,"ariaHidden":64},[63],[56,856,858,862,865,868,871],{"className":857},[68],[56,859],{"className":860,"style":861},[72],"height:0.7278em;vertical-align:-0.0833em;",[56,863,43],{"className":864},[77],[56,866],{"className":867,"style":286},[187],[56,869,552],{"className":870},[290],[56,872],{"className":873,"style":286},[187],[56,875,877,880],{"className":876},[68],[56,878],{"className":879,"style":138},[72],[56,881,43],{"className":882},[77]," convolution over the sequence.",[11,885,886,887,902,903,906,907,925,926,929,930,945,946,964,965,984,985,1030,1031,1046,1047,1066],{},"The expansion is not arbitrary. The FFN takes each token's ",[56,888,890],{"className":889},[59],[56,891,893],{"className":892,"ariaHidden":64},[63],[56,894,896,899],{"className":895},[68],[56,897],{"className":898,"style":833},[72],[56,900,548],{"className":901},[77,78],"-vector, projects\nit ",[21,904,905],{},"up"," into a wider ",[56,908,910],{"className":909},[59],[56,911,913],{"className":912,"ariaHidden":64},[63],[56,914,916,919,922],{"className":915},[68],[56,917],{"className":918,"style":833},[72],[56,920,142],{"className":921},[77],[56,923,548],{"className":924},[77,78]," space, applies a pointwise nonlinearity there, and\nprojects ",[21,927,928],{},"back down"," to ",[56,931,933],{"className":932},[59],[56,934,936],{"className":935,"ariaHidden":64},[63],[56,937,939,942],{"className":938},[68],[56,940],{"className":941,"style":833},[72],[56,943,548],{"className":944},[77,78],". The wide hidden layer is where the per-token\ncomputation happens: it gives the nonlinearity enough room to compute many\nindependent features of the token before compressing the result. The original\npaper used ",[56,947,949],{"className":948},[59],[56,950,952],{"className":951,"ariaHidden":64},[63],[56,953,955,958],{"className":954},[68],[56,956],{"className":957,"style":73},[72],[56,959,961],{"className":960},[164],[56,962,218],{"className":963},[77,168],"; most modern stacks swap in ",[56,966,968],{"className":967},[59],[56,969,971],{"className":970,"ariaHidden":64},[63],[56,972,974,977],{"className":973},[68],[56,975],{"className":976,"style":73},[72],[56,978,980],{"className":979},[164],[56,981,983],{"className":982},[77,168],"GELU","\n(a smooth gate ",[56,986,988],{"className":987},[59],[56,989,991,1011],{"className":990,"ariaHidden":64},[63],[56,992,994,998,1001,1004,1008],{"className":993},[68],[56,995],{"className":996,"style":997},[72],"height:0.4445em;",[56,999,178],{"className":1000},[77,78],[56,1002],{"className":1003,"style":286},[187],[56,1005,1007],{"className":1006},[290],"⋅",[56,1009],{"className":1010,"style":286},[187],[56,1012,1014,1017,1021,1024,1027],{"className":1013},[68],[56,1015],{"className":1016,"style":160},[72],[56,1018,1020],{"className":1019},[77],"Φ",[56,1022,174],{"className":1023},[173],[56,1025,178],{"className":1026},[77,78],[56,1028,183],{"className":1029},[182],", with ",[56,1032,1034],{"className":1033},[59],[56,1035,1037],{"className":1036,"ariaHidden":64},[63],[56,1038,1040,1043],{"className":1039},[68],[56,1041],{"className":1042,"style":73},[72],[56,1044,1020],{"className":1045},[77]," the standard-normal CDF) or a gated\nvariant like ",[56,1048,1050],{"className":1049},[59],[56,1051,1053],{"className":1052,"ariaHidden":64},[63],[56,1054,1056,1059],{"className":1055},[68],[56,1057],{"className":1058,"style":73},[72],[56,1060,1062],{"className":1061},[164],[56,1063,1065],{"className":1064},[77,168],"SwiGLU",", which lowers loss at fixed width\nfor reasons that remain partly empirical.",[11,1068,1069,1070,1087,1088,1105,1106,1145],{},"Track the shapes explicitly. A batch of ",[56,1071,1073],{"className":1072},[59],[56,1074,1076],{"className":1075,"ariaHidden":64},[63],[56,1077,1079,1082],{"className":1078},[68],[56,1080],{"className":1081,"style":73},[72],[56,1083,1086],{"className":1084,"style":1085},[77,78],"margin-right:0.0502em;","B"," sequences of length ",[56,1089,1091],{"className":1090},[59],[56,1092,1094],{"className":1093,"ariaHidden":64},[63],[56,1095,1097,1101],{"className":1096},[68],[56,1098],{"className":1099,"style":1100},[72],"height:0.4306em;",[56,1102,1104],{"className":1103},[77,78],"n"," enters as a\ntensor of shape ",[56,1107,1109],{"className":1108},[59],[56,1110,1112],{"className":1111,"ariaHidden":64},[63],[56,1113,1115,1118,1121,1124,1127,1130,1133,1136,1139,1142],{"className":1114},[68],[56,1116],{"className":1117,"style":160},[72],[56,1119,174],{"className":1120},[173],[56,1122,1086],{"className":1123,"style":1085},[77,78],[56,1125,447],{"className":1126},[446],[56,1128],{"className":1129,"style":346},[187],[56,1131,1104],{"className":1132},[77,78],[56,1134,447],{"className":1135},[446],[56,1137],{"className":1138,"style":346},[187],[56,1140,548],{"className":1141},[77,78],[56,1143,183],{"className":1144},[182],". Every operation below preserves the batch and\nsequence axes and acts only on the last (feature) axis:",[56,1147,1149],{"className":1148},[147],[56,1150,1152],{"className":1151},[59],[56,1153,1155,1489,1707,1893],{"className":1154,"ariaHidden":64},[63],[56,1156,1158,1162,1323,1326,1329,1483,1486],{"className":1157},[68],[56,1159],{"className":1160,"style":1161},[72],"height:2.9725em;vertical-align:-1.7016em;",[56,1163,1166],{"className":1164},[206,1165],"munder",[56,1167,1169,1314],{"className":1168},[240,241],[56,1170,1172,1311],{"className":1171},[245],[56,1173,1176,1196],{"className":1174,"style":1175},[249],"height:0.75em;",[56,1177,1179,1183],{"style":1178},"top:-1.4345em;",[56,1180],{"className":1181,"style":1182},[257],"height:3em;",[56,1184,1186],{"className":1185},[262,263,264,265],[56,1187,1189],{"className":1188},[77,265],[56,1190,1192],{"className":1191},[77,590,265],[56,1193,1195],{"className":1194},[77,265],"input",[56,1197,1199,1202],{"style":1198},"top:-3em;",[56,1200],{"className":1201,"style":1182},[257],[56,1203,1205],{"className":1204},[206,1165],[56,1206,1208,1302],{"className":1207},[240,241],[56,1209,1211,1299],{"className":1210},[245],[56,1212,1214,1264],{"className":1213,"style":1175},[249],[56,1215,1219,1222],{"className":1216,"style":1218},[1217],"svg-align","top:-2.102em;",[56,1220],{"className":1221,"style":1182},[257],[56,1223,1227,1244,1254],{"className":1224,"style":1226},[1225],"stretchy","height:0.548em;min-width:1.6em;",[56,1228,1232],{"className":1229,"style":1231},[1230],"brace-left","height:0.548em;",[1233,1234,1240],"svg",{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1239},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","0.548em","0 0 400000 548","xMinYMin slice",[1241,1242],"path",{"d":1243},"M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z",[56,1245,1248],{"className":1246,"style":1231},[1247],"brace-center",[1233,1249,1251],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1250},"xMidYMin slice",[1241,1252],{"d":1253},"M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z",[56,1255,1258],{"className":1256,"style":1231},[1257],"brace-right",[1233,1259,1261],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1260},"xMaxYMin slice",[1241,1262],{"d":1263},"M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z",[56,1265,1266,1269],{"style":1198},[56,1267],{"className":1268,"style":1182},[257],[56,1270,1272,1275,1278,1281,1284,1287,1290,1293,1296],{"className":1271},[77],[56,1273,174],{"className":1274},[173],[56,1276,1086],{"className":1277,"style":1085},[77,78],[56,1279,447],{"className":1280},[446],[56,1282],{"className":1283,"style":346},[187],[56,1285,1104],{"className":1286},[77,78],[56,1288,447],{"className":1289},[446],[56,1291],{"className":1292,"style":346},[187],[56,1294,548],{"className":1295},[77,78],[56,1297,183],{"className":1298},[182],[56,1300,273],{"className":1301},[272],[56,1303,1305],{"className":1304},[245],[56,1306,1309],{"className":1307,"style":1308},[249],"height:0.898em;",[56,1310],{},[56,1312,273],{"className":1313},[272],[56,1315,1317],{"className":1316},[245],[56,1318,1321],{"className":1319,"style":1320},[249],"height:1.7016em;",[56,1322],{},[56,1324],{"className":1325,"style":188},[187],[56,1327],{"className":1328,"style":188},[187],[56,1330,1333],{"className":1331},[192,1332],"x-arrow",[56,1334,1336,1474],{"className":1335},[240,241],[56,1337,1339,1471],{"className":1338},[245],[56,1340,1343,1452],{"className":1341,"style":1342},[249],"height:1.2709em;",[56,1344,1346,1349],{"style":1345},"top:-3.322em;",[56,1347],{"className":1348,"style":258},[257],[56,1350,1353],{"className":1351},[262,263,264,265,1352],"x-arrow-pad",[56,1354,1356,1360,1403,1406,1449],{"className":1355},[77,265],[56,1357],{"className":1358,"style":1359},[187,265],"margin-right:0.1952em;",[56,1361,1363,1366],{"className":1362},[77,265],[56,1364,232],{"className":1365,"style":231},[77,78,265],[56,1367,1369],{"className":1368},[236],[56,1370,1372,1394],{"className":1371},[240,241],[56,1373,1375,1391],{"className":1374},[245],[56,1376,1379],{"className":1377,"style":1378},[249],"height:0.3173em;",[56,1380,1382,1385],{"style":1381},"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;",[56,1383],{"className":1384,"style":578},[257],[56,1386,1388],{"className":1387},[262,582,583,265],[56,1389,43],{"className":1390},[77,265],[56,1392,273],{"className":1393},[272],[56,1395,1397],{"className":1396},[245],[56,1398,1401],{"className":1399,"style":1400},[249],"height:0.143em;",[56,1402],{},[56,1404,501],{"className":1405},[192,265],[56,1407,1409,1412],{"className":1408},[77,265],[56,1410,519],{"className":1411},[77,518,265],[56,1413,1415],{"className":1414},[236],[56,1416,1418],{"className":1417},[240],[56,1419,1421],{"className":1420},[245],[56,1422,1425],{"className":1423,"style":1424},[249],"height:0.927em;",[56,1426,1428,1431],{"style":1427},"top:-2.931em;margin-right:0.0714em;",[56,1429],{"className":1430,"style":578},[257],[56,1432,1434],{"className":1433},[262,582,583,265],[56,1435,1437,1440,1443,1446],{"className":1436},[77,265],[56,1438,548],{"className":1439},[77,78,265],[56,1441,552],{"className":1442},[290,265],[56,1444,142],{"className":1445},[77,265],[56,1447,548],{"className":1448},[77,78,265],[56,1450],{"className":1451,"style":1359},[187,265],[56,1453,1456,1459],{"className":1454,"style":1455},[1217],"top:-2.689em;",[56,1457],{"className":1458,"style":258},[257],[56,1460,1464],{"className":1461,"style":1463},[1462],"hide-tail","height:0.522em;min-width:1.469em;",[1233,1465,1468],{"xmlns":1235,"width":1236,"height":1466,"viewBox":1467,"preserveAspectRatio":1260},"0.522em","0 0 400000 522",[1241,1469],{"d":1470},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[56,1472,273],{"className":1473},[272],[56,1475,1477],{"className":1476},[245],[56,1478,1481],{"className":1479,"style":1480},[249],"height:0.011em;",[56,1482],{},[56,1484],{"className":1485,"style":188},[187],[56,1487],{"className":1488,"style":188},[187],[56,1490,1492,1496,1635,1638,1641,1701,1704],{"className":1491},[68],[56,1493],{"className":1494,"style":1495},[72],"height:2.6844em;vertical-align:-1.5841em;",[56,1497,1499],{"className":1498},[206,1165],[56,1500,1502,1626],{"className":1501},[240,241],[56,1503,1505,1623],{"className":1504},[245],[56,1506,1508,1527],{"className":1507,"style":1175},[249],[56,1509,1511,1514],{"style":1510},"top:-1.4159em;",[56,1512],{"className":1513,"style":1182},[257],[56,1515,1517],{"className":1516},[262,263,264,265],[56,1518,1520],{"className":1519},[77,265],[56,1521,1523],{"className":1522},[77,590,265],[56,1524,1526],{"className":1525},[77,265],"hidden",[56,1528,1529,1532],{"style":1198},[56,1530],{"className":1531,"style":1182},[257],[56,1533,1535],{"className":1534},[206,1165],[56,1536,1538,1615],{"className":1537},[240,241],[56,1539,1541,1612],{"className":1540},[245],[56,1542,1544,1574],{"className":1543,"style":1175},[249],[56,1545,1547,1550],{"className":1546,"style":1218},[1217],[56,1548],{"className":1549,"style":1182},[257],[56,1551,1553,1560,1567],{"className":1552,"style":1226},[1225],[56,1554,1556],{"className":1555,"style":1231},[1230],[1233,1557,1558],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1239},[1241,1559],{"d":1243},[56,1561,1563],{"className":1562,"style":1231},[1247],[1233,1564,1565],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1250},[1241,1566],{"d":1253},[56,1568,1570],{"className":1569,"style":1231},[1257],[1233,1571,1572],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1260},[1241,1573],{"d":1263},[56,1575,1576,1579],{"style":1198},[56,1577],{"className":1578,"style":1182},[257],[56,1580,1582,1585,1588,1591,1594,1597,1600,1603,1606,1609],{"className":1581},[77],[56,1583,174],{"className":1584},[173],[56,1586,1086],{"className":1587,"style":1085},[77,78],[56,1589,447],{"className":1590},[446],[56,1592],{"className":1593,"style":346},[187],[56,1595,1104],{"className":1596},[77,78],[56,1598,447],{"className":1599},[446],[56,1601],{"className":1602,"style":346},[187],[56,1604,142],{"className":1605},[77],[56,1607,548],{"className":1608},[77,78],[56,1610,183],{"className":1611},[182],[56,1613,273],{"className":1614},[272],[56,1616,1618],{"className":1617},[245],[56,1619,1621],{"className":1620,"style":1308},[249],[56,1622],{},[56,1624,273],{"className":1625},[272],[56,1627,1629],{"className":1628},[245],[56,1630,1633],{"className":1631,"style":1632},[249],"height:1.5841em;",[56,1634],{},[56,1636],{"className":1637,"style":188},[187],[56,1639],{"className":1640,"style":188},[187],[56,1642,1644],{"className":1643},[192,1332],[56,1645,1647,1693],{"className":1646},[240,241],[56,1648,1650,1690],{"className":1649},[245],[56,1651,1654,1677],{"className":1652,"style":1653},[249],"height:1.1003em;",[56,1655,1656,1659],{"style":1345},[56,1657],{"className":1658,"style":258},[257],[56,1660,1662],{"className":1661},[262,263,264,265,1352],[56,1663,1665,1668,1674],{"className":1664},[77,265],[56,1666],{"className":1667,"style":1359},[187,265],[56,1669,1671],{"className":1670},[164,265],[56,1672,218],{"className":1673},[77,168,265],[56,1675],{"className":1676,"style":1359},[187,265],[56,1678,1680,1683],{"className":1679,"style":1455},[1217],[56,1681],{"className":1682,"style":258},[257],[56,1684,1686],{"className":1685,"style":1463},[1462],[1233,1687,1688],{"xmlns":1235,"width":1236,"height":1466,"viewBox":1467,"preserveAspectRatio":1260},[1241,1689],{"d":1470},[56,1691,273],{"className":1692},[272],[56,1694,1696],{"className":1695},[245],[56,1697,1699],{"className":1698,"style":1480},[249],[56,1700],{},[56,1702],{"className":1703,"style":188},[187],[56,1705],{"className":1706,"style":188},[187],[56,1708,1710,1714,1717,1720,1723,1726,1729,1732,1735,1738,1741,1744,1747,1750,1887,1890],{"className":1709},[68],[56,1711],{"className":1712,"style":1713},[72],"height:1.5209em;vertical-align:-0.25em;",[56,1715,174],{"className":1716},[173],[56,1718,1086],{"className":1719,"style":1085},[77,78],[56,1721,447],{"className":1722},[446],[56,1724],{"className":1725,"style":346},[187],[56,1727,1104],{"className":1728},[77,78],[56,1730,447],{"className":1731},[446],[56,1733],{"className":1734,"style":346},[187],[56,1736,142],{"className":1737},[77],[56,1739,548],{"className":1740},[77,78],[56,1742,183],{"className":1743},[182],[56,1745],{"className":1746,"style":188},[187],[56,1748],{"className":1749,"style":188},[187],[56,1751,1753],{"className":1752},[192,1332],[56,1754,1756,1879],{"className":1755},[240,241],[56,1757,1759,1876],{"className":1758},[245],[56,1760,1762,1863],{"className":1761,"style":1342},[249],[56,1763,1764,1767],{"style":1345},[56,1765],{"className":1766,"style":258},[257],[56,1768,1770],{"className":1769},[262,263,264,265,1352],[56,1771,1773,1776,1816,1819,1860],{"className":1772},[77,265],[56,1774],{"className":1775,"style":1359},[187,265],[56,1777,1779,1782],{"className":1778},[77,265],[56,1780,232],{"className":1781,"style":231},[77,78,265],[56,1783,1785],{"className":1784},[236],[56,1786,1788,1808],{"className":1787},[240,241],[56,1789,1791,1805],{"className":1790},[245],[56,1792,1794],{"className":1793,"style":1378},[249],[56,1795,1796,1799],{"style":1381},[56,1797],{"className":1798,"style":578},[257],[56,1800,1802],{"className":1801},[262,582,583,265],[56,1803,376],{"className":1804},[77,265],[56,1806,273],{"className":1807},[272],[56,1809,1811],{"className":1810},[245],[56,1812,1814],{"className":1813,"style":1400},[249],[56,1815],{},[56,1817,501],{"className":1818},[192,265],[56,1820,1822,1825],{"className":1821},[77,265],[56,1823,519],{"className":1824},[77,518,265],[56,1826,1828],{"className":1827},[236],[56,1829,1831],{"className":1830},[240],[56,1832,1834],{"className":1833},[245],[56,1835,1837],{"className":1836,"style":1424},[249],[56,1838,1839,1842],{"style":1427},[56,1840],{"className":1841,"style":578},[257],[56,1843,1845],{"className":1844},[262,582,583,265],[56,1846,1848,1851,1854,1857],{"className":1847},[77,265],[56,1849,142],{"className":1850},[77,265],[56,1852,548],{"className":1853},[77,78,265],[56,1855,552],{"className":1856},[290,265],[56,1858,548],{"className":1859},[77,78,265],[56,1861],{"className":1862,"style":1359},[187,265],[56,1864,1866,1869],{"className":1865,"style":1455},[1217],[56,1867],{"className":1868,"style":258},[257],[56,1870,1872],{"className":1871,"style":1463},[1462],[1233,1873,1874],{"xmlns":1235,"width":1236,"height":1466,"viewBox":1467,"preserveAspectRatio":1260},[1241,1875],{"d":1470},[56,1877,273],{"className":1878},[272],[56,1880,1882],{"className":1881},[245],[56,1883,1885],{"className":1884,"style":1480},[249],[56,1886],{},[56,1888],{"className":1889,"style":188},[187],[56,1891],{"className":1892,"style":188},[187],[56,1894,1896,1900,2036,2039],{"className":1895},[68],[56,1897],{"className":1898,"style":1899},[72],"height:2.4147em;vertical-align:-1.6647em;",[56,1901,1903],{"className":1902},[206,1165],[56,1904,1906,2027],{"className":1905},[240,241],[56,1907,1909,2024],{"className":1908},[245],[56,1910,1912,1931],{"className":1911,"style":1175},[249],[56,1913,1915,1918],{"style":1914},"top:-1.4714em;",[56,1916],{"className":1917,"style":1182},[257],[56,1919,1921],{"className":1920},[262,263,264,265],[56,1922,1924],{"className":1923},[77,265],[56,1925,1927],{"className":1926},[77,590,265],[56,1928,1930],{"className":1929},[77,265],"output",[56,1932,1933,1936],{"style":1198},[56,1934],{"className":1935,"style":1182},[257],[56,1937,1939],{"className":1938},[206,1165],[56,1940,1942,2016],{"className":1941},[240,241],[56,1943,1945,2013],{"className":1944},[245],[56,1946,1948,1978],{"className":1947,"style":1175},[249],[56,1949,1951,1954],{"className":1950,"style":1218},[1217],[56,1952],{"className":1953,"style":1182},[257],[56,1955,1957,1964,1971],{"className":1956,"style":1226},[1225],[56,1958,1960],{"className":1959,"style":1231},[1230],[1233,1961,1962],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1239},[1241,1963],{"d":1243},[56,1965,1967],{"className":1966,"style":1231},[1247],[1233,1968,1969],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1250},[1241,1970],{"d":1253},[56,1972,1974],{"className":1973,"style":1231},[1257],[1233,1975,1976],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1260},[1241,1977],{"d":1263},[56,1979,1980,1983],{"style":1198},[56,1981],{"className":1982,"style":1182},[257],[56,1984,1986,1989,1992,1995,1998,2001,2004,2007,2010],{"className":1985},[77],[56,1987,174],{"className":1988},[173],[56,1990,1086],{"className":1991,"style":1085},[77,78],[56,1993,447],{"className":1994},[446],[56,1996],{"className":1997,"style":346},[187],[56,1999,1104],{"className":2000},[77,78],[56,2002,447],{"className":2003},[446],[56,2005],{"className":2006,"style":346},[187],[56,2008,548],{"className":2009},[77,78],[56,2011,183],{"className":2012},[182],[56,2014,273],{"className":2015},[272],[56,2017,2019],{"className":2018},[245],[56,2020,2022],{"className":2021,"style":1308},[249],[56,2023],{},[56,2025,273],{"className":2026},[272],[56,2028,2030],{"className":2029},[245],[56,2031,2034],{"className":2032,"style":2033},[249],"height:1.6647em;",[56,2035],{},[56,2037],{"className":2038,"style":346},[187],[56,2040,2042],{"className":2041},[77],".",[11,2044,2045,2046,2145,2146,2180],{},"The same ",[56,2047,2049],{"className":2048},[59],[56,2050,2052],{"className":2051,"ariaHidden":64},[63],[56,2053,2055,2059,2099,2102,2105],{"className":2054},[68],[56,2056],{"className":2057,"style":2058},[72],"height:0.8778em;vertical-align:-0.1944em;",[56,2060,2062,2065],{"className":2061},[77],[56,2063,232],{"className":2064,"style":231},[77,78],[56,2066,2068],{"className":2067},[236],[56,2069,2071,2091],{"className":2070},[240,241],[56,2072,2074,2088],{"className":2073},[245],[56,2075,2077],{"className":2076,"style":250},[249],[56,2078,2079,2082],{"style":253},[56,2080],{"className":2081,"style":258},[257],[56,2083,2085],{"className":2084},[262,263,264,265],[56,2086,43],{"className":2087},[77,265],[56,2089,273],{"className":2090},[272],[56,2092,2094],{"className":2093},[245],[56,2095,2097],{"className":2096,"style":280},[249],[56,2098],{},[56,2100,447],{"className":2101},[446],[56,2103],{"className":2104,"style":346},[187],[56,2106,2108,2111],{"className":2107},[77],[56,2109,232],{"className":2110,"style":231},[77,78],[56,2112,2114],{"className":2113},[236],[56,2115,2117,2137],{"className":2116},[240,241],[56,2118,2120,2134],{"className":2119},[245],[56,2121,2123],{"className":2122,"style":250},[249],[56,2124,2125,2128],{"style":253},[56,2126],{"className":2127,"style":258},[257],[56,2129,2131],{"className":2130},[262,263,264,265],[56,2132,376],{"className":2133},[77,265],[56,2135,273],{"className":2136},[272],[56,2138,2140],{"className":2139},[245],[56,2141,2143],{"className":2142,"style":280},[249],[56,2144],{}," apply at every one of the ",[56,2147,2149],{"className":2148},[59],[56,2150,2152,2171],{"className":2151,"ariaHidden":64},[63],[56,2153,2155,2159,2162,2165,2168],{"className":2154},[68],[56,2156],{"className":2157,"style":2158},[72],"height:0.7667em;vertical-align:-0.0833em;",[56,2160,1086],{"className":2161,"style":1085},[77,78],[56,2163],{"className":2164,"style":286},[187],[56,2166,552],{"className":2167},[290],[56,2169],{"className":2170,"style":286},[187],[56,2172,2174,2177],{"className":2173},[68],[56,2175],{"className":2176,"style":1100},[72],[56,2178,1104],{"className":2179},[77,78]," positions — the FFN\ncarries no positional index and no cross-token interaction, which is what makes it\na position-wise map.",[11,2182,2183,2186,2187,2252,2253,2272],{},[51,2184,2185],{},"Layer normalization"," is the other half of the wrapper, so its statistics\nmatter for what follows. Given a single token vector ",[56,2188,2190],{"className":2189},[59],[56,2191,2193,2212],{"className":2192,"ariaHidden":64},[63],[56,2194,2196,2200,2203,2206,2209],{"className":2195},[68],[56,2197],{"className":2198,"style":2199},[72],"height:0.5782em;vertical-align:-0.0391em;",[56,2201,178],{"className":2202},[77,78],[56,2204],{"className":2205,"style":188},[187],[56,2207,501],{"className":2208},[192],[56,2210],{"className":2211,"style":188},[187],[56,2213,2215,2219],{"className":2214},[68],[56,2216],{"className":2217,"style":2218},[72],"height:0.8491em;",[56,2220,2222,2225],{"className":2221},[77],[56,2223,519],{"className":2224},[77,518],[56,2226,2228],{"className":2227},[236],[56,2229,2231],{"className":2230},[240],[56,2232,2234],{"className":2233},[245],[56,2235,2237],{"className":2236,"style":2218},[249],[56,2238,2240,2243],{"style":2239},"top:-3.063em;margin-right:0.05em;",[56,2241],{"className":2242,"style":258},[257],[56,2244,2246],{"className":2245},[262,263,264,265],[56,2247,2249],{"className":2248},[77,265],[56,2250,548],{"className":2251},[77,78,265],",\nLayerNorm computes the mean and variance ",[21,2254,2255,2256,2271],{},"over the ",[56,2257,2259],{"className":2258},[59],[56,2260,2262],{"className":2261,"ariaHidden":64},[63],[56,2263,2265,2268],{"className":2264},[68],[56,2266],{"className":2267,"style":833},[72],[56,2269,548],{"className":2270},[77,78]," feature entries of that one\ntoken"," — not over the batch, not over the sequence — and standardizes:",[56,2274,2276],{"className":2275},[147],[56,2277,2279],{"className":2278},[59],[56,2280,2282,2302,2555,2746,2819,2841,3028],{"className":2281,"ariaHidden":64},[63],[56,2283,2285,2289,2293,2296,2299],{"className":2284},[68],[56,2286],{"className":2287,"style":2288},[72],"height:0.625em;vertical-align:-0.1944em;",[56,2290,2292],{"className":2291},[77,78],"μ",[56,2294],{"className":2295,"style":188},[187],[56,2297,193],{"className":2298},[192],[56,2300],{"className":2301,"style":188},[187],[56,2303,2305,2309,2380,2383,2462,2465,2505,2508,2511,2514,2546,2549,2552],{"className":2304},[68],[56,2306],{"className":2307,"style":2308},[72],"height:3.1382em;vertical-align:-1.3021em;",[56,2310,2312,2316,2377],{"className":2311},[77],[56,2313],{"className":2314},[173,2315],"nulldelimiter",[56,2317,2320],{"className":2318},[2319],"mfrac",[56,2321,2323,2368],{"className":2322},[240,241],[56,2324,2326,2365],{"className":2325},[245],[56,2327,2330,2342,2353],{"className":2328,"style":2329},[249],"height:1.3214em;",[56,2331,2333,2336],{"style":2332},"top:-2.314em;",[56,2334],{"className":2335,"style":1182},[257],[56,2337,2339],{"className":2338},[77],[56,2340,548],{"className":2341},[77,78],[56,2343,2345,2348],{"style":2344},"top:-3.23em;",[56,2346],{"className":2347,"style":1182},[257],[56,2349],{"className":2350,"style":2352},[2351],"frac-line","border-bottom-width:0.04em;",[56,2354,2356,2359],{"style":2355},"top:-3.677em;",[56,2357],{"className":2358,"style":1182},[257],[56,2360,2362],{"className":2361},[77],[56,2363,43],{"className":2364},[77],[56,2366,273],{"className":2367},[272],[56,2369,2371],{"className":2370},[245],[56,2372,2375],{"className":2373,"style":2374},[249],"height:0.686em;",[56,2376],{},[56,2378],{"className":2379},[182,2315],[56,2381],{"className":2382,"style":346},[187],[56,2384,2387],{"className":2385},[164,2386],"op-limits",[56,2388,2390,2453],{"className":2389},[240,241],[56,2391,2393,2450],{"className":2392},[245],[56,2394,2397,2421,2435],{"className":2395,"style":2396},[249],"height:1.8361em;",[56,2398,2400,2404],{"style":2399},"top:-1.8479em;margin-left:0em;",[56,2401],{"className":2402,"style":2403},[257],"height:3.05em;",[56,2405,2407],{"className":2406},[262,263,264,265],[56,2408,2410,2415,2418],{"className":2409},[77,265],[56,2411,2414],{"className":2412,"style":2413},[77,78,265],"margin-right:0.0315em;","k",[56,2416,193],{"className":2417},[192,265],[56,2419,43],{"className":2420},[77,265],[56,2422,2424,2427],{"style":2423},"top:-3.05em;",[56,2425],{"className":2426,"style":2403},[257],[56,2428,2429],{},[56,2430,2434],{"className":2431},[164,2432,2433],"op-symbol","large-op","∑",[56,2436,2438,2441],{"style":2437},"top:-4.3em;margin-left:0em;",[56,2439],{"className":2440,"style":2403},[257],[56,2442,2444],{"className":2443},[262,263,264,265],[56,2445,2447],{"className":2446},[77,265],[56,2448,548],{"className":2449},[77,78,265],[56,2451,273],{"className":2452},[272],[56,2454,2456],{"className":2455},[245],[56,2457,2460],{"className":2458,"style":2459},[249],"height:1.3021em;",[56,2461],{},[56,2463],{"className":2464,"style":346},[187],[56,2466,2468,2471],{"className":2467},[77],[56,2469,178],{"className":2470},[77,78],[56,2472,2474],{"className":2473},[236],[56,2475,2477,2497],{"className":2476},[240,241],[56,2478,2480,2494],{"className":2479},[245],[56,2481,2483],{"className":2482,"style":789},[249],[56,2484,2485,2488],{"style":316},[56,2486],{"className":2487,"style":258},[257],[56,2489,2491],{"className":2490},[262,263,264,265],[56,2492,2414],{"className":2493,"style":2413},[77,78,265],[56,2495,273],{"className":2496},[272],[56,2498,2500],{"className":2499},[245],[56,2501,2503],{"className":2502,"style":280},[249],[56,2504],{},[56,2506,447],{"className":2507},[446],[56,2509],{"className":2510,"style":451},[187],[56,2512],{"className":2513,"style":346},[187],[56,2515,2517,2522],{"className":2516},[77],[56,2518,2521],{"className":2519,"style":2520},[77,78],"margin-right:0.0359em;","σ",[56,2523,2525],{"className":2524},[236],[56,2526,2528],{"className":2527},[240],[56,2529,2531],{"className":2530},[245],[56,2532,2535],{"className":2533,"style":2534},[249],"height:0.8641em;",[56,2536,2537,2540],{"style":535},[56,2538],{"className":2539,"style":258},[257],[56,2541,2543],{"className":2542},[262,263,264,265],[56,2544,376],{"className":2545},[77,265],[56,2547],{"className":2548,"style":188},[187],[56,2550,193],{"className":2551},[192],[56,2553],{"className":2554,"style":188},[187],[56,2556,2558,2561,2623,2626,2693,2696,2736,2739,2743],{"className":2557},[68],[56,2559],{"className":2560,"style":2308},[72],[56,2562,2564,2567,2620],{"className":2563},[77],[56,2565],{"className":2566},[173,2315],[56,2568,2570],{"className":2569},[2319],[56,2571,2573,2612],{"className":2572},[240,241],[56,2574,2576,2609],{"className":2575},[245],[56,2577,2579,2590,2598],{"className":2578,"style":2329},[249],[56,2580,2581,2584],{"style":2332},[56,2582],{"className":2583,"style":1182},[257],[56,2585,2587],{"className":2586},[77],[56,2588,548],{"className":2589},[77,78],[56,2591,2592,2595],{"style":2344},[56,2593],{"className":2594,"style":1182},[257],[56,2596],{"className":2597,"style":2352},[2351],[56,2599,2600,2603],{"style":2355},[56,2601],{"className":2602,"style":1182},[257],[56,2604,2606],{"className":2605},[77],[56,2607,43],{"className":2608},[77],[56,2610,273],{"className":2611},[272],[56,2613,2615],{"className":2614},[245],[56,2616,2618],{"className":2617,"style":2374},[249],[56,2619],{},[56,2621],{"className":2622},[182,2315],[56,2624],{"className":2625,"style":346},[187],[56,2627,2629],{"className":2628},[164,2386],[56,2630,2632,2685],{"className":2631},[240,241],[56,2633,2635,2682],{"className":2634},[245],[56,2636,2638,2658,2668],{"className":2637,"style":2396},[249],[56,2639,2640,2643],{"style":2399},[56,2641],{"className":2642,"style":2403},[257],[56,2644,2646],{"className":2645},[262,263,264,265],[56,2647,2649,2652,2655],{"className":2648},[77,265],[56,2650,2414],{"className":2651,"style":2413},[77,78,265],[56,2653,193],{"className":2654},[192,265],[56,2656,43],{"className":2657},[77,265],[56,2659,2660,2663],{"style":2423},[56,2661],{"className":2662,"style":2403},[257],[56,2664,2665],{},[56,2666,2434],{"className":2667},[164,2432,2433],[56,2669,2670,2673],{"style":2437},[56,2671],{"className":2672,"style":2403},[257],[56,2674,2676],{"className":2675},[262,263,264,265],[56,2677,2679],{"className":2678},[77,265],[56,2680,548],{"className":2681},[77,78,265],[56,2683,273],{"className":2684},[272],[56,2686,2688],{"className":2687},[245],[56,2689,2691],{"className":2690,"style":2459},[249],[56,2692],{},[56,2694,174],{"className":2695},[173],[56,2697,2699,2702],{"className":2698},[77],[56,2700,178],{"className":2701},[77,78],[56,2703,2705],{"className":2704},[236],[56,2706,2708,2728],{"className":2707},[240,241],[56,2709,2711,2725],{"className":2710},[245],[56,2712,2714],{"className":2713,"style":789},[249],[56,2715,2716,2719],{"style":316},[56,2717],{"className":2718,"style":258},[257],[56,2720,2722],{"className":2721},[262,263,264,265],[56,2723,2414],{"className":2724,"style":2413},[77,78,265],[56,2726,273],{"className":2727},[272],[56,2729,2731],{"className":2730},[245],[56,2732,2734],{"className":2733,"style":280},[249],[56,2735],{},[56,2737],{"className":2738,"style":286},[187],[56,2740,2742],{"className":2741},[290],"−",[56,2744],{"className":2745,"style":286},[187],[56,2747,2749,2753,2756,2785,2788,2791,2794,2801,2804,2807,2810,2813,2816],{"className":2748},[68],[56,2750],{"className":2751,"style":2752},[72],"height:1.1141em;vertical-align:-0.25em;",[56,2754,2292],{"className":2755},[77,78],[56,2757,2759,2762],{"className":2758},[182],[56,2760,183],{"className":2761},[182],[56,2763,2765],{"className":2764},[236],[56,2766,2768],{"className":2767},[240],[56,2769,2771],{"className":2770},[245],[56,2772,2774],{"className":2773,"style":2534},[249],[56,2775,2776,2779],{"style":535},[56,2777],{"className":2778,"style":258},[257],[56,2780,2782],{"className":2781},[262,263,264,265],[56,2783,376],{"className":2784},[77,265],[56,2786,447],{"className":2787},[446],[56,2789],{"className":2790,"style":451},[187],[56,2792],{"className":2793,"style":346},[187],[56,2795,2797],{"className":2796},[164],[56,2798,2800],{"className":2799},[77,168],"LN",[56,2802,174],{"className":2803},[173],[56,2805,178],{"className":2806},[77,78],[56,2808,183],{"className":2809},[182],[56,2811],{"className":2812,"style":188},[187],[56,2814,193],{"className":2815},[192],[56,2817],{"className":2818,"style":188},[187],[56,2820,2822,2826,2831,2834,2838],{"className":2821},[68],[56,2823],{"className":2824,"style":2825},[72],"height:0.7778em;vertical-align:-0.1944em;",[56,2827,2830],{"className":2828,"style":2829},[77,78],"margin-right:0.0556em;","γ",[56,2832],{"className":2833,"style":286},[187],[56,2835,2837],{"className":2836},[290],"⊙",[56,2839],{"className":2840,"style":286},[187],[56,2842,2844,2848,3019,3022,3025],{"className":2843},[68],[56,2845],{"className":2846,"style":2847},[72],"height:2.1903em;vertical-align:-0.93em;",[56,2849,2851,2854,3016],{"className":2850},[77],[56,2852],{"className":2853},[173,2315],[56,2855,2857],{"className":2856},[2319],[56,2858,2860,3007],{"className":2859},[240,241],[56,2861,2863,3004],{"className":2862},[245],[56,2864,2867,2973,2981],{"className":2865,"style":2866},[249],"height:1.2603em;",[56,2868,2870,2873],{"style":2869},"top:-2.1966em;",[56,2871],{"className":2872,"style":1182},[257],[56,2874,2876],{"className":2875},[77],[56,2877,2880],{"className":2878},[77,2879],"sqrt",[56,2881,2883,2964],{"className":2882},[240,241],[56,2884,2886,2961],{"className":2885},[245],[56,2887,2890,2944],{"className":2888,"style":2889},[249],"height:0.9134em;",[56,2891,2893,2896],{"className":2892,"style":1198},[1217],[56,2894],{"className":2895,"style":1182},[257],[56,2897,2900,2931,2934,2937,2940],{"className":2898,"style":2899},[77],"padding-left:0.833em;",[56,2901,2903,2906],{"className":2902},[77],[56,2904,2521],{"className":2905,"style":2520},[77,78],[56,2907,2909],{"className":2908},[236],[56,2910,2912],{"className":2911},[240],[56,2913,2915],{"className":2914},[245],[56,2916,2919],{"className":2917,"style":2918},[249],"height:0.7401em;",[56,2920,2922,2925],{"style":2921},"top:-2.989em;margin-right:0.05em;",[56,2923],{"className":2924,"style":258},[257],[56,2926,2928],{"className":2927},[262,263,264,265],[56,2929,376],{"className":2930},[77,265],[56,2932],{"className":2933,"style":286},[187],[56,2935,291],{"className":2936},[290],[56,2938],{"className":2939,"style":286},[187],[56,2941,2943],{"className":2942},[77,78],"ϵ",[56,2945,2947,2950],{"style":2946},"top:-2.8734em;",[56,2948],{"className":2949,"style":1182},[257],[56,2951,2954],{"className":2952,"style":2953},[1462],"min-width:0.853em;height:1.08em;",[1233,2955,2958],{"xmlns":1235,"width":1236,"height":2956,"viewBox":2957,"preserveAspectRatio":1239},"1.08em","0 0 400000 1080",[1241,2959],{"d":2960},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[56,2962,273],{"className":2963},[272],[56,2965,2967],{"className":2966},[245],[56,2968,2971],{"className":2969,"style":2970},[249],"height:0.1266em;",[56,2972],{},[56,2974,2975,2978],{"style":2344},[56,2976],{"className":2977,"style":1182},[257],[56,2979],{"className":2980,"style":2352},[2351],[56,2982,2983,2986],{"style":2355},[56,2984],{"className":2985,"style":1182},[257],[56,2987,2989,2992,2995,2998,3001],{"className":2988},[77],[56,2990,178],{"className":2991},[77,78],[56,2993],{"className":2994,"style":286},[187],[56,2996,2742],{"className":2997},[290],[56,2999],{"className":3000,"style":286},[187],[56,3002,2292],{"className":3003},[77,78],[56,3005,273],{"className":3006},[272],[56,3008,3010],{"className":3009},[245],[56,3011,3014],{"className":3012,"style":3013},[249],"height:0.93em;",[56,3015],{},[56,3017],{"className":3018},[182,2315],[56,3020],{"className":3021,"style":286},[187],[56,3023,291],{"className":3024},[290],[56,3026],{"className":3027,"style":286},[187],[56,3029,3031,3034,3039],{"className":3030},[68],[56,3032],{"className":3033,"style":106},[72],[56,3035,3038],{"className":3036,"style":3037},[77,78],"margin-right:0.0528em;","β",[56,3040,447],{"className":3041},[446],[11,3043,3044,3045,3108,3109,3171,3172,3187,3188,3204,3205,3277,3278,3285,3286,3304,3305,3187,3320,3335],{},"with learned per-feature scale ",[56,3046,3048],{"className":3047},[59],[56,3049,3051,3070],{"className":3050,"ariaHidden":64},[63],[56,3052,3054,3058,3061,3064,3067],{"className":3053},[68],[56,3055],{"className":3056,"style":3057},[72],"height:0.7335em;vertical-align:-0.1944em;",[56,3059,2830],{"className":3060,"style":2829},[77,78],[56,3062],{"className":3063,"style":188},[187],[56,3065,501],{"className":3066},[192],[56,3068],{"className":3069,"style":188},[187],[56,3071,3073,3076],{"className":3072},[68],[56,3074],{"className":3075,"style":2218},[72],[56,3077,3079,3082],{"className":3078},[77],[56,3080,519],{"className":3081},[77,518],[56,3083,3085],{"className":3084},[236],[56,3086,3088],{"className":3087},[240],[56,3089,3091],{"className":3090},[245],[56,3092,3094],{"className":3093,"style":2218},[249],[56,3095,3096,3099],{"style":2239},[56,3097],{"className":3098,"style":258},[257],[56,3100,3102],{"className":3101},[262,263,264,265],[56,3103,3105],{"className":3104},[77,265],[56,3106,548],{"className":3107},[77,78,265]," and shift\n",[56,3110,3112],{"className":3111},[59],[56,3113,3115,3133],{"className":3114,"ariaHidden":64},[63],[56,3116,3118,3121,3124,3127,3130],{"className":3117},[68],[56,3119],{"className":3120,"style":106},[72],[56,3122,3038],{"className":3123,"style":3037},[77,78],[56,3125],{"className":3126,"style":188},[187],[56,3128,501],{"className":3129},[192],[56,3131],{"className":3132,"style":188},[187],[56,3134,3136,3139],{"className":3135},[68],[56,3137],{"className":3138,"style":2218},[72],[56,3140,3142,3145],{"className":3141},[77],[56,3143,519],{"className":3144},[77,518],[56,3146,3148],{"className":3147},[236],[56,3149,3151],{"className":3150},[240],[56,3152,3154],{"className":3153},[245],[56,3155,3157],{"className":3156,"style":2218},[249],[56,3158,3159,3162],{"style":2239},[56,3160],{"className":3161,"style":258},[257],[56,3163,3165],{"className":3164},[262,263,264,265],[56,3166,3168],{"className":3167},[77,265],[56,3169,548],{"className":3170},[77,78,265]," (initialized to ",[56,3173,3175],{"className":3174},[59],[56,3176,3178],{"className":3177,"ariaHidden":64},[63],[56,3179,3181,3184],{"className":3180},[68],[56,3182],{"className":3183,"style":138},[72],[56,3185,43],{"className":3186},[77]," and ",[56,3189,3191],{"className":3190},[59],[56,3192,3194],{"className":3193,"ariaHidden":64},[63],[56,3195,3197,3200],{"className":3196},[68],[56,3198],{"className":3199,"style":138},[72],[56,3201,3203],{"className":3202},[77],"0","), and ",[56,3206,3208],{"className":3207},[59],[56,3209,3211,3231],{"className":3210,"ariaHidden":64},[63],[56,3212,3214,3218,3221,3224,3228],{"className":3213},[68],[56,3215],{"className":3216,"style":3217},[72],"height:0.4831em;",[56,3219,2943],{"className":3220},[77,78],[56,3222],{"className":3223,"style":188},[187],[56,3225,3227],{"className":3226},[192],"≈",[56,3229],{"className":3230,"style":188},[187],[56,3232,3234,3238,3241],{"className":3233},[68],[56,3235],{"className":3236,"style":3237},[72],"height:0.8141em;",[56,3239,43],{"className":3240},[77],[56,3242,3244,3247],{"className":3243},[77],[56,3245,3203],{"className":3246},[77],[56,3248,3250],{"className":3249},[236],[56,3251,3253],{"className":3252},[240],[56,3254,3256],{"className":3255},[245],[56,3257,3259],{"className":3258,"style":3237},[249],[56,3260,3261,3264],{"style":2239},[56,3262],{"className":3263,"style":258},[257],[56,3265,3267],{"className":3266},[262,263,264,265],[56,3268,3270,3273],{"className":3269},[77,265],[56,3271,2742],{"className":3272},[77,265],[56,3274,3276],{"className":3275},[77,265],"5"," for numerical safety. Because the reduction is per-token, LayerNorm is\nindependent of batch size and of the other positions — it behaves identically at\ntraining and inference and needs no running statistics — the reason it\nreplaced BatchNorm for variable-length sequence models.",[35,3279,3280],{},[15,3281,376],{"href":3282,"ariaDescribedBy":3283,"dataFootnoteRef":6,"id":3284},"#user-content-fn-gf-norm",[41],"user-content-fnref-gf-norm"," The single\naddition it contributes is ",[56,3287,3289],{"className":3288},[59],[56,3290,3292],{"className":3291,"ariaHidden":64},[63],[56,3293,3295,3298,3301],{"className":3294},[68],[56,3296],{"className":3297,"style":833},[72],[56,3299,376],{"className":3300},[77],[56,3302,548],{"className":3303},[77,78]," parameters (",[56,3306,3308],{"className":3307},[59],[56,3309,3311],{"className":3310,"ariaHidden":64},[63],[56,3312,3314,3317],{"className":3313},[68],[56,3315],{"className":3316,"style":2288},[72],[56,3318,2830],{"className":3319,"style":2829},[77,78],[56,3321,3323],{"className":3322},[59],[56,3324,3326],{"className":3325,"ariaHidden":64},[63],[56,3327,3329,3332],{"className":3328},[68],[56,3330],{"className":3331,"style":106},[72],[56,3333,3038],{"className":3334,"style":3037},[77,78],") per LayerNorm.",[11,3337,3338,3339,3342],{},"The two wrapper styles differ only in ",[51,3340,3341],{},"where"," the normalization sits relative\nto the residual sum.",[3344,3345,3346,3362],"table",{},[3347,3348,3349],"thead",{},[3350,3351,3352,3356,3359],"tr",{},[3353,3354,3355],"th",{},"Style",[3353,3357,3358],{},"Sublayer formula",[3353,3360,3361],{},"Residual path",[3363,3364,3365,3434],"tbody",{},[3350,3366,3367,3371,3431],{},[3368,3369,3370],"td",{},"Post-norm (original)",[3368,3372,3373],{},[56,3374,3376],{"className":3375},[59],[56,3377,3379],{"className":3378,"ariaHidden":64},[63],[56,3380,3382,3385,3391,3395,3398],{"className":3381},[68],[56,3383],{"className":3384,"style":160},[72],[56,3386,3388],{"className":3387},[164],[56,3389,2800],{"className":3390},[77,168],[56,3392],{"className":3393,"style":3394},[187],"margin-right:-0.1667em;",[56,3396],{"className":3397,"style":346},[187],[56,3399,3401,3404,3407,3410,3413,3416,3419,3422,3425,3428],{"className":3400},[206],[56,3402,174],{"className":3403,"style":211},[173,210],[56,3405,178],{"className":3406},[77,78],[56,3408],{"className":3409,"style":286},[187],[56,3411,291],{"className":3412},[290],[56,3414],{"className":3415,"style":286},[187],[56,3417,111],{"className":3418,"style":110},[77,78],[56,3420,174],{"className":3421},[173],[56,3423,178],{"className":3424},[77,78],[56,3426,183],{"className":3427},[182],[56,3429,183],{"className":3430,"style":211},[182,210],[3368,3432,3433],{},"passes through LN at every layer",[3350,3435,3436,3439,3505],{},[3368,3437,3438],{},"Pre-norm (modern)",[3368,3440,3441],{},[56,3442,3444],{"className":3443},[59],[56,3445,3447,3466],{"className":3446,"ariaHidden":64},[63],[56,3448,3450,3454,3457,3460,3463],{"className":3449},[68],[56,3451],{"className":3452,"style":3453},[72],"height:0.6667em;vertical-align:-0.0833em;",[56,3455,178],{"className":3456},[77,78],[56,3458],{"className":3459,"style":286},[187],[56,3461,291],{"className":3462},[290],[56,3464],{"className":3465,"style":286},[187],[56,3467,3469,3472,3475,3478,3481],{"className":3468},[68],[56,3470],{"className":3471,"style":160},[72],[56,3473,111],{"className":3474,"style":110},[77,78],[56,3476],{"className":3477,"style":3394},[187],[56,3479],{"className":3480,"style":346},[187],[56,3482,3484,3487,3493,3496,3499,3502],{"className":3483},[206],[56,3485,174],{"className":3486,"style":211},[173,210],[56,3488,3490],{"className":3489},[164],[56,3491,2800],{"className":3492},[77,168],[56,3494,174],{"className":3495},[173],[56,3497,178],{"className":3498},[77,78],[56,3500,183],{"className":3501},[182],[56,3503,183],{"className":3504,"style":211},[182,210],[3368,3506,3507],{},"clean identity, never normalized",[11,3509,3510,3511],{},"The distinction looks cosmetic but governs whether a deep stack trains at all.",[35,3512,3513],{},[15,3514,376],{"href":3282,"ariaDescribedBy":3515,"dataFootnoteRef":6,"id":3516},[41],"user-content-fnref-gf-norm-2",[45,3518,3520,3542,3870],{"type":3519},"theorem",[11,3521,3522,3525,3526,3541],{},[51,3523,3524],{},"Theorem (Pre-norm residual identity)."," Under pre-norm wrapping, the output\nof an ",[56,3527,3529],{"className":3528},[59],[56,3530,3532],{"className":3531,"ariaHidden":64},[63],[56,3533,3535,3538],{"className":3534},[68],[56,3536],{"className":3537,"style":73},[72],[56,3539,80],{"className":3540,"style":79},[77,78],"-layer stack expands as",[56,3543,3545],{"className":3544},[147],[56,3546,3548],{"className":3547},[59],[56,3549,3551,3611,3667],{"className":3550,"ariaHidden":64},[63],[56,3552,3554,3558,3602,3605,3608],{"className":3553},[68],[56,3555],{"className":3556,"style":3557},[72],"height:0.5806em;vertical-align:-0.15em;",[56,3559,3561,3566],{"className":3560},[77],[56,3562,3565],{"className":3563,"style":3564},[77,78],"margin-right:0.044em;","z",[56,3567,3569],{"className":3568},[236],[56,3570,3572,3594],{"className":3571},[240,241],[56,3573,3575,3591],{"className":3574},[245],[56,3576,3579],{"className":3577,"style":3578},[249],"height:0.3283em;",[56,3580,3582,3585],{"style":3581},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[56,3583],{"className":3584,"style":258},[257],[56,3586,3588],{"className":3587},[262,263,264,265],[56,3589,80],{"className":3590,"style":79},[77,78,265],[56,3592,273],{"className":3593},[272],[56,3595,3597],{"className":3596},[245],[56,3598,3600],{"className":3599,"style":280},[249],[56,3601],{},[56,3603],{"className":3604,"style":188},[187],[56,3606,193],{"className":3607},[192],[56,3609],{"className":3610,"style":188},[187],[56,3612,3614,3618,3658,3661,3664],{"className":3613},[68],[56,3615],{"className":3616,"style":3617},[72],"height:0.7333em;vertical-align:-0.15em;",[56,3619,3621,3624],{"className":3620},[77],[56,3622,3565],{"className":3623,"style":3564},[77,78],[56,3625,3627],{"className":3626},[236],[56,3628,3630,3650],{"className":3629},[240,241],[56,3631,3633,3647],{"className":3632},[245],[56,3634,3636],{"className":3635,"style":250},[249],[56,3637,3638,3641],{"style":3581},[56,3639],{"className":3640,"style":258},[257],[56,3642,3644],{"className":3643},[262,263,264,265],[56,3645,3203],{"className":3646},[77,265],[56,3648,273],{"className":3649},[272],[56,3651,3653],{"className":3652},[245],[56,3654,3656],{"className":3655,"style":280},[249],[56,3657],{},[56,3659],{"className":3660,"style":286},[187],[56,3662,291],{"className":3663},[290],[56,3665],{"className":3666,"style":286},[187],[56,3668,3670,3674,3743,3746,3787,3790,3793,3864,3867],{"className":3669},[68],[56,3671],{"className":3672,"style":3673},[72],"height:3.1304em;vertical-align:-1.3021em;",[56,3675,3677],{"className":3676},[164,2386],[56,3678,3680,3735],{"className":3679},[240,241],[56,3681,3683,3732],{"className":3682},[245],[56,3684,3687,3708,3718],{"className":3685,"style":3686},[249],"height:1.8283em;",[56,3688,3689,3692],{"style":2399},[56,3690],{"className":3691,"style":2403},[257],[56,3693,3695],{"className":3694},[262,263,264,265],[56,3696,3698,3702,3705],{"className":3697},[77,265],[56,3699,3701],{"className":3700},[77,265],"ℓ",[56,3703,193],{"className":3704},[192,265],[56,3706,43],{"className":3707},[77,265],[56,3709,3710,3713],{"style":2423},[56,3711],{"className":3712,"style":2403},[257],[56,3714,3715],{},[56,3716,2434],{"className":3717},[164,2432,2433],[56,3719,3720,3723],{"style":2437},[56,3721],{"className":3722,"style":2403},[257],[56,3724,3726],{"className":3725},[262,263,264,265],[56,3727,3729],{"className":3728},[77,265],[56,3730,80],{"className":3731,"style":79},[77,78,265],[56,3733,273],{"className":3734},[272],[56,3736,3738],{"className":3737},[245],[56,3739,3741],{"className":3740,"style":2459},[249],[56,3742],{},[56,3744],{"className":3745,"style":346},[187],[56,3747,3749,3752],{"className":3748},[77],[56,3750,111],{"className":3751,"style":110},[77,78],[56,3753,3755],{"className":3754},[236],[56,3756,3758,3779],{"className":3757},[240,241],[56,3759,3761,3776],{"className":3760},[245],[56,3762,3764],{"className":3763,"style":789},[249],[56,3765,3767,3770],{"style":3766},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[56,3768],{"className":3769,"style":258},[257],[56,3771,3773],{"className":3772},[262,263,264,265],[56,3774,3701],{"className":3775},[77,265],[56,3777,273],{"className":3778},[272],[56,3780,3782],{"className":3781},[245],[56,3783,3785],{"className":3784,"style":280},[249],[56,3786],{},[56,3788],{"className":3789,"style":3394},[187],[56,3791],{"className":3792,"style":346},[187],[56,3794,3796,3799,3805,3808,3858,3861],{"className":3795},[206],[56,3797,174],{"className":3798,"style":211},[173,210],[56,3800,3802],{"className":3801},[164],[56,3803,2800],{"className":3804},[77,168],[56,3806,174],{"className":3807},[173],[56,3809,3811,3814],{"className":3810},[77],[56,3812,3565],{"className":3813,"style":3564},[77,78],[56,3815,3817],{"className":3816},[236],[56,3818,3820,3849],{"className":3819},[240,241],[56,3821,3823,3846],{"className":3822},[245],[56,3824,3826],{"className":3825,"style":789},[249],[56,3827,3828,3831],{"style":3581},[56,3829],{"className":3830,"style":258},[257],[56,3832,3834],{"className":3833},[262,263,264,265],[56,3835,3837,3840,3843],{"className":3836},[77,265],[56,3838,3701],{"className":3839},[77,265],[56,3841,2742],{"className":3842},[290,265],[56,3844,43],{"className":3845},[77,265],[56,3847,273],{"className":3848},[272],[56,3850,3852],{"className":3851},[245],[56,3853,3856],{"className":3854,"style":3855},[249],"height:0.2083em;",[56,3857],{},[56,3859,183],{"className":3860},[182],[56,3862,183],{"className":3863,"style":211},[182,210],[56,3865],{"className":3866,"style":346},[187],[56,3868,447],{"className":3869},[446],[11,3871,3872,3873,3925,3926,4029,4030,4045],{},"so the input ",[56,3874,3876],{"className":3875},[59],[56,3877,3879],{"className":3878,"ariaHidden":64},[63],[56,3880,3882,3885],{"className":3881},[68],[56,3883],{"className":3884,"style":3557},[72],[56,3886,3888,3891],{"className":3887},[77],[56,3889,3565],{"className":3890,"style":3564},[77,78],[56,3892,3894],{"className":3893},[236],[56,3895,3897,3917],{"className":3896},[240,241],[56,3898,3900,3914],{"className":3899},[245],[56,3901,3903],{"className":3902,"style":250},[249],[56,3904,3905,3908],{"style":3581},[56,3906],{"className":3907,"style":258},[257],[56,3909,3911],{"className":3910},[262,263,264,265],[56,3912,3203],{"className":3913},[77,265],[56,3915,273],{"className":3916},[272],[56,3918,3920],{"className":3919},[245],[56,3921,3923],{"className":3922,"style":280},[249],[56,3924],{}," reaches the top through an unbroken identity path, and the\ngradient ",[56,3927,3929],{"className":3928},[59],[56,3930,3932],{"className":3931,"ariaHidden":64},[63],[56,3933,3935,3938,3942,3982,3986,3989],{"className":3934},[68],[56,3936],{"className":3937,"style":160},[72],[56,3939,3941],{"className":3940,"style":2829},[77],"∂",[56,3943,3945,3948],{"className":3944},[77],[56,3946,3565],{"className":3947,"style":3564},[77,78],[56,3949,3951],{"className":3950},[236],[56,3952,3954,3974],{"className":3953},[240,241],[56,3955,3957,3971],{"className":3956},[245],[56,3958,3960],{"className":3959,"style":3578},[249],[56,3961,3962,3965],{"style":3581},[56,3963],{"className":3964,"style":258},[257],[56,3966,3968],{"className":3967},[262,263,264,265],[56,3969,80],{"className":3970,"style":79},[77,78,265],[56,3972,273],{"className":3973},[272],[56,3975,3977],{"className":3976},[245],[56,3978,3980],{"className":3979,"style":280},[249],[56,3981],{},[56,3983,3985],{"className":3984},[77],"\u002F",[56,3987,3941],{"className":3988,"style":2829},[77],[56,3990,3992,3995],{"className":3991},[77],[56,3993,3565],{"className":3994,"style":3564},[77,78],[56,3996,3998],{"className":3997},[236],[56,3999,4001,4021],{"className":4000},[240,241],[56,4002,4004,4018],{"className":4003},[245],[56,4005,4007],{"className":4006,"style":250},[249],[56,4008,4009,4012],{"style":3581},[56,4010],{"className":4011,"style":258},[257],[56,4013,4015],{"className":4014},[262,263,264,265],[56,4016,3203],{"className":4017},[77,265],[56,4019,273],{"className":4020},[272],[56,4022,4024],{"className":4023},[245],[56,4025,4027],{"className":4026,"style":280},[249],[56,4028],{}," contains a term equal to ",[56,4031,4033],{"className":4032},[59],[56,4034,4036],{"className":4035,"ariaHidden":64},[63],[56,4037,4039,4042],{"className":4038},[68],[56,4040],{"className":4041,"style":138},[72],[56,4043,43],{"className":4044},[77],"\nindependent of depth.",[45,4047,4049],{"type":4048},"proof",[11,4050,4051,4054,4055,4292,4293,929,4326,4341,4342,4620,4621,4889,4890,4905,4906],{},[51,4052,4053],{},"Proof."," Pre-norm defines ",[56,4056,4058],{"className":4057},[59],[56,4059,4061,4116,4181],{"className":4060,"ariaHidden":64},[63],[56,4062,4064,4067,4107,4110,4113],{"className":4063},[68],[56,4065],{"className":4066,"style":3557},[72],[56,4068,4070,4073],{"className":4069},[77],[56,4071,3565],{"className":4072,"style":3564},[77,78],[56,4074,4076],{"className":4075},[236],[56,4077,4079,4099],{"className":4078},[240,241],[56,4080,4082,4096],{"className":4081},[245],[56,4083,4085],{"className":4084,"style":789},[249],[56,4086,4087,4090],{"style":3581},[56,4088],{"className":4089,"style":258},[257],[56,4091,4093],{"className":4092},[262,263,264,265],[56,4094,3701],{"className":4095},[77,265],[56,4097,273],{"className":4098},[272],[56,4100,4102],{"className":4101},[245],[56,4103,4105],{"className":4104,"style":280},[249],[56,4106],{},[56,4108],{"className":4109,"style":188},[187],[56,4111,193],{"className":4112},[192],[56,4114],{"className":4115,"style":188},[187],[56,4117,4119,4123,4172,4175,4178],{"className":4118},[68],[56,4120],{"className":4121,"style":4122},[72],"height:0.7917em;vertical-align:-0.2083em;",[56,4124,4126,4129],{"className":4125},[77],[56,4127,3565],{"className":4128,"style":3564},[77,78],[56,4130,4132],{"className":4131},[236],[56,4133,4135,4164],{"className":4134},[240,241],[56,4136,4138,4161],{"className":4137},[245],[56,4139,4141],{"className":4140,"style":789},[249],[56,4142,4143,4146],{"style":3581},[56,4144],{"className":4145,"style":258},[257],[56,4147,4149],{"className":4148},[262,263,264,265],[56,4150,4152,4155,4158],{"className":4151},[77,265],[56,4153,3701],{"className":4154},[77,265],[56,4156,2742],{"className":4157},[290,265],[56,4159,43],{"className":4160},[77,265],[56,4162,273],{"className":4163},[272],[56,4165,4167],{"className":4166},[245],[56,4168,4170],{"className":4169,"style":3855},[249],[56,4171],{},[56,4173],{"className":4174,"style":286},[187],[56,4176,291],{"className":4177},[290],[56,4179],{"className":4180,"style":286},[187],[56,4182,4184,4187,4227,4230,4236,4239,4288],{"className":4183},[68],[56,4185],{"className":4186,"style":160},[72],[56,4188,4190,4193],{"className":4189},[77],[56,4191,111],{"className":4192,"style":110},[77,78],[56,4194,4196],{"className":4195},[236],[56,4197,4199,4219],{"className":4198},[240,241],[56,4200,4202,4216],{"className":4201},[245],[56,4203,4205],{"className":4204,"style":789},[249],[56,4206,4207,4210],{"style":3766},[56,4208],{"className":4209,"style":258},[257],[56,4211,4213],{"className":4212},[262,263,264,265],[56,4214,3701],{"className":4215},[77,265],[56,4217,273],{"className":4218},[272],[56,4220,4222],{"className":4221},[245],[56,4223,4225],{"className":4224,"style":280},[249],[56,4226],{},[56,4228,174],{"className":4229},[173],[56,4231,4233],{"className":4232},[164],[56,4234,2800],{"className":4235},[77,168],[56,4237,174],{"className":4238},[173],[56,4240,4242,4245],{"className":4241},[77],[56,4243,3565],{"className":4244,"style":3564},[77,78],[56,4246,4248],{"className":4247},[236],[56,4249,4251,4280],{"className":4250},[240,241],[56,4252,4254,4277],{"className":4253},[245],[56,4255,4257],{"className":4256,"style":789},[249],[56,4258,4259,4262],{"style":3581},[56,4260],{"className":4261,"style":258},[257],[56,4263,4265],{"className":4264},[262,263,264,265],[56,4266,4268,4271,4274],{"className":4267},[77,265],[56,4269,3701],{"className":4270},[77,265],[56,4272,2742],{"className":4273},[290,265],[56,4275,43],{"className":4276},[77,265],[56,4278,273],{"className":4279},[272],[56,4281,4283],{"className":4282},[245],[56,4284,4286],{"className":4285,"style":3855},[249],[56,4287],{},[56,4289,4291],{"className":4290},[182],"))",".\nUnrolling the recurrence from ",[56,4294,4296],{"className":4295},[59],[56,4297,4299,4317],{"className":4298,"ariaHidden":64},[63],[56,4300,4302,4305,4308,4311,4314],{"className":4301},[68],[56,4303],{"className":4304,"style":833},[72],[56,4306,3701],{"className":4307},[77],[56,4309],{"className":4310,"style":188},[187],[56,4312,193],{"className":4313},[192],[56,4315],{"className":4316,"style":188},[187],[56,4318,4320,4323],{"className":4319},[68],[56,4321],{"className":4322,"style":138},[72],[56,4324,43],{"className":4325},[77],[56,4327,4329],{"className":4328},[59],[56,4330,4332],{"className":4331,"ariaHidden":64},[63],[56,4333,4335,4338],{"className":4334},[68],[56,4336],{"className":4337,"style":73},[72],[56,4339,80],{"className":4340,"style":79},[77,78]," telescopes the residual sums,\ngiving ",[56,4343,4345],{"className":4344},[59],[56,4346,4348,4403,4458],{"className":4347,"ariaHidden":64},[63],[56,4349,4351,4354,4394,4397,4400],{"className":4350},[68],[56,4352],{"className":4353,"style":3557},[72],[56,4355,4357,4360],{"className":4356},[77],[56,4358,3565],{"className":4359,"style":3564},[77,78],[56,4361,4363],{"className":4362},[236],[56,4364,4366,4386],{"className":4365},[240,241],[56,4367,4369,4383],{"className":4368},[245],[56,4370,4372],{"className":4371,"style":3578},[249],[56,4373,4374,4377],{"style":3581},[56,4375],{"className":4376,"style":258},[257],[56,4378,4380],{"className":4379},[262,263,264,265],[56,4381,80],{"className":4382,"style":79},[77,78,265],[56,4384,273],{"className":4385},[272],[56,4387,4389],{"className":4388},[245],[56,4390,4392],{"className":4391,"style":280},[249],[56,4393],{},[56,4395],{"className":4396,"style":188},[187],[56,4398,193],{"className":4399},[192],[56,4401],{"className":4402,"style":188},[187],[56,4404,4406,4409,4449,4452,4455],{"className":4405},[68],[56,4407],{"className":4408,"style":3617},[72],[56,4410,4412,4415],{"className":4411},[77],[56,4413,3565],{"className":4414,"style":3564},[77,78],[56,4416,4418],{"className":4417},[236],[56,4419,4421,4441],{"className":4420},[240,241],[56,4422,4424,4438],{"className":4423},[245],[56,4425,4427],{"className":4426,"style":250},[249],[56,4428,4429,4432],{"style":3581},[56,4430],{"className":4431,"style":258},[257],[56,4433,4435],{"className":4434},[262,263,264,265],[56,4436,3203],{"className":4437},[77,265],[56,4439,273],{"className":4440},[272],[56,4442,4444],{"className":4443},[245],[56,4445,4447],{"className":4446,"style":280},[249],[56,4448],{},[56,4450],{"className":4451,"style":286},[187],[56,4453,291],{"className":4454},[290],[56,4456],{"className":4457,"style":286},[187],[56,4459,4461,4465,4513,4516,4556,4559,4565,4568,4617],{"className":4460},[68],[56,4462],{"className":4463,"style":4464},[72],"height:1.0497em;vertical-align:-0.2997em;",[56,4466,4468,4473],{"className":4467},[164],[56,4469,2434],{"className":4470,"style":4472},[164,2432,4471],"small-op","position:relative;top:0em;",[56,4474,4476],{"className":4475},[236],[56,4477,4479,4504],{"className":4478},[240,241],[56,4480,4482,4501],{"className":4481},[245],[56,4483,4486],{"className":4484,"style":4485},[249],"height:0.1864em;",[56,4487,4489,4492],{"style":4488},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[56,4490],{"className":4491,"style":258},[257],[56,4493,4495],{"className":4494},[262,263,264,265],[56,4496,4498],{"className":4497},[77,265],[56,4499,3701],{"className":4500},[77,265],[56,4502,273],{"className":4503},[272],[56,4505,4507],{"className":4506},[245],[56,4508,4511],{"className":4509,"style":4510},[249],"height:0.2997em;",[56,4512],{},[56,4514],{"className":4515,"style":346},[187],[56,4517,4519,4522],{"className":4518},[77],[56,4520,111],{"className":4521,"style":110},[77,78],[56,4523,4525],{"className":4524},[236],[56,4526,4528,4548],{"className":4527},[240,241],[56,4529,4531,4545],{"className":4530},[245],[56,4532,4534],{"className":4533,"style":789},[249],[56,4535,4536,4539],{"style":3766},[56,4537],{"className":4538,"style":258},[257],[56,4540,4542],{"className":4541},[262,263,264,265],[56,4543,3701],{"className":4544},[77,265],[56,4546,273],{"className":4547},[272],[56,4549,4551],{"className":4550},[245],[56,4552,4554],{"className":4553,"style":280},[249],[56,4555],{},[56,4557,174],{"className":4558},[173],[56,4560,4562],{"className":4561},[164],[56,4563,2800],{"className":4564},[77,168],[56,4566,174],{"className":4567},[173],[56,4569,4571,4574],{"className":4570},[77],[56,4572,3565],{"className":4573,"style":3564},[77,78],[56,4575,4577],{"className":4576},[236],[56,4578,4580,4609],{"className":4579},[240,241],[56,4581,4583,4606],{"className":4582},[245],[56,4584,4586],{"className":4585,"style":789},[249],[56,4587,4588,4591],{"style":3581},[56,4589],{"className":4590,"style":258},[257],[56,4592,4594],{"className":4593},[262,263,264,265],[56,4595,4597,4600,4603],{"className":4596},[77,265],[56,4598,3701],{"className":4599},[77,265],[56,4601,2742],{"className":4602},[290,265],[56,4604,43],{"className":4605},[77,265],[56,4607,273],{"className":4608},[272],[56,4610,4612],{"className":4611},[245],[56,4613,4615],{"className":4614,"style":3855},[249],[56,4616],{},[56,4618,4291],{"className":4619},[182],".\nDifferentiating, ",[56,4622,4624],{"className":4623},[59],[56,4625,4627,4731,4751],{"className":4626,"ariaHidden":64},[63],[56,4628,4630,4633,4636,4676,4679,4682,4722,4725,4728],{"className":4629},[68],[56,4631],{"className":4632,"style":160},[72],[56,4634,3941],{"className":4635,"style":2829},[77],[56,4637,4639,4642],{"className":4638},[77],[56,4640,3565],{"className":4641,"style":3564},[77,78],[56,4643,4645],{"className":4644},[236],[56,4646,4648,4668],{"className":4647},[240,241],[56,4649,4651,4665],{"className":4650},[245],[56,4652,4654],{"className":4653,"style":3578},[249],[56,4655,4656,4659],{"style":3581},[56,4657],{"className":4658,"style":258},[257],[56,4660,4662],{"className":4661},[262,263,264,265],[56,4663,80],{"className":4664,"style":79},[77,78,265],[56,4666,273],{"className":4667},[272],[56,4669,4671],{"className":4670},[245],[56,4672,4674],{"className":4673,"style":280},[249],[56,4675],{},[56,4677,3985],{"className":4678},[77],[56,4680,3941],{"className":4681,"style":2829},[77],[56,4683,4685,4688],{"className":4684},[77],[56,4686,3565],{"className":4687,"style":3564},[77,78],[56,4689,4691],{"className":4690},[236],[56,4692,4694,4714],{"className":4693},[240,241],[56,4695,4697,4711],{"className":4696},[245],[56,4698,4700],{"className":4699,"style":250},[249],[56,4701,4702,4705],{"style":3581},[56,4703],{"className":4704,"style":258},[257],[56,4706,4708],{"className":4707},[262,263,264,265],[56,4709,3203],{"className":4710},[77,265],[56,4712,273],{"className":4713},[272],[56,4715,4717],{"className":4716},[245],[56,4718,4720],{"className":4719,"style":280},[249],[56,4721],{},[56,4723],{"className":4724,"style":188},[187],[56,4726,193],{"className":4727},[192],[56,4729],{"className":4730,"style":188},[187],[56,4732,4734,4737,4742,4745,4748],{"className":4733},[68],[56,4735],{"className":4736,"style":2158},[72],[56,4738,4741],{"className":4739,"style":4740},[77,78],"margin-right:0.0785em;","I",[56,4743],{"className":4744,"style":286},[187],[56,4746,291],{"className":4747},[290],[56,4749],{"className":4750,"style":286},[187],[56,4752,4754,4757,4797,4800,4803,4843,4846,4849],{"className":4753},[68],[56,4755],{"className":4756,"style":4464},[72],[56,4758,4760,4763],{"className":4759},[164],[56,4761,2434],{"className":4762,"style":4472},[164,2432,4471],[56,4764,4766],{"className":4765},[236],[56,4767,4769,4789],{"className":4768},[240,241],[56,4770,4772,4786],{"className":4771},[245],[56,4773,4775],{"className":4774,"style":4485},[249],[56,4776,4777,4780],{"style":4488},[56,4778],{"className":4779,"style":258},[257],[56,4781,4783],{"className":4782},[262,263,264,265],[56,4784,3701],{"className":4785},[77,265],[56,4787,273],{"className":4788},[272],[56,4790,4792],{"className":4791},[245],[56,4793,4795],{"className":4794,"style":4510},[249],[56,4796],{},[56,4798],{"className":4799,"style":346},[187],[56,4801,3941],{"className":4802,"style":2829},[77],[56,4804,4806,4809],{"className":4805},[77],[56,4807,111],{"className":4808,"style":110},[77,78],[56,4810,4812],{"className":4811},[236],[56,4813,4815,4835],{"className":4814},[240,241],[56,4816,4818,4832],{"className":4817},[245],[56,4819,4821],{"className":4820,"style":789},[249],[56,4822,4823,4826],{"style":3766},[56,4824],{"className":4825,"style":258},[257],[56,4827,4829],{"className":4828},[262,263,264,265],[56,4830,3701],{"className":4831},[77,265],[56,4833,273],{"className":4834},[272],[56,4836,4838],{"className":4837},[245],[56,4839,4841],{"className":4840,"style":280},[249],[56,4842],{},[56,4844,3985],{"className":4845},[77],[56,4847,3941],{"className":4848,"style":2829},[77],[56,4850,4852,4855],{"className":4851},[77],[56,4853,3565],{"className":4854,"style":3564},[77,78],[56,4856,4858],{"className":4857},[236],[56,4859,4861,4881],{"className":4860},[240,241],[56,4862,4864,4878],{"className":4863},[245],[56,4865,4867],{"className":4866,"style":250},[249],[56,4868,4869,4872],{"style":3581},[56,4870],{"className":4871,"style":258},[257],[56,4873,4875],{"className":4874},[262,263,264,265],[56,4876,3203],{"className":4877},[77,265],[56,4879,273],{"className":4880},[272],[56,4882,4884],{"className":4883},[245],[56,4885,4887],{"className":4886,"style":280},[249],[56,4888],{},"; the leading ",[56,4891,4893],{"className":4892},[59],[56,4894,4896],{"className":4895,"ariaHidden":64},[63],[56,4897,4899,4902],{"className":4898},[68],[56,4900],{"className":4901,"style":73},[72],[56,4903,4741],{"className":4904,"style":4740},[77,78]," is a depth-independent identity, so no\nproduct of Jacobians can drive the gradient to zero on the skip path. ",[56,4907,4909],{"className":4908},[59],[56,4910,4912],{"className":4911,"ariaHidden":64},[63],[56,4913,4915,4919],{"className":4914},[68],[56,4916],{"className":4917,"style":4918},[72],"height:0.675em;",[56,4920,4924],{"className":4921},[4922,4923],"enclosing","qed",[56,4925,4928],{"className":4926},[77,4927],"amsrm","□",[11,4930,4931,4932,4935,4936,4951],{},"Post-norm breaks that identity: each residual sum is squeezed back through a\nLayerNorm, so the gradient path is a ",[21,4933,4934],{},"product"," of ",[56,4937,4939],{"className":4938},[59],[56,4940,4942],{"className":4941,"ariaHidden":64},[63],[56,4943,4945,4948],{"className":4944},[68],[56,4946],{"className":4947,"style":73},[72],[56,4949,80],{"className":4950,"style":79},[77,78]," normalization Jacobians and\ncan vanish or explode with depth, which is why post-norm Transformers need a\nlearning-rate warmup and pre-norm ones largely do not.",[4953,4954],"tikz-figure",{"hash":4955},"d6ce671c97176b2b643ad7955b2ca46fd4e1dbf2599996eaa1c0995765addaec",[83,4957,4959],{"id":4958},"positional-encoding","Positional encoding",[11,4961,4962,4963,4966,4967,3187,4970,4973,4974,4977],{},"Attention is ",[51,4964,4965],{},"permutation-equivariant",": shuffle the input tokens and the output\nset is the same, merely reordered. That is fatal for language, where ",[30,4968,4969],{},"dog bites man",[30,4971,4972],{},"man bites dog"," are different sentences built from identical tokens. The\nattention operator has no notion of position, so order has to be injected into the\ninputs before the first layer. The original Transformer adds a fixed ",[51,4975,4976],{},"sinusoidal\npositional encoding"," to the token embeddings.",[45,4979,4980,5166,5590],{"type":47},[11,4981,4982,4985,4986,5080,5081,5165],{},[51,4983,4984],{},"Definition (Sinusoidal positional encoding)."," For position ",[56,4987,4989],{"className":4988},[59],[56,4990,4992,5014,5067],{"className":4991,"ariaHidden":64},[63],[56,4993,4995,4998,5005,5008,5011],{"className":4994},[68],[56,4996],{"className":4997,"style":3057},[72],[56,4999,5001],{"className":5000},[77,590],[56,5002,5004],{"className":5003},[77],"pos",[56,5006],{"className":5007,"style":188},[187],[56,5009,501],{"className":5010},[192],[56,5012],{"className":5013,"style":188},[187],[56,5015,5017,5020,5024,5027,5030,5033,5036,5039,5042,5046,5049,5052,5055,5058,5061,5064],{"className":5016},[68],[56,5018],{"className":5019,"style":160},[72],[56,5021,5023],{"className":5022},[173],"{",[56,5025,3203],{"className":5026},[77],[56,5028,447],{"className":5029},[446],[56,5031],{"className":5032,"style":346},[187],[56,5034,43],{"className":5035},[77],[56,5037,447],{"className":5038},[446],[56,5040],{"className":5041,"style":346},[187],[56,5043,5045],{"className":5044},[206],"…",[56,5047],{"className":5048,"style":346},[187],[56,5050,447],{"className":5051},[446],[56,5053],{"className":5054,"style":346},[187],[56,5056,1104],{"className":5057},[77,78],[56,5059],{"className":5060,"style":286},[187],[56,5062,2742],{"className":5063},[290],[56,5065],{"className":5066,"style":286},[187],[56,5068,5070,5073,5076],{"className":5069},[68],[56,5071],{"className":5072,"style":160},[72],[56,5074,43],{"className":5075},[77],[56,5077,5079],{"className":5078},[182],"}"," and feature index ",[56,5082,5084],{"className":5083},[59],[56,5085,5087,5107,5153],{"className":5086,"ariaHidden":64},[63],[56,5088,5090,5094,5098,5101,5104],{"className":5089},[68],[56,5091],{"className":5092,"style":5093},[72],"height:0.6986em;vertical-align:-0.0391em;",[56,5095,5097],{"className":5096},[77,78],"i",[56,5099],{"className":5100,"style":188},[187],[56,5102,501],{"className":5103},[192],[56,5105],{"className":5106,"style":188},[187],[56,5108,5110,5113,5116,5119,5122,5125,5128,5131,5134,5137,5140,5144,5147,5150],{"className":5109},[68],[56,5111],{"className":5112,"style":160},[72],[56,5114,5023],{"className":5115},[173],[56,5117,3203],{"className":5118},[77],[56,5120,447],{"className":5121},[446],[56,5123],{"className":5124,"style":346},[187],[56,5126,5045],{"className":5127},[206],[56,5129],{"className":5130,"style":346},[187],[56,5132,447],{"className":5133},[446],[56,5135],{"className":5136,"style":346},[187],[56,5138,548],{"className":5139},[77,78],[56,5141,5143],{"className":5142},[77],"\u002F2",[56,5145],{"className":5146,"style":286},[187],[56,5148,2742],{"className":5149},[290],[56,5151],{"className":5152,"style":286},[187],[56,5154,5156,5159,5162],{"className":5155},[68],[56,5157],{"className":5158,"style":160},[72],[56,5160,43],{"className":5161},[77],[56,5163,5079],{"className":5164},[182],", the\nencoding fills even and odd feature slots with a sine\u002Fcosine pair whose\nfrequency decreases geometrically across the width:",[56,5167,5169],{"className":5168},[147],[56,5170,5172],{"className":5171},[59],[56,5173,5175,5221,5420,5441],{"className":5174,"ariaHidden":64},[63],[56,5176,5178,5181,5188,5191,5197,5200,5203,5206,5209,5212,5215,5218],{"className":5177},[68],[56,5179],{"className":5180,"style":160},[72],[56,5182,5184],{"className":5183},[164],[56,5185,5187],{"className":5186},[77,168],"PE",[56,5189,174],{"className":5190},[173],[56,5192,5194],{"className":5193},[77,590],[56,5195,5004],{"className":5196},[77],[56,5198,447],{"className":5199},[446],[56,5201],{"className":5202,"style":346},[187],[56,5204,376],{"className":5205},[77],[56,5207,5097],{"className":5208},[77,78],[56,5210,183],{"className":5211},[182],[56,5213],{"className":5214,"style":188},[187],[56,5216,193],{"className":5217},[192],[56,5219],{"className":5220,"style":188},[187],[56,5222,5224,5228,5235,5238,5241,5372,5375,5378,5381,5384,5390,5393,5399,5402,5405,5408,5411,5414,5417],{"className":5223},[68],[56,5225],{"className":5226,"style":5227},[72],"height:1.854em;vertical-align:-0.704em;",[56,5229,5231],{"className":5230},[164],[56,5232,5234],{"className":5233},[77,168],"sin",[56,5236],{"className":5237,"style":3394},[187],[56,5239],{"className":5240,"style":346},[187],[56,5242,5244,5252,5366],{"className":5243},[206],[56,5245,5247],{"className":5246,"style":211},[173,210],[56,5248,174],{"className":5249},[5250,5251],"delimsizing","size2",[56,5253,5255,5258,5363],{"className":5254},[77],[56,5256],{"className":5257},[173,2315],[56,5259,5261],{"className":5260},[2319],[56,5262,5264,5354],{"className":5263},[240,241],[56,5265,5267,5351],{"className":5266},[245],[56,5268,5271,5329,5337],{"className":5269,"style":5270},[249],"height:1.1076em;",[56,5272,5274,5277],{"style":5273},"top:-2.296em;",[56,5275],{"className":5276,"style":1182},[257],[56,5278,5280,5284],{"className":5279},[77],[56,5281,5283],{"className":5282},[77],"1000",[56,5285,5287,5290],{"className":5286},[77],[56,5288,3203],{"className":5289},[77],[56,5291,5293],{"className":5292},[236],[56,5294,5296],{"className":5295},[240],[56,5297,5299],{"className":5298},[245],[56,5300,5303],{"className":5301,"style":5302},[249],"height:0.814em;",[56,5304,5305,5308],{"style":2921},[56,5306],{"className":5307,"style":258},[257],[56,5309,5311],{"className":5310},[262,263,264,265],[56,5312,5314,5317,5320,5323,5326],{"className":5313},[77,265],[56,5315],{"className":5316,"style":1359},[187,265],[56,5318,376],{"className":5319},[77,265],[56,5321,5097],{"className":5322},[77,78,265],[56,5324,3985],{"className":5325},[77,265],[56,5327,548],{"className":5328},[77,78,265],[56,5330,5331,5334],{"style":2344},[56,5332],{"className":5333,"style":1182},[257],[56,5335],{"className":5336,"style":2352},[2351],[56,5338,5339,5342],{"style":2355},[56,5340],{"className":5341,"style":1182},[257],[56,5343,5345],{"className":5344},[77],[56,5346,5348],{"className":5347},[77,590],[56,5349,5004],{"className":5350},[77],[56,5352,273],{"className":5353},[272],[56,5355,5357],{"className":5356},[245],[56,5358,5361],{"className":5359,"style":5360},[249],"height:0.704em;",[56,5362],{},[56,5364],{"className":5365},[182,2315],[56,5367,5369],{"className":5368,"style":211},[182,210],[56,5370,183],{"className":5371},[5250,5251],[56,5373],{"className":5374,"style":346},[187],[56,5376,447],{"className":5377},[446],[56,5379],{"className":5380,"style":451},[187],[56,5382],{"className":5383,"style":346},[187],[56,5385,5387],{"className":5386},[164],[56,5388,5187],{"className":5389},[77,168],[56,5391,174],{"className":5392},[173],[56,5394,5396],{"className":5395},[77,590],[56,5397,5004],{"className":5398},[77],[56,5400,447],{"className":5401},[446],[56,5403],{"className":5404,"style":346},[187],[56,5406,376],{"className":5407},[77],[56,5409,5097],{"className":5410},[77,78],[56,5412],{"className":5413,"style":286},[187],[56,5415,291],{"className":5416},[290],[56,5418],{"className":5419,"style":286},[187],[56,5421,5423,5426,5429,5432,5435,5438],{"className":5422},[68],[56,5424],{"className":5425,"style":160},[72],[56,5427,43],{"className":5428},[77],[56,5430,183],{"className":5431},[182],[56,5433],{"className":5434,"style":188},[187],[56,5436,193],{"className":5437},[192],[56,5439],{"className":5440,"style":188},[187],[56,5442,5444,5447,5454,5457,5460,5584,5587],{"className":5443},[68],[56,5445],{"className":5446,"style":5227},[72],[56,5448,5450],{"className":5449},[164],[56,5451,5453],{"className":5452},[77,168],"cos",[56,5455],{"className":5456,"style":3394},[187],[56,5458],{"className":5459,"style":346},[187],[56,5461,5463,5469,5578],{"className":5462},[206],[56,5464,5466],{"className":5465,"style":211},[173,210],[56,5467,174],{"className":5468},[5250,5251],[56,5470,5472,5475,5575],{"className":5471},[77],[56,5473],{"className":5474},[173,2315],[56,5476,5478],{"className":5477},[2319],[56,5479,5481,5567],{"className":5480},[240,241],[56,5482,5484,5564],{"className":5483},[245],[56,5485,5487,5542,5550],{"className":5486,"style":5270},[249],[56,5488,5489,5492],{"style":5273},[56,5490],{"className":5491,"style":1182},[257],[56,5493,5495,5498],{"className":5494},[77],[56,5496,5283],{"className":5497},[77],[56,5499,5501,5504],{"className":5500},[77],[56,5502,3203],{"className":5503},[77],[56,5505,5507],{"className":5506},[236],[56,5508,5510],{"className":5509},[240],[56,5511,5513],{"className":5512},[245],[56,5514,5516],{"className":5515,"style":5302},[249],[56,5517,5518,5521],{"style":2921},[56,5519],{"className":5520,"style":258},[257],[56,5522,5524],{"className":5523},[262,263,264,265],[56,5525,5527,5530,5533,5536,5539],{"className":5526},[77,265],[56,5528],{"className":5529,"style":1359},[187,265],[56,5531,376],{"className":5532},[77,265],[56,5534,5097],{"className":5535},[77,78,265],[56,5537,3985],{"className":5538},[77,265],[56,5540,548],{"className":5541},[77,78,265],[56,5543,5544,5547],{"style":2344},[56,5545],{"className":5546,"style":1182},[257],[56,5548],{"className":5549,"style":2352},[2351],[56,5551,5552,5555],{"style":2355},[56,5553],{"className":5554,"style":1182},[257],[56,5556,5558],{"className":5557},[77],[56,5559,5561],{"className":5560},[77,590],[56,5562,5004],{"className":5563},[77],[56,5565,273],{"className":5566},[272],[56,5568,5570],{"className":5569},[245],[56,5571,5573],{"className":5572,"style":5360},[249],[56,5574],{},[56,5576],{"className":5577},[182,2315],[56,5579,5581],{"className":5580,"style":211},[182,210],[56,5582,183],{"className":5583},[5250,5251],[56,5585],{"className":5586,"style":346},[187],[56,5588,2042],{"className":5589},[77],[11,5591,5592,5593,5670,5671,5686,5687,2042],{},"The vector ",[56,5594,5596],{"className":5595},[59],[56,5597,5599,5632],{"className":5598,"ariaHidden":64},[63],[56,5600,5602,5605,5611,5614,5620,5623,5626,5629],{"className":5601},[68],[56,5603],{"className":5604,"style":160},[72],[56,5606,5608],{"className":5607},[164],[56,5609,5187],{"className":5610},[77,168],[56,5612,174],{"className":5613},[173],[56,5615,5617],{"className":5616},[77,590],[56,5618,5004],{"className":5619},[77],[56,5621,183],{"className":5622},[182],[56,5624],{"className":5625,"style":188},[187],[56,5627,501],{"className":5628},[192],[56,5630],{"className":5631,"style":188},[187],[56,5633,5635,5638],{"className":5634},[68],[56,5636],{"className":5637,"style":2218},[72],[56,5639,5641,5644],{"className":5640},[77],[56,5642,519],{"className":5643},[77,518],[56,5645,5647],{"className":5646},[236],[56,5648,5650],{"className":5649},[240],[56,5651,5653],{"className":5652},[245],[56,5654,5656],{"className":5655,"style":2218},[249],[56,5657,5658,5661],{"style":2239},[56,5659],{"className":5660,"style":258},[257],[56,5662,5664],{"className":5663},[262,263,264,265],[56,5665,5667],{"className":5666},[77,265],[56,5668,548],{"className":5669},[77,78,265]," is added to the\ntoken embedding at that position, giving the layer-",[56,5672,5674],{"className":5673},[59],[56,5675,5677],{"className":5676,"ariaHidden":64},[63],[56,5678,5680,5683],{"className":5679},[68],[56,5681],{"className":5682,"style":138},[72],[56,5684,3203],{"className":5685},[77]," input ",[56,5688,5690],{"className":5689},[59],[56,5691,5693,5748,5779],{"className":5692,"ariaHidden":64},[63],[56,5694,5696,5699,5739,5742,5745],{"className":5695},[68],[56,5697],{"className":5698,"style":3557},[72],[56,5700,5702,5705],{"className":5701},[77],[56,5703,3565],{"className":5704,"style":3564},[77,78],[56,5706,5708],{"className":5707},[236],[56,5709,5711,5731],{"className":5710},[240,241],[56,5712,5714,5728],{"className":5713},[245],[56,5715,5717],{"className":5716,"style":250},[249],[56,5718,5719,5722],{"style":3581},[56,5720],{"className":5721,"style":258},[257],[56,5723,5725],{"className":5724},[262,263,264,265],[56,5726,3203],{"className":5727},[77,265],[56,5729,273],{"className":5730},[272],[56,5732,5734],{"className":5733},[245],[56,5735,5737],{"className":5736,"style":280},[249],[56,5738],{},[56,5740],{"className":5741,"style":188},[187],[56,5743,193],{"className":5744},[192],[56,5746],{"className":5747,"style":188},[187],[56,5749,5751,5754,5761,5764,5767,5770,5773,5776],{"className":5750},[68],[56,5752],{"className":5753,"style":160},[72],[56,5755,5757],{"className":5756},[77,590],[56,5758,5760],{"className":5759},[77],"Embed",[56,5762,174],{"className":5763},[173],[56,5765,178],{"className":5766},[77,78],[56,5768,183],{"className":5769},[182],[56,5771],{"className":5772,"style":286},[187],[56,5774,291],{"className":5775},[290],[56,5777],{"className":5778,"style":286},[187],[56,5780,5782,5785],{"className":5781},[68],[56,5783],{"className":5784,"style":73},[72],[56,5786,5788],{"className":5787},[164],[56,5789,5187],{"className":5790},[77,168],[11,5792,5793,5794,5851,5852,5855,5856,5890,5891,5910,5911,5965,5966,6003],{},"The ",[56,5795,5797],{"className":5796},[59],[56,5798,5800],{"className":5799,"ariaHidden":64},[63],[56,5801,5803,5807,5810],{"className":5802},[68],[56,5804],{"className":5805,"style":5806},[72],"height:0.888em;",[56,5808,5283],{"className":5809},[77],[56,5811,5813,5816],{"className":5812},[77],[56,5814,3203],{"className":5815},[77],[56,5817,5819],{"className":5818},[236],[56,5820,5822],{"className":5821},[240],[56,5823,5825],{"className":5824},[245],[56,5826,5828],{"className":5827,"style":5806},[249],[56,5829,5830,5833],{"style":2239},[56,5831],{"className":5832,"style":258},[257],[56,5834,5836],{"className":5835},[262,263,264,265],[56,5837,5839,5842,5845,5848],{"className":5838},[77,265],[56,5840,376],{"className":5841},[77,265],[56,5843,5097],{"className":5844},[77,78,265],[56,5846,3985],{"className":5847},[77,265],[56,5849,548],{"className":5850},[77,78,265]," denominator sets the ",[51,5853,5854],{},"wavelength"," of each feature: the lowest\nfeature (",[56,5857,5859],{"className":5858},[59],[56,5860,5862,5881],{"className":5861,"ariaHidden":64},[63],[56,5863,5865,5869,5872,5875,5878],{"className":5864},[68],[56,5866],{"className":5867,"style":5868},[72],"height:0.6595em;",[56,5870,5097],{"className":5871},[77,78],[56,5873],{"className":5874,"style":188},[187],[56,5876,193],{"className":5877},[192],[56,5879],{"className":5880,"style":188},[187],[56,5882,5884,5887],{"className":5883},[68],[56,5885],{"className":5886,"style":138},[72],[56,5888,3203],{"className":5889},[77],") oscillates with period ",[56,5892,5894],{"className":5893},[59],[56,5895,5897],{"className":5896,"ariaHidden":64},[63],[56,5898,5900,5903,5906],{"className":5899},[68],[56,5901],{"className":5902,"style":138},[72],[56,5904,376],{"className":5905},[77],[56,5907,5909],{"className":5908,"style":2520},[77,78],"π"," tokens, and the highest (",[56,5912,5914],{"className":5913},[59],[56,5915,5917,5935,5956],{"className":5916,"ariaHidden":64},[63],[56,5918,5920,5923,5926,5929,5932],{"className":5919},[68],[56,5921],{"className":5922,"style":5868},[72],[56,5924,5097],{"className":5925},[77,78],[56,5927],{"className":5928,"style":188},[187],[56,5930,193],{"className":5931},[192],[56,5933],{"className":5934,"style":188},[187],[56,5936,5938,5941,5944,5947,5950,5953],{"className":5937},[68],[56,5939],{"className":5940,"style":160},[72],[56,5942,548],{"className":5943},[77,78],[56,5945,5143],{"className":5946},[77],[56,5948],{"className":5949,"style":286},[187],[56,5951,2742],{"className":5952},[290],[56,5954],{"className":5955,"style":286},[187],[56,5957,5959,5962],{"className":5958},[68],[56,5960],{"className":5961,"style":138},[72],[56,5963,43],{"className":5964},[77],") with period ",[56,5967,5969],{"className":5968},[59],[56,5970,5972,5993],{"className":5971,"ariaHidden":64},[63],[56,5973,5975,5978,5981,5984,5987,5990],{"className":5974},[68],[56,5976],{"className":5977,"style":138},[72],[56,5979,376],{"className":5980},[77],[56,5982,5909],{"className":5983,"style":2520},[77,78],[56,5985],{"className":5986,"style":286},[187],[56,5988,1007],{"className":5989},[290],[56,5991],{"className":5992,"style":286},[187],[56,5994,5996,5999],{"className":5995},[68],[56,5997],{"className":5998,"style":138},[72],[56,6000,6002],{"className":6001},[77],"10000"," tokens. Low-frequency channels change slowly\nand encode coarse, long-range position; high-frequency channels distinguish\nadjacent tokens. Together they give each position a unique fingerprint across a\ngeometric band of scales, the same multi-resolution idea a place-value numeral uses\nto name any integer with a fixed set of digits.",[4953,6005],{"hash":6006},"9246ea2730ba777edb7cc9c149081657e223097713af609d24b4c6f8cefae95d",[11,6008,6009],{},"Two properties make the sinusoidal choice more than a lookup table:",[6011,6012,6013,6096],"ul",{},[6014,6015,6016,6019,6020,6035,6036,6072,6073,6091,6092,6095],"li",{},[51,6017,6018],{},"Relative position is linear."," For any fixed offset ",[56,6021,6023],{"className":6022},[59],[56,6024,6026],{"className":6025,"ariaHidden":64},[63],[56,6027,6029,6032],{"className":6028},[68],[56,6030],{"className":6031,"style":833},[72],[56,6033,2414],{"className":6034,"style":2413},[77,78],", the encoding at\n",[56,6037,6039],{"className":6038},[59],[56,6040,6042,6063],{"className":6041,"ariaHidden":64},[63],[56,6043,6045,6048,6054,6057,6060],{"className":6044},[68],[56,6046],{"className":6047,"style":2825},[72],[56,6049,6051],{"className":6050},[77,590],[56,6052,5004],{"className":6053},[77],[56,6055],{"className":6056,"style":286},[187],[56,6058,291],{"className":6059},[290],[56,6061],{"className":6062,"style":286},[187],[56,6064,6066,6069],{"className":6065},[68],[56,6067],{"className":6068,"style":833},[72],[56,6070,2414],{"className":6071,"style":2413},[77,78]," is a fixed linear function (a rotation, from the angle-sum\nidentities) of the encoding at ",[56,6074,6076],{"className":6075},[59],[56,6077,6079],{"className":6078,"ariaHidden":64},[63],[56,6080,6082,6085],{"className":6081},[68],[56,6083],{"className":6084,"style":2288},[72],[56,6086,6088],{"className":6087},[77,590],[56,6089,5004],{"className":6090},[77],". A single learned projection inside\nan attention head can therefore read ",[21,6093,6094],{},"relative"," distance, not just absolute\nindex, which is what a language model actually needs.",[6014,6097,6098,6101,6102,6120],{},[51,6099,6100],{},"Length extrapolation."," Because the formula is defined for every real\n",[56,6103,6105],{"className":6104},[59],[56,6106,6108],{"className":6107,"ariaHidden":64},[63],[56,6109,6111,6114],{"className":6110},[68],[56,6112],{"className":6113,"style":2288},[72],[56,6115,6117],{"className":6116},[77,590],[56,6118,5004],{"className":6119},[77],", a model can be evaluated on sequences longer than any it saw in\ntraining without a new parameter — the encoding simply continues.",[11,6122,6123,6124,6127,6128,6291,6292,6350],{},"The alternative is a ",[51,6125,6126],{},"learned positional embedding",": a trainable table\n",[56,6129,6131],{"className":6130},[59],[56,6132,6134,6201],{"className":6133,"ariaHidden":64},[63],[56,6135,6137,6141,6192,6195,6198],{"className":6136},[68],[56,6138],{"className":6139,"style":6140},[72],"height:0.9694em;vertical-align:-0.2861em;",[56,6142,6144,6149],{"className":6143},[77],[56,6145,6148],{"className":6146,"style":6147},[77,78],"margin-right:0.0576em;","E",[56,6150,6152],{"className":6151},[236],[56,6153,6155,6183],{"className":6154},[240,241],[56,6156,6158,6180],{"className":6157},[245],[56,6159,6162],{"className":6160,"style":6161},[249],"height:0.1514em;",[56,6163,6165,6168],{"style":6164},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[56,6166],{"className":6167,"style":258},[257],[56,6169,6171],{"className":6170},[262,263,264,265],[56,6172,6174],{"className":6173},[77,265],[56,6175,6177],{"className":6176},[77,590,265],[56,6178,5004],{"className":6179},[77,265],[56,6181,273],{"className":6182},[272],[56,6184,6186],{"className":6185},[245],[56,6187,6190],{"className":6188,"style":6189},[249],"height:0.2861em;",[56,6191],{},[56,6193],{"className":6194,"style":188},[187],[56,6196,501],{"className":6197},[192],[56,6199],{"className":6200,"style":188},[187],[56,6202,6204,6207],{"className":6203},[68],[56,6205],{"className":6206,"style":2218},[72],[56,6208,6210,6213],{"className":6209},[77],[56,6211,519],{"className":6212},[77,518],[56,6214,6216],{"className":6215},[236],[56,6217,6219],{"className":6218},[240],[56,6220,6222],{"className":6221},[245],[56,6223,6225],{"className":6224,"style":2218},[249],[56,6226,6227,6230],{"style":2239},[56,6228],{"className":6229,"style":258},[257],[56,6231,6233],{"className":6232},[262,263,264,265],[56,6234,6236,6285,6288],{"className":6235},[77,265],[56,6237,6239,6242],{"className":6238},[77,265],[56,6240,1104],{"className":6241},[77,78,265],[56,6243,6245],{"className":6244},[236],[56,6246,6248,6277],{"className":6247},[240,241],[56,6249,6251,6274],{"className":6250},[245],[56,6252,6255],{"className":6253,"style":6254},[249],"height:0.1645em;",[56,6256,6258,6261],{"style":6257},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[56,6259],{"className":6260,"style":578},[257],[56,6262,6264],{"className":6263},[262,582,583,265],[56,6265,6267],{"className":6266},[77,265],[56,6268,6270],{"className":6269},[164,265],[56,6271,6273],{"className":6272},[77,168,265],"max",[56,6275,273],{"className":6276},[272],[56,6278,6280],{"className":6279},[245],[56,6281,6283],{"className":6282,"style":1400},[249],[56,6284],{},[56,6286,552],{"className":6287},[290,265],[56,6289,548],{"className":6290},[77,78,265]," with one row per position, added\njust like a word embedding. Learned embeddings match or slightly beat sinusoids on\nin-distribution data and are the common choice for encoder-only models (BERT) and\nViT, but they cap the context at the table's row count ",[56,6293,6295],{"className":6294},[59],[56,6296,6298],{"className":6297,"ariaHidden":64},[63],[56,6299,6301,6304],{"className":6300},[68],[56,6302],{"className":6303,"style":3557},[72],[56,6305,6307,6310],{"className":6306},[77],[56,6308,1104],{"className":6309},[77,78],[56,6311,6313],{"className":6312},[236],[56,6314,6316,6342],{"className":6315},[240,241],[56,6317,6319,6339],{"className":6318},[245],[56,6320,6322],{"className":6321,"style":6161},[249],[56,6323,6324,6327],{"style":316},[56,6325],{"className":6326,"style":258},[257],[56,6328,6330],{"className":6329},[262,263,264,265],[56,6331,6333],{"className":6332},[77,265],[56,6334,6336],{"className":6335},[164,265],[56,6337,6273],{"className":6338},[77,168,265],[56,6340,273],{"className":6341},[272],[56,6343,6345],{"className":6344},[245],[56,6346,6348],{"className":6347,"style":280},[249],[56,6349],{}," and cannot\nextrapolate past it. Modern decoder-only models mostly use neither and instead\nrotate the queries and keys inside attention (rotary embeddings, RoPE), which keeps\nthe linear-relative property while removing the additive table entirely.",[83,6352,6354],{"id":6353},"one-encoder-layer","One encoder layer",[11,6356,6357,6358,447],{},"An encoder layer is two wrapped sublayers in series: multi-head self-attention,\nthen a position-wise FFN. With pre-norm wrapping and an input ",[56,6359,6361],{"className":6360},[59],[56,6362,6364],{"className":6363,"ariaHidden":64},[63],[56,6365,6367,6370],{"className":6366},[68],[56,6368],{"className":6369,"style":1100},[72],[56,6371,178],{"className":6372},[77,78],[56,6374,6376],{"className":6375},[147],[56,6377,6379],{"className":6378},[59],[56,6380,6382,6400,6418,6486,6504],{"className":6381,"ariaHidden":64},[63],[56,6383,6385,6388,6391,6394,6397],{"className":6384},[68],[56,6386],{"className":6387,"style":1100},[72],[56,6389,15],{"className":6390},[77,78],[56,6392],{"className":6393,"style":188},[187],[56,6395,193],{"className":6396},[192],[56,6398],{"className":6399,"style":188},[187],[56,6401,6403,6406,6409,6412,6415],{"className":6402},[68],[56,6404],{"className":6405,"style":3453},[72],[56,6407,178],{"className":6408},[77,78],[56,6410],{"className":6411,"style":286},[187],[56,6413,291],{"className":6414},[290],[56,6416],{"className":6417,"style":286},[187],[56,6419,6421,6424,6431,6434,6437,6461,6464,6467,6470,6473,6477,6480,6483],{"className":6420},[68],[56,6422],{"className":6423,"style":160},[72],[56,6425,6427],{"className":6426},[164],[56,6428,6430],{"className":6429},[77,168],"MHA",[56,6432],{"className":6433,"style":3394},[187],[56,6435],{"className":6436,"style":346},[187],[56,6438,6440,6443,6449,6452,6455,6458],{"className":6439},[206],[56,6441,174],{"className":6442,"style":211},[173,210],[56,6444,6446],{"className":6445},[164],[56,6447,2800],{"className":6448},[77,168],[56,6450,174],{"className":6451},[173],[56,6453,178],{"className":6454},[77,78],[56,6456,183],{"className":6457},[182],[56,6459,183],{"className":6460,"style":211},[182,210],[56,6462],{"className":6463,"style":346},[187],[56,6465,447],{"className":6466},[446],[56,6468],{"className":6469,"style":451},[187],[56,6471],{"className":6472,"style":346},[187],[56,6474,6476],{"className":6475,"style":2520},[77,78],"y",[56,6478],{"className":6479,"style":188},[187],[56,6481,193],{"className":6482},[192],[56,6484],{"className":6485,"style":188},[187],[56,6487,6489,6492,6495,6498,6501],{"className":6488},[68],[56,6490],{"className":6491,"style":3453},[72],[56,6493,15],{"className":6494},[77,78],[56,6496],{"className":6497,"style":286},[187],[56,6499,291],{"className":6500},[290],[56,6502],{"className":6503,"style":286},[187],[56,6505,6507,6510,6516,6519,6522,6546,6549],{"className":6506},[68],[56,6508],{"className":6509,"style":160},[72],[56,6511,6513],{"className":6512},[164],[56,6514,169],{"className":6515},[77,168],[56,6517],{"className":6518,"style":3394},[187],[56,6520],{"className":6521,"style":346},[187],[56,6523,6525,6528,6534,6537,6540,6543],{"className":6524},[206],[56,6526,174],{"className":6527,"style":211},[173,210],[56,6529,6531],{"className":6530},[164],[56,6532,2800],{"className":6533},[77,168],[56,6535,174],{"className":6536},[173],[56,6538,15],{"className":6539},[77,78],[56,6541,183],{"className":6542},[182],[56,6544,183],{"className":6545,"style":211},[182,210],[56,6547],{"className":6548,"style":346},[187],[56,6550,2042],{"className":6551},[77],[11,6553,6554,6555,6558,6559,6562],{},"The self-attention is ",[21,6556,6557],{},"unrestricted",": every position attends to every other,\nso each output position is a content-weighted summary of the whole input. This\nis the right behavior for an ",[21,6560,6561],{},"encoder",": the entire sequence is available and\nthere is no causality constraint.",[11,6564,6565,6566,6605,6606,6621,6622,6656,6657,6692,6693,6788,6789,6866,6867,143],{},"Every tensor in the block has the same shape ",[56,6567,6569],{"className":6568},[59],[56,6570,6572],{"className":6571,"ariaHidden":64},[63],[56,6573,6575,6578,6581,6584,6587,6590,6593,6596,6599,6602],{"className":6574},[68],[56,6576],{"className":6577,"style":160},[72],[56,6579,174],{"className":6580},[173],[56,6582,1086],{"className":6583,"style":1085},[77,78],[56,6585,447],{"className":6586},[446],[56,6588],{"className":6589,"style":346},[187],[56,6591,1104],{"className":6592},[77,78],[56,6594,447],{"className":6595},[446],[56,6597],{"className":6598,"style":346},[187],[56,6600,548],{"className":6601},[77,78],[56,6603,183],{"className":6604},[182],": the width ",[56,6607,6609],{"className":6608},[59],[56,6610,6612],{"className":6611,"ariaHidden":64},[63],[56,6613,6615,6618],{"className":6614},[68],[56,6616],{"className":6617,"style":833},[72],[56,6619,548],{"className":6620},[77,78]," is the\ninvariant of the residual stream, so a layer's output plugs into the next layer's\ninput without any reshaping. Trace one block for a concrete configuration\n",[56,6623,6625],{"className":6624},[59],[56,6626,6628,6646],{"className":6627,"ariaHidden":64},[63],[56,6629,6631,6634,6637,6640,6643],{"className":6630},[68],[56,6632],{"className":6633,"style":833},[72],[56,6635,548],{"className":6636},[77,78],[56,6638],{"className":6639,"style":188},[187],[56,6641,193],{"className":6642},[192],[56,6644],{"className":6645,"style":188},[187],[56,6647,6649,6652],{"className":6648},[68],[56,6650],{"className":6651,"style":138},[72],[56,6653,6655],{"className":6654},[77],"512",", ",[56,6658,6660],{"className":6659},[59],[56,6661,6663,6682],{"className":6662,"ariaHidden":64},[63],[56,6664,6666,6669,6673,6676,6679],{"className":6665},[68],[56,6667],{"className":6668,"style":833},[72],[56,6670,6672],{"className":6671},[77,78],"h",[56,6674],{"className":6675,"style":188},[187],[56,6677,193],{"className":6678},[192],[56,6680],{"className":6681,"style":188},[187],[56,6683,6685,6688],{"className":6684},[68],[56,6686],{"className":6687,"style":138},[72],[56,6689,6691],{"className":6690},[77],"8"," heads (so head width ",[56,6694,6696],{"className":6695},[59],[56,6697,6699,6754,6778],{"className":6698,"ariaHidden":64},[63],[56,6700,6702,6705,6745,6748,6751],{"className":6701},[68],[56,6703],{"className":6704,"style":770},[72],[56,6706,6708,6711],{"className":6707},[77],[56,6709,548],{"className":6710},[77,78],[56,6712,6714],{"className":6713},[236],[56,6715,6717,6737],{"className":6716},[240,241],[56,6718,6720,6734],{"className":6719},[245],[56,6721,6723],{"className":6722,"style":789},[249],[56,6724,6725,6728],{"style":316},[56,6726],{"className":6727,"style":258},[257],[56,6729,6731],{"className":6730},[262,263,264,265],[56,6732,2414],{"className":6733,"style":2413},[77,78,265],[56,6735,273],{"className":6736},[272],[56,6738,6740],{"className":6739},[245],[56,6741,6743],{"className":6742,"style":280},[249],[56,6744],{},[56,6746],{"className":6747,"style":188},[187],[56,6749,193],{"className":6750},[192],[56,6752],{"className":6753,"style":188},[187],[56,6755,6757,6760,6763,6766,6769,6772,6775],{"className":6756},[68],[56,6758],{"className":6759,"style":160},[72],[56,6761,548],{"className":6762},[77,78],[56,6764,3985],{"className":6765},[77],[56,6767,6672],{"className":6768},[77,78],[56,6770],{"className":6771,"style":188},[187],[56,6773,193],{"className":6774},[192],[56,6776],{"className":6777,"style":188},[187],[56,6779,6781,6784],{"className":6780},[68],[56,6782],{"className":6783,"style":138},[72],[56,6785,6787],{"className":6786},[77],"64","), ",[56,6790,6792],{"className":6791},[59],[56,6793,6795,6856],{"className":6794,"ariaHidden":64},[63],[56,6796,6798,6801,6847,6850,6853],{"className":6797},[68],[56,6799],{"className":6800,"style":770},[72],[56,6802,6804,6807],{"className":6803},[77],[56,6805,548],{"className":6806},[77,78],[56,6808,6810],{"className":6809},[236],[56,6811,6813,6839],{"className":6812},[240,241],[56,6814,6816,6836],{"className":6815},[245],[56,6817,6819],{"className":6818,"style":789},[249],[56,6820,6821,6824],{"style":316},[56,6822],{"className":6823,"style":258},[257],[56,6825,6827],{"className":6826},[262,263,264,265],[56,6828,6830],{"className":6829},[77,265],[56,6831,6833],{"className":6832},[77,590,265],[56,6834,594],{"className":6835},[77,265],[56,6837,273],{"className":6838},[272],[56,6840,6842],{"className":6841},[245],[56,6843,6845],{"className":6844,"style":280},[249],[56,6846],{},[56,6848],{"className":6849,"style":188},[187],[56,6851,193],{"className":6852},[192],[56,6854],{"className":6855,"style":188},[187],[56,6857,6859,6862],{"className":6858},[68],[56,6860],{"className":6861,"style":138},[72],[56,6863,6865],{"className":6864},[77],"2048",",\ninput ",[56,6868,6870],{"className":6869},[59],[56,6871,6873],{"className":6872,"ariaHidden":64},[63],[56,6874,6876,6879,6882,6885,6888,6891,6894,6897,6900,6903],{"className":6875},[68],[56,6877],{"className":6878,"style":160},[72],[56,6880,174],{"className":6881},[173],[56,6883,1086],{"className":6884,"style":1085},[77,78],[56,6886,447],{"className":6887},[446],[56,6889],{"className":6890,"style":346},[187],[56,6892,1104],{"className":6893},[77,78],[56,6895,447],{"className":6896},[446],[56,6898],{"className":6899,"style":346},[187],[56,6901,6655],{"className":6902},[77],[56,6904,183],{"className":6905},[182],[3344,6907,6908,6921],{},[3347,6909,6910],{},[3350,6911,6912,6915,6918],{},[3353,6913,6914],{},"Step",[3353,6916,6917],{},"Operation",[3353,6919,6920],{},"Output shape",[3363,6922,6923,6986,7077,7189,7347,7395,7517,7642],{},[3350,6924,6925,6927,6945],{},[3368,6926,3203],{},[3368,6928,6929,6930],{},"input ",[56,6931,6933],{"className":6932},[59],[56,6934,6936],{"className":6935,"ariaHidden":64},[63],[56,6937,6939,6942],{"className":6938},[68],[56,6940],{"className":6941,"style":1100},[72],[56,6943,178],{"className":6944},[77,78],[3368,6946,6947],{},[56,6948,6950],{"className":6949},[59],[56,6951,6953],{"className":6952,"ariaHidden":64},[63],[56,6954,6956,6959,6962,6965,6968,6971,6974,6977,6980,6983],{"className":6955},[68],[56,6957],{"className":6958,"style":160},[72],[56,6960,174],{"className":6961},[173],[56,6963,1086],{"className":6964,"style":1085},[77,78],[56,6966,447],{"className":6967},[446],[56,6969],{"className":6970,"style":346},[187],[56,6972,1104],{"className":6973},[77,78],[56,6975,447],{"className":6976},[446],[56,6978],{"className":6979,"style":346},[187],[56,6981,6655],{"className":6982},[77],[56,6984,183],{"className":6985},[182],[3350,6987,6988,6990,7036],{},[3368,6989,43],{},[3368,6991,6992,7019,7020,7035],{},[56,6993,6995],{"className":6994},[59],[56,6996,6998],{"className":6997,"ariaHidden":64},[63],[56,6999,7001,7004,7010,7013,7016],{"className":7000},[68],[56,7002],{"className":7003,"style":160},[72],[56,7005,7007],{"className":7006},[164],[56,7008,2800],{"className":7009},[77,168],[56,7011,174],{"className":7012},[173],[56,7014,178],{"className":7015},[77,78],[56,7017,183],{"className":7018},[182]," (per-token, over the ",[56,7021,7023],{"className":7022},[59],[56,7024,7026],{"className":7025,"ariaHidden":64},[63],[56,7027,7029,7032],{"className":7028},[68],[56,7030],{"className":7031,"style":138},[72],[56,7033,6655],{"className":7034},[77]," features)",[3368,7037,7038],{},[56,7039,7041],{"className":7040},[59],[56,7042,7044],{"className":7043,"ariaHidden":64},[63],[56,7045,7047,7050,7053,7056,7059,7062,7065,7068,7071,7074],{"className":7046},[68],[56,7048],{"className":7049,"style":160},[72],[56,7051,174],{"className":7052},[173],[56,7054,1086],{"className":7055,"style":1085},[77,78],[56,7057,447],{"className":7058},[446],[56,7060],{"className":7061,"style":346},[187],[56,7063,1104],{"className":7064},[77,78],[56,7066,447],{"className":7067},[446],[56,7069],{"className":7070,"style":346},[187],[56,7072,6655],{"className":7073},[77],[56,7075,183],{"className":7076},[182],[3350,7078,7079,7081,7138],{},[3368,7080,376],{},[3368,7082,7083,7084,7121,7122,7137],{},"project to ",[56,7085,7087],{"className":7086},[59],[56,7088,7090],{"className":7089,"ariaHidden":64},[63],[56,7091,7093,7096,7100,7103,7106,7111,7114,7117],{"className":7092},[68],[56,7094],{"className":7095,"style":2058},[72],[56,7097,7099],{"className":7098},[77,78],"Q",[56,7101,447],{"className":7102},[446],[56,7104],{"className":7105,"style":346},[187],[56,7107,7110],{"className":7108,"style":7109},[77,78],"margin-right:0.0715em;","K",[56,7112,447],{"className":7113},[446],[56,7115],{"className":7116,"style":346},[187],[56,7118,7120],{"className":7119,"style":286},[77,78],"V",", split into ",[56,7123,7125],{"className":7124},[59],[56,7126,7128],{"className":7127,"ariaHidden":64},[63],[56,7129,7131,7134],{"className":7130},[68],[56,7132],{"className":7133,"style":138},[72],[56,7135,6691],{"className":7136},[77]," heads",[3368,7139,7140,7188],{},[56,7141,7143],{"className":7142},[59],[56,7144,7146],{"className":7145,"ariaHidden":64},[63],[56,7147,7149,7152,7155,7158,7161,7164,7167,7170,7173,7176,7179,7182,7185],{"className":7148},[68],[56,7150],{"className":7151,"style":160},[72],[56,7153,174],{"className":7154},[173],[56,7156,1086],{"className":7157,"style":1085},[77,78],[56,7159,447],{"className":7160},[446],[56,7162],{"className":7163,"style":346},[187],[56,7165,6691],{"className":7166},[77],[56,7168,447],{"className":7169},[446],[56,7171],{"className":7172,"style":346},[187],[56,7174,1104],{"className":7175},[77,78],[56,7177,447],{"className":7178},[446],[56,7180],{"className":7181,"style":346},[187],[56,7183,6787],{"className":7184},[77],[56,7186,183],{"className":7187},[182]," each",[3350,7190,7191,7194,7297],{},[3368,7192,7193],{},"3",[3368,7195,7196,7197,7296],{},"scores ",[56,7198,7200],{"className":7199},[59],[56,7201,7203],{"className":7202,"ariaHidden":64},[63],[56,7204,7206,7210,7213,7243,7246],{"className":7205},[68],[56,7207],{"className":7208,"style":7209},[72],"height:1.1572em;vertical-align:-0.25em;",[56,7211,7099],{"className":7212},[77,78],[56,7214,7216,7219],{"className":7215},[77],[56,7217,7110],{"className":7218,"style":7109},[77,78],[56,7220,7222],{"className":7221},[236],[56,7223,7225],{"className":7224},[240],[56,7226,7228],{"className":7227},[245],[56,7229,7231],{"className":7230,"style":2218},[249],[56,7232,7233,7236],{"style":2239},[56,7234],{"className":7235,"style":258},[257],[56,7237,7239],{"className":7238},[262,263,264,265],[56,7240,7242],{"className":7241},[77,265],"⊤",[56,7244,3985],{"className":7245},[77],[56,7247,7249],{"className":7248},[77,2879],[56,7250,7252,7287],{"className":7251},[240,241],[56,7253,7255,7284],{"className":7254},[245],[56,7256,7259,7271],{"className":7257,"style":7258},[249],"height:0.9072em;",[56,7260,7262,7265],{"className":7261,"style":1198},[1217],[56,7263],{"className":7264,"style":1182},[257],[56,7266,7268],{"className":7267,"style":2899},[77],[56,7269,6787],{"className":7270},[77],[56,7272,7274,7277],{"style":7273},"top:-2.8672em;",[56,7275],{"className":7276,"style":1182},[257],[56,7278,7280],{"className":7279,"style":2953},[1462],[1233,7281,7282],{"xmlns":1235,"width":1236,"height":2956,"viewBox":2957,"preserveAspectRatio":1239},[1241,7283],{"d":2960},[56,7285,273],{"className":7286},[272],[56,7288,7290],{"className":7289},[245],[56,7291,7294],{"className":7292,"style":7293},[249],"height:0.1328em;",[56,7295],{},", softmax over keys",[3368,7298,7299],{},[56,7300,7302],{"className":7301},[59],[56,7303,7305],{"className":7304,"ariaHidden":64},[63],[56,7306,7308,7311,7314,7317,7320,7323,7326,7329,7332,7335,7338,7341,7344],{"className":7307},[68],[56,7309],{"className":7310,"style":160},[72],[56,7312,174],{"className":7313},[173],[56,7315,1086],{"className":7316,"style":1085},[77,78],[56,7318,447],{"className":7319},[446],[56,7321],{"className":7322,"style":346},[187],[56,7324,6691],{"className":7325},[77],[56,7327,447],{"className":7328},[446],[56,7330],{"className":7331,"style":346},[187],[56,7333,1104],{"className":7334},[77,78],[56,7336,447],{"className":7337},[446],[56,7339],{"className":7340,"style":346},[187],[56,7342,1104],{"className":7343},[77,78],[56,7345,183],{"className":7346},[182],[3350,7348,7349,7351,7354],{},[3368,7350,142],{},[3368,7352,7353],{},"weighted values, concat heads",[3368,7355,7356],{},[56,7357,7359],{"className":7358},[59],[56,7360,7362],{"className":7361,"ariaHidden":64},[63],[56,7363,7365,7368,7371,7374,7377,7380,7383,7386,7389,7392],{"className":7364},[68],[56,7366],{"className":7367,"style":160},[72],[56,7369,174],{"className":7370},[173],[56,7372,1086],{"className":7373,"style":1085},[77,78],[56,7375,447],{"className":7376},[446],[56,7378],{"className":7379,"style":346},[187],[56,7381,1104],{"className":7382},[77,78],[56,7384,447],{"className":7385},[446],[56,7387],{"className":7388,"style":346},[187],[56,7390,6655],{"className":7391},[77],[56,7393,183],{"className":7394},[182],[3350,7396,7397,7399,7476],{},[3368,7398,3276],{},[3368,7400,7401,7402,7457,7458],{},"output projection ",[56,7403,7405],{"className":7404},[59],[56,7406,7408],{"className":7407,"ariaHidden":64},[63],[56,7409,7411,7415],{"className":7410},[68],[56,7412],{"className":7413,"style":7414},[72],"height:0.8333em;vertical-align:-0.15em;",[56,7416,7418,7421],{"className":7417},[77],[56,7419,232],{"className":7420,"style":231},[77,78],[56,7422,7424],{"className":7423},[236],[56,7425,7427,7449],{"className":7426},[240,241],[56,7428,7430,7446],{"className":7429},[245],[56,7431,7433],{"className":7432,"style":3578},[249],[56,7434,7435,7438],{"style":253},[56,7436],{"className":7437,"style":258},[257],[56,7439,7441],{"className":7440},[262,263,264,265],[56,7442,7445],{"className":7443,"style":7444},[77,78,265],"margin-right:0.0278em;","O",[56,7447,273],{"className":7448},[272],[56,7450,7452],{"className":7451},[245],[56,7453,7455],{"className":7454,"style":280},[249],[56,7456],{},", add residual ",[56,7459,7461],{"className":7460},[59],[56,7462,7464],{"className":7463,"ariaHidden":64},[63],[56,7465,7467,7470,7473],{"className":7466},[68],[56,7468],{"className":7469,"style":3453},[72],[56,7471,178],{"className":7472},[77,78],[56,7474,291],{"className":7475},[77],[3368,7477,7478],{},[56,7479,7481],{"className":7480},[59],[56,7482,7484],{"className":7483,"ariaHidden":64},[63],[56,7485,7487,7490,7493,7496,7499,7502,7505,7508,7511,7514],{"className":7486},[68],[56,7488],{"className":7489,"style":160},[72],[56,7491,174],{"className":7492},[173],[56,7494,1086],{"className":7495,"style":1085},[77,78],[56,7497,447],{"className":7498},[446],[56,7500],{"className":7501,"style":346},[187],[56,7503,1104],{"className":7504},[77,78],[56,7506,447],{"className":7507},[446],[56,7509],{"className":7510,"style":346},[187],[56,7512,6655],{"className":7513},[77],[56,7515,183],{"className":7516},[182],[3350,7518,7519,7522,7601],{},[3368,7520,7521],{},"6",[3368,7523,7524,7542,7543],{},[56,7525,7527],{"className":7526},[59],[56,7528,7530],{"className":7529,"ariaHidden":64},[63],[56,7531,7533,7536],{"className":7532},[68],[56,7534],{"className":7535,"style":73},[72],[56,7537,7539],{"className":7538},[164],[56,7540,2800],{"className":7541},[77,168],", up-project to ",[56,7544,7546],{"className":7545},[59],[56,7547,7549],{"className":7548,"ariaHidden":64},[63],[56,7550,7552,7555],{"className":7551},[68],[56,7553],{"className":7554,"style":770},[72],[56,7556,7558,7561],{"className":7557},[77],[56,7559,548],{"className":7560},[77,78],[56,7562,7564],{"className":7563},[236],[56,7565,7567,7593],{"className":7566},[240,241],[56,7568,7570,7590],{"className":7569},[245],[56,7571,7573],{"className":7572,"style":789},[249],[56,7574,7575,7578],{"style":316},[56,7576],{"className":7577,"style":258},[257],[56,7579,7581],{"className":7580},[262,263,264,265],[56,7582,7584],{"className":7583},[77,265],[56,7585,7587],{"className":7586},[77,590,265],[56,7588,594],{"className":7589},[77,265],[56,7591,273],{"className":7592},[272],[56,7594,7596],{"className":7595},[245],[56,7597,7599],{"className":7598,"style":280},[249],[56,7600],{},[3368,7602,7603],{},[56,7604,7606],{"className":7605},[59],[56,7607,7609],{"className":7608,"ariaHidden":64},[63],[56,7610,7612,7615,7618,7621,7624,7627,7630,7633,7636,7639],{"className":7611},[68],[56,7613],{"className":7614,"style":160},[72],[56,7616,174],{"className":7617},[173],[56,7619,1086],{"className":7620,"style":1085},[77,78],[56,7622,447],{"className":7623},[446],[56,7625],{"className":7626,"style":346},[187],[56,7628,1104],{"className":7629},[77,78],[56,7631,447],{"className":7632},[446],[56,7634],{"className":7635,"style":346},[187],[56,7637,6865],{"className":7638},[77],[56,7640,183],{"className":7641},[182],[3350,7643,7644,7647,7650],{},[3368,7645,7646],{},"7",[3368,7648,7649],{},"ReLU, down-project, add residual",[3368,7651,7652],{},[56,7653,7655],{"className":7654},[59],[56,7656,7658],{"className":7657,"ariaHidden":64},[63],[56,7659,7661,7664,7667,7670,7673,7676,7679,7682,7685,7688],{"className":7660},[68],[56,7662],{"className":7663,"style":160},[72],[56,7665,174],{"className":7666},[173],[56,7668,1086],{"className":7669,"style":1085},[77,78],[56,7671,447],{"className":7672},[446],[56,7674],{"className":7675,"style":346},[187],[56,7677,1104],{"className":7678},[77,78],[56,7680,447],{"className":7681},[446],[56,7683],{"className":7684,"style":346},[187],[56,7686,6655],{"className":7687},[77],[56,7689,183],{"className":7690},[182],[11,7692,7693,7694,7742,7743,7782,7783,7798],{},"The only place the shape swells is the ",[56,7695,7697],{"className":7696},[59],[56,7698,7700],{"className":7699,"ariaHidden":64},[63],[56,7701,7703,7706,7709,7712,7715,7718,7721,7724,7727,7730,7733,7736,7739],{"className":7702},[68],[56,7704],{"className":7705,"style":160},[72],[56,7707,174],{"className":7708},[173],[56,7710,1086],{"className":7711,"style":1085},[77,78],[56,7713,447],{"className":7714},[446],[56,7716],{"className":7717,"style":346},[187],[56,7719,6691],{"className":7720},[77],[56,7722,447],{"className":7723},[446],[56,7725],{"className":7726,"style":346},[187],[56,7728,1104],{"className":7729},[77,78],[56,7731,447],{"className":7732},[446],[56,7734],{"className":7735,"style":346},[187],[56,7737,1104],{"className":7738},[77,78],[56,7740,183],{"className":7741},[182]," score tensor in step 3 and\nthe ",[56,7744,7746],{"className":7745},[59],[56,7747,7749],{"className":7748,"ariaHidden":64},[63],[56,7750,7752,7755,7758,7761,7764,7767,7770,7773,7776,7779],{"className":7751},[68],[56,7753],{"className":7754,"style":160},[72],[56,7756,174],{"className":7757},[173],[56,7759,1086],{"className":7760,"style":1085},[77,78],[56,7762,447],{"className":7763},[446],[56,7765],{"className":7766,"style":346},[187],[56,7768,1104],{"className":7769},[77,78],[56,7771,447],{"className":7772},[446],[56,7774],{"className":7775,"style":346},[187],[56,7777,6865],{"className":7778},[77],[56,7780,183],{"className":7781},[182]," FFN hidden in step 6 — the two costs, quadratic-in-",[56,7784,7786],{"className":7785},[59],[56,7787,7789],{"className":7788,"ariaHidden":64},[63],[56,7790,7792,7795],{"className":7791},[68],[56,7793],{"className":7794,"style":1100},[72],[56,7796,1104],{"className":7797},[77,78]," and\nwide-FFN, that the accounting section makes precise.",[4953,7800],{"hash":7801},"7cacdfcad2b10ed197c265b5330e0fbcf7c1f572e5e269b398b3def3e55b39f5",[4953,7803],{"hash":7804},"0e9b89062c79a5c37cdd4f177fc8bd439a35bcf110e9a6cfe596ef67b45c56b9",[83,7806,7808],{"id":7807},"one-decoder-layer","One decoder layer",[11,7810,7811,7812,7815],{},"A decoder layer has ",[21,7813,7814],{},"three"," wrapped sublayers. It must generate one token at a\ntime without access to tokens it has not yet produced, and it must read the\nencoder. Two additions handle these requirements.",[6011,7817,7818,8009],{},[6014,7819,7820,7823,7824,7905,7906,7942,7943,7958,7959,7962,7963,7980,7981,2042],{},[51,7821,7822],{},"Masked self-attention."," Before the softmax, the decoder sets the score\n",[56,7825,7827],{"className":7826},[59],[56,7828,7830,7892],{"className":7829,"ariaHidden":64},[63],[56,7831,7833,7836,7883,7886,7889],{"className":7832},[68],[56,7834],{"className":7835,"style":6140},[72],[56,7837,7839,7843],{"className":7838},[77],[56,7840,7842],{"className":7841,"style":6147},[77,78],"S",[56,7844,7846],{"className":7845},[236],[56,7847,7849,7875],{"className":7848},[240,241],[56,7850,7852,7872],{"className":7851},[245],[56,7853,7856],{"className":7854,"style":7855},[249],"height:0.3117em;",[56,7857,7858,7861],{"style":6164},[56,7859],{"className":7860,"style":258},[257],[56,7862,7864],{"className":7863},[262,263,264,265],[56,7865,7867],{"className":7866},[77,265],[56,7868,7871],{"className":7869,"style":7870},[77,78,265],"margin-right:0.0572em;","ij",[56,7873,273],{"className":7874},[272],[56,7876,7878],{"className":7877},[245],[56,7879,7881],{"className":7880,"style":6189},[249],[56,7882],{},[56,7884],{"className":7885,"style":188},[187],[56,7887,193],{"className":7888},[192],[56,7890],{"className":7891,"style":188},[187],[56,7893,7895,7898,7901],{"className":7894},[68],[56,7896],{"className":7897,"style":3453},[72],[56,7899,2742],{"className":7900},[77],[56,7902,7904],{"className":7903},[77],"∞"," for every ",[56,7907,7909],{"className":7908},[59],[56,7910,7912,7933],{"className":7911,"ariaHidden":64},[63],[56,7913,7915,7919,7923,7926,7930],{"className":7914},[68],[56,7916],{"className":7917,"style":7918},[72],"height:0.854em;vertical-align:-0.1944em;",[56,7920,7922],{"className":7921,"style":7870},[77,78],"j",[56,7924],{"className":7925,"style":188},[187],[56,7927,7929],{"className":7928},[192],">",[56,7931],{"className":7932,"style":188},[187],[56,7934,7936,7939],{"className":7935},[68],[56,7937],{"className":7938,"style":5868},[72],[56,7940,5097],{"className":7941},[77,78],", forbidding position ",[56,7944,7946],{"className":7945},[59],[56,7947,7949],{"className":7948,"ariaHidden":64},[63],[56,7950,7952,7955],{"className":7951},[68],[56,7953],{"className":7954,"style":5868},[72],[56,7956,5097],{"className":7957},[77,78]," from attending\nto any later position. Generation stays ",[51,7960,7961],{},"causal",": token ",[56,7964,7966],{"className":7965},[59],[56,7967,7969],{"className":7968,"ariaHidden":64},[63],[56,7970,7972,7976],{"className":7971},[68],[56,7973],{"className":7974,"style":7975},[72],"height:0.6151em;",[56,7977,7979],{"className":7978},[77,78],"t"," depends only on\ntokens ",[56,7982,7984],{"className":7983},[59],[56,7985,7987,8000],{"className":7986,"ariaHidden":64},[63],[56,7988,7990,7993,7997],{"className":7989},[68],[56,7991],{"className":7992,"style":2199},[72],[56,7994,7996],{"className":7995},[192],"\u003C",[56,7998],{"className":7999,"style":188},[187],[56,8001,8003,8006],{"className":8002},[68],[56,8004],{"className":8005,"style":7975},[72],[56,8007,7979],{"className":8008},[77,78],[6014,8010,8011,8014,8015],{},[51,8012,8013],{},"Cross-attention."," A middle sublayer draws its queries from the decoder\nstate but its keys and values from the encoder's output. This is the channel\nthrough which a generated token reads the entire source sequence; in\ntranslation it is how each output word reads the sentence being translated.",[35,8016,8017],{},[15,8018,7193],{"href":8019,"ariaDescribedBy":8020,"dataFootnoteRef":6,"id":8021},"#user-content-fn-chollet-decoder",[41],"user-content-fnref-chollet-decoder",[3344,8023,8024,8040],{},[3347,8025,8026],{},[3350,8027,8028,8031,8034,8037],{},[3353,8029,8030],{},"Sublayer",[3353,8032,8033],{},"Queries from",[3353,8035,8036],{},"Keys \u002F values from",[3353,8038,8039],{},"Mask",[3363,8041,8042,8055,8068],{},[3350,8043,8044,8047,8050,8052],{},[3368,8045,8046],{},"Masked self-attention",[3368,8048,8049],{},"decoder",[3368,8051,8049],{},[3368,8053,8054],{},"causal (lower-triangular)",[3350,8056,8057,8060,8062,8065],{},[3368,8058,8059],{},"Cross-attention",[3368,8061,8049],{},[3368,8063,8064],{},"encoder output",[3368,8066,8067],{},"none",[3350,8069,8070,8073,8076,8078],{},[3368,8071,8072],{},"Feed-forward",[3368,8074,8075],{},"—",[3368,8077,8075],{},[3368,8079,8075],{},[83,8081,8083],{"id":8082},"the-full-encoderdecoder","The full encoder–decoder",[11,8085,8086,8087,8102,8103,8118,8119,8122],{},"The complete Transformer stacks ",[56,8088,8090],{"className":8089},[59],[56,8091,8093],{"className":8092,"ariaHidden":64},[63],[56,8094,8096,8099],{"className":8095},[68],[56,8097],{"className":8098,"style":73},[72],[56,8100,80],{"className":8101,"style":79},[77,78]," encoder layers and ",[56,8104,8106],{"className":8105},[59],[56,8107,8109],{"className":8108,"ariaHidden":64},[63],[56,8110,8112,8115],{"className":8111},[68],[56,8113],{"className":8114,"style":73},[72],[56,8116,80],{"className":8117,"style":79},[77,78]," decoder layers, feeds\nboth stacks token embeddings plus positional encodings, and routes the encoder's\nfinal output into the cross-attention sublayer of ",[21,8120,8121],{},"every"," decoder layer. A linear\nprojection and softmax convert the decoder's top state into a distribution over\nthe vocabulary.",[4953,8124],{"hash":8125},"f15e98a0903dca7a539173f9fdedc5ae5795eb2cef9a9c789da04c8bce4ac7e7",[11,8127,8128],{},"The asymmetry is the whole point. The encoder reads bidirectionally because it\nsees the input all at once; the decoder reads causally because it produces the\noutput left to right. Cross-attention is the only place the two streams meet.",[83,8130,8132],{"id":8131},"causal-masking-in-detail","Causal masking in detail",[11,8134,8135,8136,8207,8208,8282,8283,3187,8317,8282,8393,8426],{},"Masking is implemented additively, before the softmax. Define a mask matrix\n",[56,8137,8139],{"className":8138},[59],[56,8140,8142,8162],{"className":8141,"ariaHidden":64},[63],[56,8143,8145,8149,8153,8156,8159],{"className":8144},[68],[56,8146],{"className":8147,"style":8148},[72],"height:0.7224em;vertical-align:-0.0391em;",[56,8150,8152],{"className":8151,"style":79},[77,78],"M",[56,8154],{"className":8155,"style":188},[187],[56,8157,501],{"className":8158},[192],[56,8160],{"className":8161,"style":188},[187],[56,8163,8165,8169],{"className":8164},[68],[56,8166],{"className":8167,"style":8168},[72],"height:0.7713em;",[56,8170,8172,8175],{"className":8171},[77],[56,8173,519],{"className":8174},[77,518],[56,8176,8178],{"className":8177},[236],[56,8179,8181],{"className":8180},[240],[56,8182,8184],{"className":8183},[245],[56,8185,8187],{"className":8186,"style":8168},[249],[56,8188,8189,8192],{"style":2239},[56,8190],{"className":8191,"style":258},[257],[56,8193,8195],{"className":8194},[262,263,264,265],[56,8196,8198,8201,8204],{"className":8197},[77,265],[56,8199,1104],{"className":8200},[77,78,265],[56,8202,552],{"className":8203},[290,265],[56,8205,1104],{"className":8206},[77,78,265]," with ",[56,8209,8211],{"className":8210},[59],[56,8212,8214,8273],{"className":8213,"ariaHidden":64},[63],[56,8215,8217,8220,8264,8267,8270],{"className":8216},[68],[56,8218],{"className":8219,"style":6140},[72],[56,8221,8223,8226],{"className":8222},[77],[56,8224,8152],{"className":8225,"style":79},[77,78],[56,8227,8229],{"className":8228},[236],[56,8230,8232,8256],{"className":8231},[240,241],[56,8233,8235,8253],{"className":8234},[245],[56,8236,8238],{"className":8237,"style":7855},[249],[56,8239,8241,8244],{"style":8240},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[56,8242],{"className":8243,"style":258},[257],[56,8245,8247],{"className":8246},[262,263,264,265],[56,8248,8250],{"className":8249},[77,265],[56,8251,7871],{"className":8252,"style":7870},[77,78,265],[56,8254,273],{"className":8255},[272],[56,8257,8259],{"className":8258},[245],[56,8260,8262],{"className":8261,"style":6189},[249],[56,8263],{},[56,8265],{"className":8266,"style":188},[187],[56,8268,193],{"className":8269},[192],[56,8271],{"className":8272,"style":188},[187],[56,8274,8276,8279],{"className":8275},[68],[56,8277],{"className":8278,"style":138},[72],[56,8280,3203],{"className":8281},[77]," for ",[56,8284,8286],{"className":8285},[59],[56,8287,8289,8308],{"className":8288,"ariaHidden":64},[63],[56,8290,8292,8295,8298,8301,8305],{"className":8291},[68],[56,8293],{"className":8294,"style":7918},[72],[56,8296,7922],{"className":8297,"style":7870},[77,78],[56,8299],{"className":8300,"style":188},[187],[56,8302,8304],{"className":8303},[192],"≤",[56,8306],{"className":8307,"style":188},[187],[56,8309,8311,8314],{"className":8310},[68],[56,8312],{"className":8313,"style":5868},[72],[56,8315,5097],{"className":8316},[77,78],[56,8318,8320],{"className":8319},[59],[56,8321,8323,8381],{"className":8322,"ariaHidden":64},[63],[56,8324,8326,8329,8372,8375,8378],{"className":8325},[68],[56,8327],{"className":8328,"style":6140},[72],[56,8330,8332,8335],{"className":8331},[77],[56,8333,8152],{"className":8334,"style":79},[77,78],[56,8336,8338],{"className":8337},[236],[56,8339,8341,8364],{"className":8340},[240,241],[56,8342,8344,8361],{"className":8343},[245],[56,8345,8347],{"className":8346,"style":7855},[249],[56,8348,8349,8352],{"style":8240},[56,8350],{"className":8351,"style":258},[257],[56,8353,8355],{"className":8354},[262,263,264,265],[56,8356,8358],{"className":8357},[77,265],[56,8359,7871],{"className":8360,"style":7870},[77,78,265],[56,8362,273],{"className":8363},[272],[56,8365,8367],{"className":8366},[245],[56,8368,8370],{"className":8369,"style":6189},[249],[56,8371],{},[56,8373],{"className":8374,"style":188},[187],[56,8376,193],{"className":8377},[192],[56,8379],{"className":8380,"style":188},[187],[56,8382,8384,8387,8390],{"className":8383},[68],[56,8385],{"className":8386,"style":3453},[72],[56,8388,2742],{"className":8389},[77],[56,8391,7904],{"className":8392},[77],[56,8394,8396],{"className":8395},[59],[56,8397,8399,8417],{"className":8398,"ariaHidden":64},[63],[56,8400,8402,8405,8408,8411,8414],{"className":8401},[68],[56,8403],{"className":8404,"style":7918},[72],[56,8406,7922],{"className":8407,"style":7870},[77,78],[56,8409],{"className":8410,"style":188},[187],[56,8412,7929],{"className":8413},[192],[56,8415],{"className":8416,"style":188},[187],[56,8418,8420,8423],{"className":8419},[68],[56,8421],{"className":8422,"style":5868},[72],[56,8424,5097],{"className":8425},[77,78],", and add it to the raw scores:",[56,8428,8430],{"className":8429},[147],[56,8431,8433],{"className":8432},[59],[56,8434,8436,8455,8743,8771],{"className":8435,"ariaHidden":64},[63],[56,8437,8439,8442,8446,8449,8452],{"className":8438},[68],[56,8440],{"className":8441,"style":73},[72],[56,8443,8445],{"className":8444},[77,78],"A",[56,8447],{"className":8448,"style":188},[187],[56,8450,193],{"className":8451},[192],[56,8453],{"className":8454,"style":188},[187],[56,8456,8458,8462,8469,8472,8475,8679,8682,8685,8688,8691,8734,8737,8740],{"className":8457},[68],[56,8459],{"className":8460,"style":8461},[72],"height:2.4761em;vertical-align:-0.95em;",[56,8463,8465],{"className":8464},[164],[56,8466,8468],{"className":8467},[77,168],"softmax",[56,8470],{"className":8471,"style":3394},[187],[56,8473],{"className":8474,"style":346},[187],[56,8476,8478,8484,8661,8664,8667,8670,8673],{"className":8477},[206],[56,8479,8481],{"className":8480,"style":211},[173,210],[56,8482,174],{"className":8483},[5250,264],[56,8485,8487,8490,8658],{"className":8486},[77],[56,8488],{"className":8489},[173,2315],[56,8491,8493],{"className":8492},[2319],[56,8494,8496,8650],{"className":8495},[240,241],[56,8497,8499,8647],{"className":8498},[245],[56,8500,8503,8599,8607],{"className":8501,"style":8502},[249],"height:1.5261em;",[56,8504,8506,8509],{"style":8505},"top:-2.2528em;",[56,8507],{"className":8508,"style":1182},[257],[56,8510,8512],{"className":8511},[77],[56,8513,8515],{"className":8514},[77,2879],[56,8516,8518,8590],{"className":8517},[240,241],[56,8519,8521,8587],{"className":8520},[245],[56,8522,8525,8574],{"className":8523,"style":8524},[249],"height:0.8572em;",[56,8526,8528,8531],{"className":8527,"style":1198},[1217],[56,8529],{"className":8530,"style":1182},[257],[56,8532,8534],{"className":8533,"style":2899},[77],[56,8535,8537,8540],{"className":8536},[77],[56,8538,548],{"className":8539},[77,78],[56,8541,8543],{"className":8542},[236],[56,8544,8546,8566],{"className":8545},[240,241],[56,8547,8549,8563],{"className":8548},[245],[56,8550,8552],{"className":8551,"style":789},[249],[56,8553,8554,8557],{"style":316},[56,8555],{"className":8556,"style":258},[257],[56,8558,8560],{"className":8559},[262,263,264,265],[56,8561,2414],{"className":8562,"style":2413},[77,78,265],[56,8564,273],{"className":8565},[272],[56,8567,8569],{"className":8568},[245],[56,8570,8572],{"className":8571,"style":280},[249],[56,8573],{},[56,8575,8577,8580],{"style":8576},"top:-2.8172em;",[56,8578],{"className":8579,"style":1182},[257],[56,8581,8583],{"className":8582,"style":2953},[1462],[1233,8584,8585],{"xmlns":1235,"width":1236,"height":2956,"viewBox":2957,"preserveAspectRatio":1239},[1241,8586],{"d":2960},[56,8588,273],{"className":8589},[272],[56,8591,8593],{"className":8592},[245],[56,8594,8597],{"className":8595,"style":8596},[249],"height:0.1828em;",[56,8598],{},[56,8600,8601,8604],{"style":2344},[56,8602],{"className":8603,"style":1182},[257],[56,8605],{"className":8606,"style":2352},[2351],[56,8608,8609,8612],{"style":2355},[56,8610],{"className":8611,"style":1182},[257],[56,8613,8615,8618],{"className":8614},[77],[56,8616,7099],{"className":8617},[77,78],[56,8619,8621,8624],{"className":8620},[77],[56,8622,7110],{"className":8623,"style":7109},[77,78],[56,8625,8627],{"className":8626},[236],[56,8628,8630],{"className":8629},[240],[56,8631,8633],{"className":8632},[245],[56,8634,8636],{"className":8635,"style":2218},[249],[56,8637,8638,8641],{"style":2239},[56,8639],{"className":8640,"style":258},[257],[56,8642,8644],{"className":8643},[262,263,264,265],[56,8645,7242],{"className":8646},[77,265],[56,8648,273],{"className":8649},[272],[56,8651,8653],{"className":8652},[245],[56,8654,8656],{"className":8655,"style":3013},[249],[56,8657],{},[56,8659],{"className":8660},[182,2315],[56,8662],{"className":8663,"style":286},[187],[56,8665,291],{"className":8666},[290],[56,8668],{"className":8669,"style":286},[187],[56,8671,8152],{"className":8672,"style":79},[77,78],[56,8674,8676],{"className":8675,"style":211},[182,210],[56,8677,183],{"className":8678},[5250,264],[56,8680],{"className":8681,"style":346},[187],[56,8683,447],{"className":8684},[446],[56,8686],{"className":8687,"style":451},[187],[56,8689],{"className":8690,"style":346},[187],[56,8692,8694,8697],{"className":8693},[77],[56,8695,8445],{"className":8696},[77,78],[56,8698,8700],{"className":8699},[236],[56,8701,8703,8726],{"className":8702},[240,241],[56,8704,8706,8723],{"className":8705},[245],[56,8707,8709],{"className":8708,"style":7855},[249],[56,8710,8711,8714],{"style":316},[56,8712],{"className":8713,"style":258},[257],[56,8715,8717],{"className":8716},[262,263,264,265],[56,8718,8720],{"className":8719},[77,265],[56,8721,7871],{"className":8722,"style":7870},[77,78,265],[56,8724,273],{"className":8725},[272],[56,8727,8729],{"className":8728},[245],[56,8730,8732],{"className":8731,"style":6189},[249],[56,8733],{},[56,8735],{"className":8736,"style":188},[187],[56,8738,193],{"className":8739},[192],[56,8741],{"className":8742,"style":188},[187],[56,8744,8746,8749,8752,8759,8762,8765,8768],{"className":8745},[68],[56,8747],{"className":8748,"style":106},[72],[56,8750,3203],{"className":8751},[77],[56,8753,8755],{"className":8754},[77,590],[56,8756,8758],{"className":8757},[77]," for all ",[56,8760,7922],{"className":8761,"style":7870},[77,78],[56,8763],{"className":8764,"style":188},[187],[56,8766,7929],{"className":8767},[192],[56,8769],{"className":8770,"style":188},[187],[56,8772,8774,8777,8780],{"className":8773},[68],[56,8775],{"className":8776,"style":5868},[72],[56,8778,5097],{"className":8779},[77,78],[56,8781,2042],{"className":8782},[77],[11,8784,5793,8785,8803,8804,8870,8871,8874,8875,4935,8890,8905,8906,8921,8922,2042],{},[56,8786,8788],{"className":8787},[59],[56,8789,8791],{"className":8790,"ariaHidden":64},[63],[56,8792,8794,8797,8800],{"className":8793},[68],[56,8795],{"className":8796,"style":3453},[72],[56,8798,2742],{"className":8799},[77],[56,8801,7904],{"className":8802},[77]," entries become ",[56,8805,8807],{"className":8806},[59],[56,8808,8810,8861],{"className":8809,"ariaHidden":64},[63],[56,8811,8813,8816,8852,8855,8858],{"className":8812},[68],[56,8814],{"className":8815,"style":8168},[72],[56,8817,8819,8823],{"className":8818},[77],[56,8820,8822],{"className":8821},[77,78],"e",[56,8824,8826],{"className":8825},[236],[56,8827,8829],{"className":8828},[240],[56,8830,8832],{"className":8831},[245],[56,8833,8835],{"className":8834,"style":8168},[249],[56,8836,8837,8840],{"style":2239},[56,8838],{"className":8839,"style":258},[257],[56,8841,8843],{"className":8842},[262,263,264,265],[56,8844,8846,8849],{"className":8845},[77,265],[56,8847,2742],{"className":8848},[77,265],[56,8850,7904],{"className":8851},[77,265],[56,8853],{"className":8854,"style":188},[187],[56,8856,193],{"className":8857},[192],[56,8859],{"className":8860,"style":188},[187],[56,8862,8864,8867],{"className":8863},[68],[56,8865],{"className":8866,"style":138},[72],[56,8868,3203],{"className":8869},[77]," after exponentiation, so the\nsoftmax renormalizes over only the allowed (lower-triangular) positions. The\nresult is ",[51,8872,8873],{},"row-causal",": row ",[56,8876,8878],{"className":8877},[59],[56,8879,8881],{"className":8880,"ariaHidden":64},[63],[56,8882,8884,8887],{"className":8883},[68],[56,8885],{"className":8886,"style":5868},[72],[56,8888,5097],{"className":8889},[77,78],[56,8891,8893],{"className":8892},[59],[56,8894,8896],{"className":8895,"ariaHidden":64},[63],[56,8897,8899,8902],{"className":8898},[68],[56,8900],{"className":8901,"style":73},[72],[56,8903,8445],{"className":8904},[77,78]," has support only on columns ",[56,8907,8909],{"className":8908},[59],[56,8910,8912],{"className":8911,"ariaHidden":64},[63],[56,8913,8915,8918],{"className":8914},[68],[56,8916],{"className":8917,"style":138},[72],[56,8919,43],{"className":8920},[77]," through\n",[56,8923,8925],{"className":8924},[59],[56,8926,8928],{"className":8927,"ariaHidden":64},[63],[56,8929,8931,8934],{"className":8930},[68],[56,8932],{"className":8933,"style":5868},[72],[56,8935,5097],{"className":8936},[77,78],[45,8938,8939],{"type":3519},[11,8940,8941,8944,8945,9070,9071,9086,9087,9207,9208,9427],{},[51,8942,8943],{},"Theorem (Autoregressive factorization)."," With causal masking, the decoder\ncomputes ",[56,8946,8948],{"className":8947},[59],[56,8949,8951,9014],{"className":8950,"ariaHidden":64},[63],[56,8952,8954,8957,8960,8963,9004,9007,9011],{"className":8953},[68],[56,8955],{"className":8956,"style":160},[72],[56,8958,11],{"className":8959},[77,78],[56,8961,174],{"className":8962},[173],[56,8964,8966,8969],{"className":8965},[77],[56,8967,178],{"className":8968},[77,78],[56,8970,8972],{"className":8971},[236],[56,8973,8975,8996],{"className":8974},[240,241],[56,8976,8978,8993],{"className":8977},[245],[56,8979,8982],{"className":8980,"style":8981},[249],"height:0.2806em;",[56,8983,8984,8987],{"style":316},[56,8985],{"className":8986,"style":258},[257],[56,8988,8990],{"className":8989},[262,263,264,265],[56,8991,7979],{"className":8992},[77,78,265],[56,8994,273],{"className":8995},[272],[56,8997,8999],{"className":8998},[245],[56,9000,9002],{"className":9001,"style":280},[249],[56,9003],{},[56,9005],{"className":9006,"style":188},[187],[56,9008,9010],{"className":9009},[192],"∣",[56,9012],{"className":9013,"style":188},[187],[56,9015,9017,9020,9067],{"className":9016},[68],[56,9018],{"className":9019,"style":160},[72],[56,9021,9023,9026],{"className":9022},[77],[56,9024,178],{"className":9025},[77,78],[56,9027,9029],{"className":9028},[236],[56,9030,9032,9058],{"className":9031},[240,241],[56,9033,9035,9055],{"className":9034},[245],[56,9036,9038],{"className":9037,"style":8981},[249],[56,9039,9040,9043],{"style":316},[56,9041],{"className":9042,"style":258},[257],[56,9044,9046],{"className":9045},[262,263,264,265],[56,9047,9049,9052],{"className":9048},[77,265],[56,9050,7996],{"className":9051},[192,265],[56,9053,7979],{"className":9054},[77,78,265],[56,9056,273],{"className":9057},[272],[56,9059,9061],{"className":9060},[245],[56,9062,9065],{"className":9063,"style":9064},[249],"height:0.1774em;",[56,9066],{},[56,9068,183],{"className":9069},[182]," at every position ",[56,9072,9074],{"className":9073},[59],[56,9075,9077],{"className":9076,"ariaHidden":64},[63],[56,9078,9080,9083],{"className":9079},[68],[56,9081],{"className":9082,"style":7975},[72],[56,9084,7979],{"className":9085},[77,78]," using only inputs ",[56,9088,9090],{"className":9089},[59],[56,9091,9093],{"className":9092,"ariaHidden":64},[63],[56,9094,9096,9100,9140,9143,9146,9149,9152,9155,9158],{"className":9095},[68],[56,9097],{"className":9098,"style":9099},[72],"height:0.6389em;vertical-align:-0.2083em;",[56,9101,9103,9106],{"className":9102},[77],[56,9104,178],{"className":9105},[77,78],[56,9107,9109],{"className":9108},[236],[56,9110,9112,9132],{"className":9111},[240,241],[56,9113,9115,9129],{"className":9114},[245],[56,9116,9118],{"className":9117,"style":250},[249],[56,9119,9120,9123],{"style":316},[56,9121],{"className":9122,"style":258},[257],[56,9124,9126],{"className":9125},[262,263,264,265],[56,9127,43],{"className":9128},[77,265],[56,9130,273],{"className":9131},[272],[56,9133,9135],{"className":9134},[245],[56,9136,9138],{"className":9137,"style":280},[249],[56,9139],{},[56,9141,447],{"className":9142},[446],[56,9144],{"className":9145,"style":346},[187],[56,9147,5045],{"className":9148},[206],[56,9150],{"className":9151,"style":346},[187],[56,9153,447],{"className":9154},[446],[56,9156],{"className":9157,"style":346},[187],[56,9159,9161,9164],{"className":9160},[77],[56,9162,178],{"className":9163},[77,78],[56,9165,9167],{"className":9166},[236],[56,9168,9170,9199],{"className":9169},[240,241],[56,9171,9173,9196],{"className":9172},[245],[56,9174,9176],{"className":9175,"style":250},[249],[56,9177,9178,9181],{"style":316},[56,9179],{"className":9180,"style":258},[257],[56,9182,9184],{"className":9183},[262,263,264,265],[56,9185,9187,9190,9193],{"className":9186},[77,265],[56,9188,7979],{"className":9189},[77,78,265],[56,9191,2742],{"className":9192},[290,265],[56,9194,43],{"className":9195},[77,265],[56,9197,273],{"className":9198},[272],[56,9200,9202],{"className":9201},[245],[56,9203,9205],{"className":9204,"style":3855},[249],[56,9206],{},", so a single forward pass yields every factor of the chain rule\n",[56,9209,9211],{"className":9210},[59],[56,9212,9214,9241,9372],{"className":9213,"ariaHidden":64},[63],[56,9215,9217,9220,9223,9226,9229,9232,9235,9238],{"className":9216},[68],[56,9218],{"className":9219,"style":160},[72],[56,9221,11],{"className":9222},[77,78],[56,9224,174],{"className":9225},[173],[56,9227,178],{"className":9228},[77,78],[56,9230,183],{"className":9231},[182],[56,9233],{"className":9234,"style":188},[187],[56,9236,193],{"className":9237},[192],[56,9239],{"className":9240,"style":188},[187],[56,9242,9244,9248,9314,9317,9320,9323,9363,9366,9369],{"className":9243},[68],[56,9245],{"className":9246,"style":9247},[72],"height:1.104em;vertical-align:-0.2997em;",[56,9249,9251,9255],{"className":9250},[164],[56,9252,9254],{"className":9253,"style":4472},[164,2432,4471],"∏",[56,9256,9258],{"className":9257},[236],[56,9259,9261,9306],{"className":9260},[240,241],[56,9262,9264,9303],{"className":9263},[245],[56,9265,9268,9288],{"className":9266,"style":9267},[249],"height:0.8043em;",[56,9269,9270,9273],{"style":4488},[56,9271],{"className":9272,"style":258},[257],[56,9274,9276],{"className":9275},[262,263,264,265],[56,9277,9279,9282,9285],{"className":9278},[77,265],[56,9280,7979],{"className":9281},[77,78,265],[56,9283,193],{"className":9284},[192,265],[56,9286,43],{"className":9287},[77,265],[56,9289,9291,9294],{"style":9290},"top:-3.2029em;margin-right:0.05em;",[56,9292],{"className":9293,"style":258},[257],[56,9295,9297],{"className":9296},[262,263,264,265],[56,9298,9300],{"className":9299},[77,265],[56,9301,1104],{"className":9302},[77,78,265],[56,9304,273],{"className":9305},[272],[56,9307,9309],{"className":9308},[245],[56,9310,9312],{"className":9311,"style":4510},[249],[56,9313],{},[56,9315],{"className":9316,"style":346},[187],[56,9318,11],{"className":9319},[77,78],[56,9321,174],{"className":9322},[173],[56,9324,9326,9329],{"className":9325},[77],[56,9327,178],{"className":9328},[77,78],[56,9330,9332],{"className":9331},[236],[56,9333,9335,9355],{"className":9334},[240,241],[56,9336,9338,9352],{"className":9337},[245],[56,9339,9341],{"className":9340,"style":8981},[249],[56,9342,9343,9346],{"style":316},[56,9344],{"className":9345,"style":258},[257],[56,9347,9349],{"className":9348},[262,263,264,265],[56,9350,7979],{"className":9351},[77,78,265],[56,9353,273],{"className":9354},[272],[56,9356,9358],{"className":9357},[245],[56,9359,9361],{"className":9360,"style":280},[249],[56,9362],{},[56,9364],{"className":9365,"style":188},[187],[56,9367,9010],{"className":9368},[192],[56,9370],{"className":9371,"style":188},[187],[56,9373,9375,9378,9424],{"className":9374},[68],[56,9376],{"className":9377,"style":160},[72],[56,9379,9381,9384],{"className":9380},[77],[56,9382,178],{"className":9383},[77,78],[56,9385,9387],{"className":9386},[236],[56,9388,9390,9416],{"className":9389},[240,241],[56,9391,9393,9413],{"className":9392},[245],[56,9394,9396],{"className":9395,"style":8981},[249],[56,9397,9398,9401],{"style":316},[56,9399],{"className":9400,"style":258},[257],[56,9402,9404],{"className":9403},[262,263,264,265],[56,9405,9407,9410],{"className":9406},[77,265],[56,9408,7996],{"className":9409},[192,265],[56,9411,7979],{"className":9412},[77,78,265],[56,9414,273],{"className":9415},[272],[56,9417,9419],{"className":9418},[245],[56,9420,9422],{"className":9421,"style":9064},[249],[56,9423],{},[56,9425,183],{"className":9426},[182]," in parallel.",[45,9429,9430],{"type":4048},[11,9431,9432,9434,9435,9450,9451,9466,9467,9500,9501,9516,9517,9532,9533,9561,9562,9596,9597,9656,9657,9779,9780,9795,9796],{},[51,9433,4053],{}," Each decoder output at position ",[56,9436,9438],{"className":9437},[59],[56,9439,9441],{"className":9440,"ariaHidden":64},[63],[56,9442,9444,9447],{"className":9443},[68],[56,9445],{"className":9446,"style":7975},[72],[56,9448,7979],{"className":9449},[77,78]," is a function of the masked\nself-attention output at ",[56,9452,9454],{"className":9453},[59],[56,9455,9457],{"className":9456,"ariaHidden":64},[63],[56,9458,9460,9463],{"className":9459},[68],[56,9461],{"className":9462,"style":7975},[72],[56,9464,7979],{"className":9465},[77,78],", whose attention row has zero weight on all\n",[56,9468,9470],{"className":9469},[59],[56,9471,9473,9491],{"className":9472,"ariaHidden":64},[63],[56,9474,9476,9479,9482,9485,9488],{"className":9475},[68],[56,9477],{"className":9478,"style":7918},[72],[56,9480,7922],{"className":9481,"style":7870},[77,78],[56,9483],{"className":9484,"style":188},[187],[56,9486,7929],{"className":9487},[192],[56,9489],{"className":9490,"style":188},[187],[56,9492,9494,9497],{"className":9493},[68],[56,9495],{"className":9496,"style":7975},[72],[56,9498,7979],{"className":9499},[77,78]," by construction of ",[56,9502,9504],{"className":9503},[59],[56,9505,9507],{"className":9506,"ariaHidden":64},[63],[56,9508,9510,9513],{"className":9509},[68],[56,9511],{"className":9512,"style":73},[72],[56,9514,8152],{"className":9515,"style":79},[77,78],". By induction over the stacked layers, every\nintermediate representation at position ",[56,9518,9520],{"className":9519},[59],[56,9521,9523],{"className":9522,"ariaHidden":64},[63],[56,9524,9526,9529],{"className":9525},[68],[56,9527],{"className":9528,"style":7975},[72],[56,9530,7979],{"className":9531},[77,78]," depends only on positions ",[56,9534,9536],{"className":9535},[59],[56,9537,9539,9552],{"className":9538,"ariaHidden":64},[63],[56,9540,9542,9546,9549],{"className":9541},[68],[56,9543],{"className":9544,"style":9545},[72],"height:0.7719em;vertical-align:-0.136em;",[56,9547,8304],{"className":9548},[192],[56,9550],{"className":9551,"style":188},[187],[56,9553,9555,9558],{"className":9554},[68],[56,9556],{"className":9557,"style":7975},[72],[56,9559,7979],{"className":9560},[77,78],";\nthe read-out head at ",[56,9563,9565],{"className":9564},[59],[56,9566,9568,9587],{"className":9567,"ariaHidden":64},[63],[56,9569,9571,9575,9578,9581,9584],{"className":9570},[68],[56,9572],{"className":9573,"style":9574},[72],"height:0.6984em;vertical-align:-0.0833em;",[56,9576,7979],{"className":9577},[77,78],[56,9579],{"className":9580,"style":286},[187],[56,9582,2742],{"className":9583},[290],[56,9585],{"className":9586,"style":286},[187],[56,9588,9590,9593],{"className":9589},[68],[56,9591],{"className":9592,"style":138},[72],[56,9594,43],{"className":9595},[77]," therefore depends only on ",[56,9598,9600],{"className":9599},[59],[56,9601,9603],{"className":9602,"ariaHidden":64},[63],[56,9604,9606,9610],{"className":9605},[68],[56,9607],{"className":9608,"style":9609},[72],"height:0.6079em;vertical-align:-0.1774em;",[56,9611,9613,9616],{"className":9612},[77],[56,9614,178],{"className":9615},[77,78],[56,9617,9619],{"className":9618},[236],[56,9620,9622,9648],{"className":9621},[240,241],[56,9623,9625,9645],{"className":9624},[245],[56,9626,9628],{"className":9627,"style":8981},[249],[56,9629,9630,9633],{"style":316},[56,9631],{"className":9632,"style":258},[257],[56,9634,9636],{"className":9635},[262,263,264,265],[56,9637,9639,9642],{"className":9638},[77,265],[56,9640,7996],{"className":9641},[192,265],[56,9643,7979],{"className":9644},[77,78,265],[56,9646,273],{"className":9647},[272],[56,9649,9651],{"className":9650},[245],[56,9652,9654],{"className":9653,"style":9064},[249],[56,9655],{},", giving exactly\nthe conditional ",[56,9658,9660],{"className":9659},[59],[56,9661,9663,9724],{"className":9662,"ariaHidden":64},[63],[56,9664,9666,9669,9672,9675,9715,9718,9721],{"className":9665},[68],[56,9667],{"className":9668,"style":160},[72],[56,9670,11],{"className":9671},[77,78],[56,9673,174],{"className":9674},[173],[56,9676,9678,9681],{"className":9677},[77],[56,9679,178],{"className":9680},[77,78],[56,9682,9684],{"className":9683},[236],[56,9685,9687,9707],{"className":9686},[240,241],[56,9688,9690,9704],{"className":9689},[245],[56,9691,9693],{"className":9692,"style":8981},[249],[56,9694,9695,9698],{"style":316},[56,9696],{"className":9697,"style":258},[257],[56,9699,9701],{"className":9700},[262,263,264,265],[56,9702,7979],{"className":9703},[77,78,265],[56,9705,273],{"className":9706},[272],[56,9708,9710],{"className":9709},[245],[56,9711,9713],{"className":9712,"style":280},[249],[56,9714],{},[56,9716],{"className":9717,"style":188},[187],[56,9719,9010],{"className":9720},[192],[56,9722],{"className":9723,"style":188},[187],[56,9725,9727,9730,9776],{"className":9726},[68],[56,9728],{"className":9729,"style":160},[72],[56,9731,9733,9736],{"className":9732},[77],[56,9734,178],{"className":9735},[77,78],[56,9737,9739],{"className":9738},[236],[56,9740,9742,9768],{"className":9741},[240,241],[56,9743,9745,9765],{"className":9744},[245],[56,9746,9748],{"className":9747,"style":8981},[249],[56,9749,9750,9753],{"style":316},[56,9751],{"className":9752,"style":258},[257],[56,9754,9756],{"className":9755},[262,263,264,265],[56,9757,9759,9762],{"className":9758},[77,265],[56,9760,7996],{"className":9761},[192,265],[56,9763,7979],{"className":9764},[77,78,265],[56,9766,273],{"className":9767},[272],[56,9769,9771],{"className":9770},[245],[56,9772,9774],{"className":9773,"style":9064},[249],[56,9775],{},[56,9777,183],{"className":9778},[182],". All ",[56,9781,9783],{"className":9782},[59],[56,9784,9786],{"className":9785,"ariaHidden":64},[63],[56,9787,9789,9792],{"className":9788},[68],[56,9790],{"className":9791,"style":1100},[72],[56,9793,1104],{"className":9794},[77,78]," positions are computed in one\npass because the dependencies are encoded in the mask, not in sequential\nevaluation. ",[56,9797,9799],{"className":9798},[59],[56,9800,9802],{"className":9801,"ariaHidden":64},[63],[56,9803,9805,9808],{"className":9804},[68],[56,9806],{"className":9807,"style":4918},[72],[56,9809,9811],{"className":9810},[4922,4923],[56,9812,4928],{"className":9813},[77,4927],[4953,9815],{"hash":9816},"0059ea8284efc4aadd7974cc24538e4d5f228170f7667a0b2dd57d4959a5a141",[9818,9819,9823],"pre",{"className":9820,"code":9821,"language":9822,"meta":6,"style":6},"language-algorithm shiki shiki-themes Vesper Light - Orange Boost (Quick Open Adjusted) vesper","caption: $\\textsc{MaskedSelfAttention}(X)$ — causal scaled dot-product attention\n$Q \\gets X W_Q$; $K \\gets X W_K$; $V \\gets X W_V$\n$S \\gets Q K^{T} \u002F \\sqrt{d_k}$ \u002F\u002F $n \\times n$ raw scores\nfor each $i, j$ with $j > i$ do\n  $S_{ij} \\gets -\\infty$ \u002F\u002F forbid attending to the future\nfor each row $i$ do\n  $A_{i} \\gets \\softmax(S_{i})$ \u002F\u002F mass only on $j \\le i$\nreturn $A V$ \u002F\u002F each row blends past values only\n","algorithm",[9824,9825,9826,9833,9839,9845,9851,9857,9863,9869],"code",{"__ignoreMap":6},[56,9827,9830],{"class":9828,"line":9829},"line",1,[56,9831,9832],{},"caption: $\\textsc{MaskedSelfAttention}(X)$ — causal scaled dot-product attention\n",[56,9834,9836],{"class":9828,"line":9835},2,[56,9837,9838],{},"$Q \\gets X W_Q$; $K \\gets X W_K$; $V \\gets X W_V$\n",[56,9840,9842],{"class":9828,"line":9841},3,[56,9843,9844],{},"$S \\gets Q K^{T} \u002F \\sqrt{d_k}$ \u002F\u002F $n \\times n$ raw scores\n",[56,9846,9848],{"class":9828,"line":9847},4,[56,9849,9850],{},"for each $i, j$ with $j > i$ do\n",[56,9852,9854],{"class":9828,"line":9853},5,[56,9855,9856],{},"  $S_{ij} \\gets -\\infty$ \u002F\u002F forbid attending to the future\n",[56,9858,9860],{"class":9828,"line":9859},6,[56,9861,9862],{},"for each row $i$ do\n",[56,9864,9866],{"class":9828,"line":9865},7,[56,9867,9868],{},"  $A_{i} \\gets \\softmax(S_{i})$ \u002F\u002F mass only on $j \\le i$\n",[56,9870,9872],{"class":9828,"line":9871},8,[56,9873,9874],{},"return $A V$ \u002F\u002F each row blends past values only\n",[83,9876,9878],{"id":9877},"the-three-families","The three families",[11,9880,9881],{},"The encoder and decoder were designed to work as a pair, but each half is a\ncomplete model on its own. Modern practice splits the architecture into three\nfamilies, distinguished by which stack they keep, how they mask attention, and\nwhat objective they train against.",[3344,9883,9884,9903],{},[3347,9885,9886],{},[3350,9887,9888,9891,9894,9897,9900],{},[3353,9889,9890],{},"Family",[3353,9892,9893],{},"Structure",[3353,9895,9896],{},"Attention masking",[3353,9898,9899],{},"Training objective",[3353,9901,9902],{},"Examples",[3363,9904,9905,9922,9938],{},[3350,9906,9907,9910,9913,9916,9919],{},[3368,9908,9909],{},"Encoder-only",[3368,9911,9912],{},"encoder stack, bidirectional",[3368,9914,9915],{},"none (full self-attention)",[3368,9917,9918],{},"masked language modeling (predict held-out tokens)",[3368,9920,9921],{},"BERT, RoBERTa",[3350,9923,9924,9927,9930,9932,9935],{},[3368,9925,9926],{},"Decoder-only",[3368,9928,9929],{},"decoder stack, no cross-attention",[3368,9931,8054],{},[3368,9933,9934],{},"autoregressive LM (next-token prediction)",[3368,9936,9937],{},"GPT, LLaMA",[3350,9939,9940,9943,9946,9949,9952],{},[3368,9941,9942],{},"Encoder–decoder",[3368,9944,9945],{},"both stacks, cross-attention",[3368,9947,9948],{},"encoder full, decoder causal",[3368,9950,9951],{},"seq2seq (conditional generation)",[3368,9953,9954],{},"original Transformer, T5",[11,9956,9957,9958,9961,9962,9965,9966,9969,9970,9973,9974,9977,9978,9981,9982],{},"The split follows directly from the masking. An ",[51,9959,9960],{},"encoder-only"," model sees the\nwhole sequence, so it is built for ",[21,9963,9964],{},"understanding"," (classification, retrieval,\ntoken tagging) and is trained by corrupting input tokens and reconstructing\nthem. A ",[51,9967,9968],{},"decoder-only"," model masks causally, so each position predicts the\nnext token, making it a pure ",[21,9971,9972],{},"generator","; this is the family that scaled into\nlarge language models. An ",[51,9975,9976],{},"encoder–decoder"," keeps both and is built for\n",[21,9979,9980],{},"transduction",": mapping one sequence to another, as in translation or\nsummarization.",[35,9983,9984],{},[15,9985,142],{"href":9986,"ariaDescribedBy":9987,"dataFootnoteRef":6,"id":9988},"#user-content-fn-chollet-families",[41],"user-content-fnref-chollet-families",[4953,9990],{"hash":9991},"b25d3e058486111736ec5a3f07ac94e34c428ecad378919f94f609c6203ee565",[83,9993,9995],{"id":9994},"the-residual-stream","The residual stream",[11,9997,9998,9999,10002,10003,10018,10019,10022,10023,10026],{},"A productive way to read the stack is as a ",[51,10000,10001],{},"residual stream",": a fixed-width\n",[56,10004,10006],{"className":10005},[59],[56,10007,10009],{"className":10008,"ariaHidden":64},[63],[56,10010,10012,10015],{"className":10011},[68],[56,10013],{"className":10014,"style":833},[72],[56,10016,548],{"className":10017},[77,78],"-dimensional bus running from the embeddings to the output head. Each sublayer\n",[21,10020,10021],{},"reads"," a normalized copy of the stream, computes an update, and ",[21,10024,10025],{},"writes"," that\nupdate back by addition. No sublayer overwrites the stream; they only accumulate\ninto it.",[56,10028,10030],{"className":10029},[147],[56,10031,10033],{"className":10032},[59],[56,10034,10036,10091,10155,10260,10443,10498],{"className":10035,"ariaHidden":64},[63],[56,10037,10039,10042,10082,10085,10088],{"className":10038},[68],[56,10040],{"className":10041,"style":3557},[72],[56,10043,10045,10048],{"className":10044},[77],[56,10046,3565],{"className":10047,"style":3564},[77,78],[56,10049,10051],{"className":10050},[236],[56,10052,10054,10074],{"className":10053},[240,241],[56,10055,10057,10071],{"className":10056},[245],[56,10058,10060],{"className":10059,"style":789},[249],[56,10061,10062,10065],{"style":3581},[56,10063],{"className":10064,"style":258},[257],[56,10066,10068],{"className":10067},[262,263,264,265],[56,10069,3701],{"className":10070},[77,265],[56,10072,273],{"className":10073},[272],[56,10075,10077],{"className":10076},[245],[56,10078,10080],{"className":10079,"style":280},[249],[56,10081],{},[56,10083],{"className":10084,"style":188},[187],[56,10086,193],{"className":10087},[192],[56,10089],{"className":10090,"style":188},[187],[56,10092,10094,10097,10146,10149,10152],{"className":10093},[68],[56,10095],{"className":10096,"style":4122},[72],[56,10098,10100,10103],{"className":10099},[77],[56,10101,3565],{"className":10102,"style":3564},[77,78],[56,10104,10106],{"className":10105},[236],[56,10107,10109,10138],{"className":10108},[240,241],[56,10110,10112,10135],{"className":10111},[245],[56,10113,10115],{"className":10114,"style":789},[249],[56,10116,10117,10120],{"style":3581},[56,10118],{"className":10119,"style":258},[257],[56,10121,10123],{"className":10122},[262,263,264,265],[56,10124,10126,10129,10132],{"className":10125},[77,265],[56,10127,3701],{"className":10128},[77,265],[56,10130,2742],{"className":10131},[290,265],[56,10133,43],{"className":10134},[77,265],[56,10136,273],{"className":10137},[272],[56,10139,10141],{"className":10140},[245],[56,10142,10144],{"className":10143,"style":3855},[249],[56,10145],{},[56,10147],{"className":10148,"style":286},[187],[56,10150,291],{"className":10151},[290],[56,10153],{"className":10154,"style":286},[187],[56,10156,10158,10161,10202,10205,10208,10211,10251,10254,10257],{"className":10157},[68],[56,10159],{"className":10160,"style":2058},[72],[56,10162,10164,10168],{"className":10163},[77],[56,10165,10167],{"className":10166},[77],"Δ",[56,10169,10171],{"className":10170},[236],[56,10172,10174,10194],{"className":10173},[240,241],[56,10175,10177,10191],{"className":10176},[245],[56,10178,10180],{"className":10179,"style":789},[249],[56,10181,10182,10185],{"style":316},[56,10183],{"className":10184,"style":258},[257],[56,10186,10188],{"className":10187},[262,263,264,265],[56,10189,3701],{"className":10190},[77,265],[56,10192,273],{"className":10193},[272],[56,10195,10197],{"className":10196},[245],[56,10198,10200],{"className":10199,"style":280},[249],[56,10201],{},[56,10203,447],{"className":10204},[446],[56,10206],{"className":10207,"style":451},[187],[56,10209],{"className":10210,"style":346},[187],[56,10212,10214,10217],{"className":10213},[77],[56,10215,10167],{"className":10216},[77],[56,10218,10220],{"className":10219},[236],[56,10221,10223,10243],{"className":10222},[240,241],[56,10224,10226,10240],{"className":10225},[245],[56,10227,10229],{"className":10228,"style":789},[249],[56,10230,10231,10234],{"style":316},[56,10232],{"className":10233,"style":258},[257],[56,10235,10237],{"className":10236},[262,263,264,265],[56,10238,3701],{"className":10239},[77,265],[56,10241,273],{"className":10242},[272],[56,10244,10246],{"className":10245},[245],[56,10247,10249],{"className":10248,"style":280},[249],[56,10250],{},[56,10252],{"className":10253,"style":188},[187],[56,10255,193],{"className":10256},[192],[56,10258],{"className":10259,"style":188},[187],[56,10261,10263,10266,10306,10309,10312,10382,10385,10388,10391,10394,10434,10437,10440],{"className":10262},[68],[56,10264],{"className":10265,"style":160},[72],[56,10267,10269,10272],{"className":10268},[77],[56,10270,111],{"className":10271,"style":110},[77,78],[56,10273,10275],{"className":10274},[236],[56,10276,10278,10298],{"className":10277},[240,241],[56,10279,10281,10295],{"className":10280},[245],[56,10282,10284],{"className":10283,"style":789},[249],[56,10285,10286,10289],{"style":3766},[56,10287],{"className":10288,"style":258},[257],[56,10290,10292],{"className":10291},[262,263,264,265],[56,10293,3701],{"className":10294},[77,265],[56,10296,273],{"className":10297},[272],[56,10299,10301],{"className":10300},[245],[56,10302,10304],{"className":10303,"style":280},[249],[56,10305],{},[56,10307],{"className":10308,"style":3394},[187],[56,10310],{"className":10311,"style":346},[187],[56,10313,10315,10318,10324,10327,10376,10379],{"className":10314},[206],[56,10316,174],{"className":10317,"style":211},[173,210],[56,10319,10321],{"className":10320},[164],[56,10322,2800],{"className":10323},[77,168],[56,10325,174],{"className":10326},[173],[56,10328,10330,10333],{"className":10329},[77],[56,10331,3565],{"className":10332,"style":3564},[77,78],[56,10334,10336],{"className":10335},[236],[56,10337,10339,10368],{"className":10338},[240,241],[56,10340,10342,10365],{"className":10341},[245],[56,10343,10345],{"className":10344,"style":789},[249],[56,10346,10347,10350],{"style":3581},[56,10348],{"className":10349,"style":258},[257],[56,10351,10353],{"className":10352},[262,263,264,265],[56,10354,10356,10359,10362],{"className":10355},[77,265],[56,10357,3701],{"className":10358},[77,265],[56,10360,2742],{"className":10361},[290,265],[56,10363,43],{"className":10364},[77,265],[56,10366,273],{"className":10367},[272],[56,10369,10371],{"className":10370},[245],[56,10372,10374],{"className":10373,"style":3855},[249],[56,10375],{},[56,10377,183],{"className":10378},[182],[56,10380,183],{"className":10381,"style":211},[182,210],[56,10383],{"className":10384,"style":346},[187],[56,10386,447],{"className":10387},[446],[56,10389],{"className":10390,"style":451},[187],[56,10392],{"className":10393,"style":346},[187],[56,10395,10397,10400],{"className":10396},[77],[56,10398,3565],{"className":10399,"style":3564},[77,78],[56,10401,10403],{"className":10402},[236],[56,10404,10406,10426],{"className":10405},[240,241],[56,10407,10409,10423],{"className":10408},[245],[56,10410,10412],{"className":10411,"style":3578},[249],[56,10413,10414,10417],{"style":3581},[56,10415],{"className":10416,"style":258},[257],[56,10418,10420],{"className":10419},[262,263,264,265],[56,10421,80],{"className":10422,"style":79},[77,78,265],[56,10424,273],{"className":10425},[272],[56,10427,10429],{"className":10428},[245],[56,10430,10432],{"className":10431,"style":280},[249],[56,10433],{},[56,10435],{"className":10436,"style":188},[187],[56,10438,193],{"className":10439},[192],[56,10441],{"className":10442,"style":188},[187],[56,10444,10446,10449,10489,10492,10495],{"className":10445},[68],[56,10447],{"className":10448,"style":3617},[72],[56,10450,10452,10455],{"className":10451},[77],[56,10453,3565],{"className":10454,"style":3564},[77,78],[56,10456,10458],{"className":10457},[236],[56,10459,10461,10481],{"className":10460},[240,241],[56,10462,10464,10478],{"className":10463},[245],[56,10465,10467],{"className":10466,"style":250},[249],[56,10468,10469,10472],{"style":3581},[56,10470],{"className":10471,"style":258},[257],[56,10473,10475],{"className":10474},[262,263,264,265],[56,10476,3203],{"className":10477},[77,265],[56,10479,273],{"className":10480},[272],[56,10482,10484],{"className":10483},[245],[56,10485,10487],{"className":10486,"style":280},[249],[56,10488],{},[56,10490],{"className":10491,"style":286},[187],[56,10493,291],{"className":10494},[290],[56,10496],{"className":10497,"style":286},[187],[56,10499,10501,10504,10571,10574,10614],{"className":10500},[68],[56,10502],{"className":10503,"style":3673},[72],[56,10505,10507],{"className":10506},[164,2386],[56,10508,10510,10563],{"className":10509},[240,241],[56,10511,10513,10560],{"className":10512},[245],[56,10514,10516,10536,10546],{"className":10515,"style":3686},[249],[56,10517,10518,10521],{"style":2399},[56,10519],{"className":10520,"style":2403},[257],[56,10522,10524],{"className":10523},[262,263,264,265],[56,10525,10527,10530,10533],{"className":10526},[77,265],[56,10528,3701],{"className":10529},[77,265],[56,10531,193],{"className":10532},[192,265],[56,10534,43],{"className":10535},[77,265],[56,10537,10538,10541],{"style":2423},[56,10539],{"className":10540,"style":2403},[257],[56,10542,10543],{},[56,10544,2434],{"className":10545},[164,2432,2433],[56,10547,10548,10551],{"style":2437},[56,10549],{"className":10550,"style":2403},[257],[56,10552,10554],{"className":10553},[262,263,264,265],[56,10555,10557],{"className":10556},[77,265],[56,10558,80],{"className":10559,"style":79},[77,78,265],[56,10561,273],{"className":10562},[272],[56,10564,10566],{"className":10565},[245],[56,10567,10569],{"className":10568,"style":2459},[249],[56,10570],{},[56,10572],{"className":10573,"style":346},[187],[56,10575,10577,10580],{"className":10576},[77],[56,10578,10167],{"className":10579},[77],[56,10581,10583],{"className":10582},[236],[56,10584,10586,10606],{"className":10585},[240,241],[56,10587,10589,10603],{"className":10588},[245],[56,10590,10592],{"className":10591,"style":789},[249],[56,10593,10594,10597],{"style":316},[56,10595],{"className":10596,"style":258},[257],[56,10598,10600],{"className":10599},[262,263,264,265],[56,10601,3701],{"className":10602},[77,265],[56,10604,273],{"className":10605},[272],[56,10607,10609],{"className":10608},[245],[56,10610,10612],{"className":10611,"style":280},[249],[56,10613],{},[56,10615,2042],{"className":10616},[77],[11,10618,10619],{},"This linear-accumulation view explains why Transformers are so editable: because\ncontributions add, an attention head and an FFN can read each other's writes, and\nthe final representation is literally the embedding plus every increment the\nsublayers added.",[4953,10621],{"hash":10622},"272e623b47105a0ccce820783ca7f87425ae84725cf3a114befa4e199f3ab22f",[83,10624,10626],{"id":10625},"where-the-parameters-and-the-compute-live","Where the parameters and the compute live",[11,10628,10629,10630],{},"Two accounting questions decide how a Transformer scales: where do its weights\nsit, and what dominates its runtime. Both have clean closed forms.",[35,10631,10632],{},[15,10633,3276],{"href":10634,"ariaDescribedBy":10635,"dataFootnoteRef":6,"id":10636},"#user-content-fn-gf-attention-mem",[41],"user-content-fnref-gf-attention-mem",[11,10638,10639,10642,10643,10833,10834,10868,10869,10913,10914,3187,11062,11210,11211,11290,11291,11400],{},[51,10640,10641],{},"Parameters."," Per layer, attention contributes the four projection matrices\n",[56,10644,10646],{"className":10645},[59],[56,10647,10649],{"className":10648,"ariaHidden":64},[63],[56,10650,10652,10655,10695,10698,10701,10741,10744,10747,10787,10790,10793],{"className":10651},[68],[56,10653],{"className":10654,"style":6140},[72],[56,10656,10658,10661],{"className":10657},[77],[56,10659,232],{"className":10660,"style":231},[77,78],[56,10662,10664],{"className":10663},[236],[56,10665,10667,10687],{"className":10666},[240,241],[56,10668,10670,10684],{"className":10669},[245],[56,10671,10673],{"className":10672,"style":3578},[249],[56,10674,10675,10678],{"style":253},[56,10676],{"className":10677,"style":258},[257],[56,10679,10681],{"className":10680},[262,263,264,265],[56,10682,7099],{"className":10683},[77,78,265],[56,10685,273],{"className":10686},[272],[56,10688,10690],{"className":10689},[245],[56,10691,10693],{"className":10692,"style":6189},[249],[56,10694],{},[56,10696,447],{"className":10697},[446],[56,10699],{"className":10700,"style":346},[187],[56,10702,10704,10707],{"className":10703},[77],[56,10705,232],{"className":10706,"style":231},[77,78],[56,10708,10710],{"className":10709},[236],[56,10711,10713,10733],{"className":10712},[240,241],[56,10714,10716,10730],{"className":10715},[245],[56,10717,10719],{"className":10718,"style":3578},[249],[56,10720,10721,10724],{"style":253},[56,10722],{"className":10723,"style":258},[257],[56,10725,10727],{"className":10726},[262,263,264,265],[56,10728,7110],{"className":10729,"style":7109},[77,78,265],[56,10731,273],{"className":10732},[272],[56,10734,10736],{"className":10735},[245],[56,10737,10739],{"className":10738,"style":280},[249],[56,10740],{},[56,10742,447],{"className":10743},[446],[56,10745],{"className":10746,"style":346},[187],[56,10748,10750,10753],{"className":10749},[77],[56,10751,232],{"className":10752,"style":231},[77,78],[56,10754,10756],{"className":10755},[236],[56,10757,10759,10779],{"className":10758},[240,241],[56,10760,10762,10776],{"className":10761},[245],[56,10763,10765],{"className":10764,"style":3578},[249],[56,10766,10767,10770],{"style":253},[56,10768],{"className":10769,"style":258},[257],[56,10771,10773],{"className":10772},[262,263,264,265],[56,10774,7120],{"className":10775,"style":286},[77,78,265],[56,10777,273],{"className":10778},[272],[56,10780,10782],{"className":10781},[245],[56,10783,10785],{"className":10784,"style":280},[249],[56,10786],{},[56,10788,447],{"className":10789},[446],[56,10791],{"className":10792,"style":346},[187],[56,10794,10796,10799],{"className":10795},[77],[56,10797,232],{"className":10798,"style":231},[77,78],[56,10800,10802],{"className":10801},[236],[56,10803,10805,10825],{"className":10804},[240,241],[56,10806,10808,10822],{"className":10807},[245],[56,10809,10811],{"className":10810,"style":3578},[249],[56,10812,10813,10816],{"style":253},[56,10814],{"className":10815,"style":258},[257],[56,10817,10819],{"className":10818},[262,263,264,265],[56,10820,7445],{"className":10821,"style":7444},[77,78,265],[56,10823,273],{"className":10824},[272],[56,10826,10828],{"className":10827},[245],[56,10829,10831],{"className":10830,"style":280},[249],[56,10832],{},", each ",[56,10835,10837],{"className":10836},[59],[56,10838,10840,10859],{"className":10839,"ariaHidden":64},[63],[56,10841,10843,10847,10850,10853,10856],{"className":10842},[68],[56,10844],{"className":10845,"style":10846},[72],"height:0.7778em;vertical-align:-0.0833em;",[56,10848,548],{"className":10849},[77,78],[56,10851],{"className":10852,"style":286},[187],[56,10854,552],{"className":10855},[290],[56,10857],{"className":10858,"style":286},[187],[56,10860,10862,10865],{"className":10861},[68],[56,10863],{"className":10864,"style":833},[72],[56,10866,548],{"className":10867},[77,78],", for ",[56,10870,10872],{"className":10871},[59],[56,10873,10875],{"className":10874,"ariaHidden":64},[63],[56,10876,10878,10881,10884],{"className":10877},[68],[56,10879],{"className":10880,"style":3237},[72],[56,10882,142],{"className":10883},[77],[56,10885,10887,10890],{"className":10886},[77],[56,10888,548],{"className":10889},[77,78],[56,10891,10893],{"className":10892},[236],[56,10894,10896],{"className":10895},[240],[56,10897,10899],{"className":10898},[245],[56,10900,10902],{"className":10901,"style":3237},[249],[56,10903,10904,10907],{"style":2239},[56,10905],{"className":10906,"style":258},[257],[56,10908,10910],{"className":10909},[262,263,264,265],[56,10911,376],{"className":10912},[77,265],". The FFN contributes\n",[56,10915,10917],{"className":10916},[59],[56,10918,10920,10975],{"className":10919,"ariaHidden":64},[63],[56,10921,10923,10926,10966,10969,10972],{"className":10922},[68],[56,10924],{"className":10925,"style":7414},[72],[56,10927,10929,10932],{"className":10928},[77],[56,10930,232],{"className":10931,"style":231},[77,78],[56,10933,10935],{"className":10934},[236],[56,10936,10938,10958],{"className":10937},[240,241],[56,10939,10941,10955],{"className":10940},[245],[56,10942,10944],{"className":10943,"style":250},[249],[56,10945,10946,10949],{"style":253},[56,10947],{"className":10948,"style":258},[257],[56,10950,10952],{"className":10951},[262,263,264,265],[56,10953,43],{"className":10954},[77,265],[56,10956,273],{"className":10957},[272],[56,10959,10961],{"className":10960},[245],[56,10962,10964],{"className":10963,"style":280},[249],[56,10965],{},[56,10967],{"className":10968,"style":188},[187],[56,10970,501],{"className":10971},[192],[56,10973],{"className":10974,"style":188},[187],[56,10976,10978,10981],{"className":10977},[68],[56,10979],{"className":10980,"style":2218},[72],[56,10982,10984,10987],{"className":10983},[77],[56,10985,519],{"className":10986},[77,518],[56,10988,10990],{"className":10989},[236],[56,10991,10993],{"className":10992},[240],[56,10994,10996],{"className":10995},[245],[56,10997,10999],{"className":10998,"style":2218},[249],[56,11000,11001,11004],{"style":2239},[56,11002],{"className":11003,"style":258},[257],[56,11005,11007],{"className":11006},[262,263,264,265],[56,11008,11010,11013,11016],{"className":11009},[77,265],[56,11011,548],{"className":11012},[77,78,265],[56,11014,552],{"className":11015},[290,265],[56,11017,11019,11022],{"className":11018},[77,265],[56,11020,548],{"className":11021},[77,78,265],[56,11023,11025],{"className":11024},[236],[56,11026,11028,11054],{"className":11027},[240,241],[56,11029,11031,11051],{"className":11030},[245],[56,11032,11034],{"className":11033,"style":571},[249],[56,11035,11036,11039],{"style":574},[56,11037],{"className":11038,"style":578},[257],[56,11040,11042],{"className":11041},[262,582,583,265],[56,11043,11045],{"className":11044},[77,265],[56,11046,11048],{"className":11047},[77,590,265],[56,11049,594],{"className":11050},[77,265],[56,11052,273],{"className":11053},[272],[56,11055,11057],{"className":11056},[245],[56,11058,11060],{"className":11059,"style":604},[249],[56,11061],{},[56,11063,11065],{"className":11064},[59],[56,11066,11068,11123],{"className":11067,"ariaHidden":64},[63],[56,11069,11071,11074,11114,11117,11120],{"className":11070},[68],[56,11072],{"className":11073,"style":7414},[72],[56,11075,11077,11080],{"className":11076},[77],[56,11078,232],{"className":11079,"style":231},[77,78],[56,11081,11083],{"className":11082},[236],[56,11084,11086,11106],{"className":11085},[240,241],[56,11087,11089,11103],{"className":11088},[245],[56,11090,11092],{"className":11091,"style":250},[249],[56,11093,11094,11097],{"style":253},[56,11095],{"className":11096,"style":258},[257],[56,11098,11100],{"className":11099},[262,263,264,265],[56,11101,376],{"className":11102},[77,265],[56,11104,273],{"className":11105},[272],[56,11107,11109],{"className":11108},[245],[56,11110,11112],{"className":11111,"style":280},[249],[56,11113],{},[56,11115],{"className":11116,"style":188},[187],[56,11118,501],{"className":11119},[192],[56,11121],{"className":11122,"style":188},[187],[56,11124,11126,11129],{"className":11125},[68],[56,11127],{"className":11128,"style":2218},[72],[56,11130,11132,11135],{"className":11131},[77],[56,11133,519],{"className":11134},[77,518],[56,11136,11138],{"className":11137},[236],[56,11139,11141],{"className":11140},[240],[56,11142,11144],{"className":11143},[245],[56,11145,11147],{"className":11146,"style":2218},[249],[56,11148,11149,11152],{"style":2239},[56,11150],{"className":11151,"style":258},[257],[56,11153,11155],{"className":11154},[262,263,264,265],[56,11156,11158,11204,11207],{"className":11157},[77,265],[56,11159,11161,11164],{"className":11160},[77,265],[56,11162,548],{"className":11163},[77,78,265],[56,11165,11167],{"className":11166},[236],[56,11168,11170,11196],{"className":11169},[240,241],[56,11171,11173,11193],{"className":11172},[245],[56,11174,11176],{"className":11175,"style":571},[249],[56,11177,11178,11181],{"style":574},[56,11179],{"className":11180,"style":578},[257],[56,11182,11184],{"className":11183},[262,582,583,265],[56,11185,11187],{"className":11186},[77,265],[56,11188,11190],{"className":11189},[77,590,265],[56,11191,594],{"className":11192},[77,265],[56,11194,273],{"className":11195},[272],[56,11197,11199],{"className":11198},[245],[56,11200,11202],{"className":11201,"style":604},[249],[56,11203],{},[56,11205,552],{"className":11206},[290,265],[56,11208,548],{"className":11209},[77,78,265],"; with ",[56,11212,11214],{"className":11213},[59],[56,11215,11217,11278],{"className":11216,"ariaHidden":64},[63],[56,11218,11220,11223,11269,11272,11275],{"className":11219},[68],[56,11221],{"className":11222,"style":770},[72],[56,11224,11226,11229],{"className":11225},[77],[56,11227,548],{"className":11228},[77,78],[56,11230,11232],{"className":11231},[236],[56,11233,11235,11261],{"className":11234},[240,241],[56,11236,11238,11258],{"className":11237},[245],[56,11239,11241],{"className":11240,"style":789},[249],[56,11242,11243,11246],{"style":316},[56,11244],{"className":11245,"style":258},[257],[56,11247,11249],{"className":11248},[262,263,264,265],[56,11250,11252],{"className":11251},[77,265],[56,11253,11255],{"className":11254},[77,590,265],[56,11256,594],{"className":11257},[77,265],[56,11259,273],{"className":11260},[272],[56,11262,11264],{"className":11263},[245],[56,11265,11267],{"className":11266,"style":280},[249],[56,11268],{},[56,11270],{"className":11271,"style":188},[187],[56,11273,193],{"className":11274},[192],[56,11276],{"className":11277,"style":188},[187],[56,11279,11281,11284,11287],{"className":11280},[68],[56,11282],{"className":11283,"style":833},[72],[56,11285,142],{"className":11286},[77],[56,11288,548],{"className":11289},[77,78]," that is ",[56,11292,11294],{"className":11293},[59],[56,11295,11297,11315,11362],{"className":11296,"ariaHidden":64},[63],[56,11298,11300,11303,11306,11309,11312],{"className":11299},[68],[56,11301],{"className":11302,"style":138},[72],[56,11304,376],{"className":11305},[77],[56,11307],{"className":11308,"style":286},[187],[56,11310,1007],{"className":11311},[290],[56,11313],{"className":11314,"style":286},[187],[56,11316,11318,11321,11324,11353,11356,11359],{"className":11317},[68],[56,11319],{"className":11320,"style":3237},[72],[56,11322,142],{"className":11323},[77],[56,11325,11327,11330],{"className":11326},[77],[56,11328,548],{"className":11329},[77,78],[56,11331,11333],{"className":11332},[236],[56,11334,11336],{"className":11335},[240],[56,11337,11339],{"className":11338},[245],[56,11340,11342],{"className":11341,"style":3237},[249],[56,11343,11344,11347],{"style":2239},[56,11345],{"className":11346,"style":258},[257],[56,11348,11350],{"className":11349},[262,263,264,265],[56,11351,376],{"className":11352},[77,265],[56,11354],{"className":11355,"style":188},[187],[56,11357,193],{"className":11358},[192],[56,11360],{"className":11361,"style":188},[187],[56,11363,11365,11368,11371],{"className":11364},[68],[56,11366],{"className":11367,"style":3237},[72],[56,11369,6691],{"className":11370},[77],[56,11372,11374,11377],{"className":11373},[77],[56,11375,548],{"className":11376},[77,78],[56,11378,11380],{"className":11379},[236],[56,11381,11383],{"className":11382},[240],[56,11384,11386],{"className":11385},[245],[56,11387,11389],{"className":11388,"style":3237},[249],[56,11390,11391,11394],{"style":2239},[56,11392],{"className":11393,"style":258},[257],[56,11395,11397],{"className":11396},[262,263,264,265],[56,11398,376],{"className":11399},[77,265],". So per layer,",[56,11402,11404],{"className":11403},[147],[56,11405,11407],{"className":11406},[59],[56,11408,11410,11569,11725,11855,11992],{"className":11409,"ariaHidden":64},[63],[56,11411,11413,11417,11560,11563,11566],{"className":11412},[68],[56,11414],{"className":11415,"style":11416},[72],"height:2.1796em;vertical-align:-1.3155em;",[56,11418,11420],{"className":11419},[206,1165],[56,11421,11423,11551],{"className":11422},[240,241],[56,11424,11426,11548],{"className":11425},[245],[56,11427,11429,11448],{"className":11428,"style":2534},[249],[56,11430,11432,11435],{"style":11431},"top:-1.6845em;",[56,11433],{"className":11434,"style":1182},[257],[56,11436,11438],{"className":11437},[262,263,264,265],[56,11439,11441],{"className":11440},[77,265],[56,11442,11444],{"className":11443},[77,590,265],[56,11445,11447],{"className":11446},[77,265],"attention",[56,11449,11450,11453],{"style":1198},[56,11451],{"className":11452,"style":1182},[257],[56,11454,11456],{"className":11455},[206,1165],[56,11457,11459,11539],{"className":11458},[240,241],[56,11460,11462,11536],{"className":11461},[245],[56,11463,11465,11496],{"className":11464,"style":2534},[249],[56,11466,11469,11472],{"className":11467,"style":11468},[1217],"top:-2.352em;",[56,11470],{"className":11471,"style":1182},[257],[56,11473,11475,11482,11489],{"className":11474,"style":1226},[1225],[56,11476,11478],{"className":11477,"style":1231},[1230],[1233,11479,11480],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1239},[1241,11481],{"d":1243},[56,11483,11485],{"className":11484,"style":1231},[1247],[1233,11486,11487],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1250},[1241,11488],{"d":1253},[56,11490,11492],{"className":11491,"style":1231},[1257],[1233,11493,11494],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1260},[1241,11495],{"d":1263},[56,11497,11498,11501],{"style":1198},[56,11499],{"className":11500,"style":1182},[257],[56,11502,11504,11507],{"className":11503},[77],[56,11505,142],{"className":11506},[77],[56,11508,11510,11513],{"className":11509},[77],[56,11511,548],{"className":11512},[77,78],[56,11514,11516],{"className":11515},[236],[56,11517,11519],{"className":11518},[240],[56,11520,11522],{"className":11521},[245],[56,11523,11525],{"className":11524,"style":2534},[249],[56,11526,11527,11530],{"style":535},[56,11528],{"className":11529,"style":258},[257],[56,11531,11533],{"className":11532},[262,263,264,265],[56,11534,376],{"className":11535},[77,265],[56,11537,273],{"className":11538},[272],[56,11540,11542],{"className":11541},[245],[56,11543,11546],{"className":11544,"style":11545},[249],"height:0.648em;",[56,11547],{},[56,11549,273],{"className":11550},[272],[56,11552,11554],{"className":11553},[245],[56,11555,11558],{"className":11556,"style":11557},[249],"height:1.3155em;",[56,11559],{},[56,11561],{"className":11562,"style":286},[187],[56,11564,291],{"className":11565},[290],[56,11567],{"className":11568,"style":286},[187],[56,11570,11572,11576,11716,11719,11722],{"className":11571},[68],[56,11573],{"className":11574,"style":11575},[72],"height:2.1904em;vertical-align:-1.3263em;",[56,11577,11579],{"className":11578},[206,1165],[56,11580,11582,11707],{"className":11581},[240,241],[56,11583,11585,11704],{"className":11584},[245],[56,11586,11588,11606],{"className":11587,"style":2534},[249],[56,11589,11591,11594],{"style":11590},"top:-1.6737em;",[56,11592],{"className":11593,"style":1182},[257],[56,11595,11597],{"className":11596},[262,263,264,265],[56,11598,11600],{"className":11599},[77,265],[56,11601,11603],{"className":11602},[77,590,265],[56,11604,169],{"className":11605},[77,265],[56,11607,11608,11611],{"style":1198},[56,11609],{"className":11610,"style":1182},[257],[56,11612,11614],{"className":11613},[206,1165],[56,11615,11617,11696],{"className":11616},[240,241],[56,11618,11620,11693],{"className":11619},[245],[56,11621,11623,11653],{"className":11622,"style":2534},[249],[56,11624,11626,11629],{"className":11625,"style":11468},[1217],[56,11627],{"className":11628,"style":1182},[257],[56,11630,11632,11639,11646],{"className":11631,"style":1226},[1225],[56,11633,11635],{"className":11634,"style":1231},[1230],[1233,11636,11637],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1239},[1241,11638],{"d":1243},[56,11640,11642],{"className":11641,"style":1231},[1247],[1233,11643,11644],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1250},[1241,11645],{"d":1253},[56,11647,11649],{"className":11648,"style":1231},[1257],[1233,11650,11651],{"xmlns":1235,"width":1236,"height":1237,"viewBox":1238,"preserveAspectRatio":1260},[1241,11652],{"d":1263},[56,11654,11655,11658],{"style":1198},[56,11656],{"className":11657,"style":1182},[257],[56,11659,11661,11664],{"className":11660},[77],[56,11662,6691],{"className":11663},[77],[56,11665,11667,11670],{"className":11666},[77],[56,11668,548],{"className":11669},[77,78],[56,11671,11673],{"className":11672},[236],[56,11674,11676],{"className":11675},[240],[56,11677,11679],{"className":11678},[245],[56,11680,11682],{"className":11681,"style":2534},[249],[56,11683,11684,11687],{"style":535},[56,11685],{"className":11686,"style":258},[257],[56,11688,11690],{"className":11689},[262,263,264,265],[56,11691,376],{"className":11692},[77,265],[56,11694,273],{"className":11695},[272],[56,11697,11699],{"className":11698},[245],[56,11700,11702],{"className":11701,"style":11545},[249],[56,11703],{},[56,11705,273],{"className":11706},[272],[56,11708,11710],{"className":11709},[245],[56,11711,11714],{"className":11712,"style":11713},[249],"height:1.3263em;",[56,11715],{},[56,11717],{"className":11718,"style":188},[187],[56,11720,193],{"className":11721},[192],[56,11723],{"className":11724,"style":188},[187],[56,11726,11728,11732,11736,11765,11768,11771,11774,11846,11849,11852],{"className":11727},[68],[56,11729],{"className":11730,"style":11731},[72],"height:2.2408em;vertical-align:-0.8804em;",[56,11733,11735],{"className":11734},[77],"12",[56,11737,11739,11742],{"className":11738},[77],[56,11740,548],{"className":11741},[77,78],[56,11743,11745],{"className":11744},[236],[56,11746,11748],{"className":11747},[240],[56,11749,11751],{"className":11750},[245],[56,11752,11754],{"className":11753,"style":2534},[249],[56,11755,11756,11759],{"style":535},[56,11757],{"className":11758,"style":258},[257],[56,11760,11762],{"className":11761},[262,263,264,265],[56,11763,376],{"className":11764},[77,265],[56,11766,447],{"className":11767},[446],[56,11769],{"className":11770,"style":451},[187],[56,11772],{"className":11773,"style":346},[187],[56,11775,11777,11780,11843],{"className":11776},[77],[56,11778],{"className":11779},[173,2315],[56,11781,11783],{"className":11782},[2319],[56,11784,11786,11834],{"className":11785},[240,241],[56,11787,11789,11831],{"className":11788},[245],[56,11790,11793,11808,11816],{"className":11791,"style":11792},[249],"height:1.3603em;",[56,11794,11795,11798],{"style":2332},[56,11796],{"className":11797,"style":1182},[257],[56,11799,11801],{"className":11800},[77],[56,11802,11804],{"className":11803},[77,590],[56,11805,11807],{"className":11806},[77],"layer params",[56,11809,11810,11813],{"style":2344},[56,11811],{"className":11812,"style":1182},[257],[56,11814],{"className":11815,"style":2352},[2351],[56,11817,11818,11821],{"style":2355},[56,11819],{"className":11820,"style":1182},[257],[56,11822,11824],{"className":11823},[77],[56,11825,11827],{"className":11826},[77,590],[56,11828,11830],{"className":11829},[77],"FFN params",[56,11832,273],{"className":11833},[272],[56,11835,11837],{"className":11836},[245],[56,11838,11841],{"className":11839,"style":11840},[249],"height:0.8804em;",[56,11842],{},[56,11844],{"className":11845},[182,2315],[56,11847],{"className":11848,"style":188},[187],[56,11850,193],{"className":11851},[192],[56,11853],{"className":11854,"style":188},[187],[56,11856,11858,11862,11983,11986,11989],{"className":11857},[68],[56,11859],{"className":11860,"style":11861},[72],"height:2.1771em;vertical-align:-0.686em;",[56,11863,11865,11868,11980],{"className":11864},[77],[56,11866],{"className":11867},[173,2315],[56,11869,11871],{"className":11870},[2319],[56,11872,11874,11972],{"className":11873},[240,241],[56,11875,11877,11969],{"className":11876},[245],[56,11878,11881,11921,11929],{"className":11879,"style":11880},[249],"height:1.4911em;",[56,11882,11883,11886],{"style":2332},[56,11884],{"className":11885,"style":1182},[257],[56,11887,11889,11892],{"className":11888},[77],[56,11890,11735],{"className":11891},[77],[56,11893,11895,11898],{"className":11894},[77],[56,11896,548],{"className":11897},[77,78],[56,11899,11901],{"className":11900},[236],[56,11902,11904],{"className":11903},[240],[56,11905,11907],{"className":11906},[245],[56,11908,11910],{"className":11909,"style":2918},[249],[56,11911,11912,11915],{"style":2921},[56,11913],{"className":11914,"style":258},[257],[56,11916,11918],{"className":11917},[262,263,264,265],[56,11919,376],{"className":11920},[77,265],[56,11922,11923,11926],{"style":2344},[56,11924],{"className":11925,"style":1182},[257],[56,11927],{"className":11928,"style":2352},[2351],[56,11930,11931,11934],{"style":2355},[56,11932],{"className":11933,"style":1182},[257],[56,11935,11937,11940],{"className":11936},[77],[56,11938,6691],{"className":11939},[77],[56,11941,11943,11946],{"className":11942},[77],[56,11944,548],{"className":11945},[77,78],[56,11947,11949],{"className":11948},[236],[56,11950,11952],{"className":11951},[240],[56,11953,11955],{"className":11954},[245],[56,11956,11958],{"className":11957,"style":3237},[249],[56,11959,11960,11963],{"style":2239},[56,11961],{"className":11962,"style":258},[257],[56,11964,11966],{"className":11965},[262,263,264,265],[56,11967,376],{"className":11968},[77,265],[56,11970,273],{"className":11971},[272],[56,11973,11975],{"className":11974},[245],[56,11976,11978],{"className":11977,"style":2374},[249],[56,11979],{},[56,11981],{"className":11982},[182,2315],[56,11984],{"className":11985,"style":188},[187],[56,11987,193],{"className":11988},[192],[56,11990],{"className":11991,"style":188},[187],[56,11993,11995,11999,12061],{"className":11994},[68],[56,11996],{"className":11997,"style":11998},[72],"height:2.0074em;vertical-align:-0.686em;",[56,12000,12002,12005,12058],{"className":12001},[77],[56,12003],{"className":12004},[173,2315],[56,12006,12008],{"className":12007},[2319],[56,12009,12011,12050],{"className":12010},[240,241],[56,12012,12014,12047],{"className":12013},[245],[56,12015,12017,12028,12036],{"className":12016,"style":2329},[249],[56,12018,12019,12022],{"style":2332},[56,12020],{"className":12021,"style":1182},[257],[56,12023,12025],{"className":12024},[77],[56,12026,7193],{"className":12027},[77],[56,12029,12030,12033],{"style":2344},[56,12031],{"className":12032,"style":1182},[257],[56,12034],{"className":12035,"style":2352},[2351],[56,12037,12038,12041],{"style":2355},[56,12039],{"className":12040,"style":1182},[257],[56,12042,12044],{"className":12043},[77],[56,12045,376],{"className":12046},[77],[56,12048,273],{"className":12049},[272],[56,12051,12053],{"className":12052},[245],[56,12054,12056],{"className":12055,"style":2374},[249],[56,12057],{},[56,12059],{"className":12060},[182,2315],[56,12062,2042],{"className":12063},[77],[11,12065,12066],{},"Two-thirds of a Transformer's weights live in the feed-forward networks, not the\nattention — a fact that motivates much of the work on sparsifying or scaling the\nFFN (mixture-of-experts) rather than attention.",[11,12068,5793,12069,12113,12114,12146,12147,12171,12172,12190,12191,12206,12207,6656,12240,12316],{},[56,12070,12072],{"className":12071},[59],[56,12073,12075],{"className":12074,"ariaHidden":64},[63],[56,12076,12078,12081,12084],{"className":12077},[68],[56,12079],{"className":12080,"style":3237},[72],[56,12082,11735],{"className":12083},[77],[56,12085,12087,12090],{"className":12086},[77],[56,12088,548],{"className":12089},[77,78],[56,12091,12093],{"className":12092},[236],[56,12094,12096],{"className":12095},[240],[56,12097,12099],{"className":12098},[245],[56,12100,12102],{"className":12101,"style":3237},[249],[56,12103,12104,12107],{"style":2239},[56,12105],{"className":12106,"style":258},[257],[56,12108,12110],{"className":12109},[262,263,264,265],[56,12111,376],{"className":12112},[77,265]," count ignores the small additive terms — the biases (",[56,12115,12117],{"className":12116},[59],[56,12118,12120,12134],{"className":12119,"ariaHidden":64},[63],[56,12121,12123,12127,12131],{"className":12122},[68],[56,12124],{"className":12125,"style":12126},[72],"height:0.3669em;",[56,12128,12130],{"className":12129},[192],"∼",[56,12132],{"className":12133,"style":188},[187],[56,12135,12137,12140,12143],{"className":12136},[68],[56,12138],{"className":12139,"style":833},[72],[56,12141,3276],{"className":12142},[77],[56,12144,548],{"className":12145},[77,78]," per\nlayer) and the two LayerNorms' ",[56,12148,12150],{"className":12149},[59],[56,12151,12153],{"className":12152,"ariaHidden":64},[63],[56,12154,12156,12159,12162,12165,12168],{"className":12155},[68],[56,12157],{"className":12158,"style":106},[72],[56,12160,2830],{"className":12161,"style":2829},[77,78],[56,12163,447],{"className":12164},[446],[56,12166],{"className":12167,"style":346},[187],[56,12169,3038],{"className":12170,"style":3037},[77,78]," (",[56,12173,12175],{"className":12174},[59],[56,12176,12178],{"className":12177,"ariaHidden":64},[63],[56,12179,12181,12184,12187],{"className":12180},[68],[56,12182],{"className":12183,"style":833},[72],[56,12185,142],{"className":12186},[77],[56,12188,548],{"className":12189},[77,78]," per layer) — which are\nlinear in ",[56,12192,12194],{"className":12193},[59],[56,12195,12197],{"className":12196,"ariaHidden":64},[63],[56,12198,12200,12203],{"className":12199},[68],[56,12201],{"className":12202,"style":833},[72],[56,12204,548],{"className":12205},[77,78]," and vanish against the quadratic weights for any real width. Put\n",[56,12208,12210],{"className":12209},[59],[56,12211,12213,12231],{"className":12212,"ariaHidden":64},[63],[56,12214,12216,12219,12222,12225,12228],{"className":12215},[68],[56,12217],{"className":12218,"style":833},[72],[56,12220,548],{"className":12221},[77,78],[56,12223],{"className":12224,"style":188},[187],[56,12226,193],{"className":12227},[192],[56,12229],{"className":12230,"style":188},[187],[56,12232,12234,12237],{"className":12233},[68],[56,12235],{"className":12236,"style":138},[72],[56,12238,6655],{"className":12239},[77],[56,12241,12243],{"className":12242},[59],[56,12244,12246,12307],{"className":12245,"ariaHidden":64},[63],[56,12247,12249,12252,12298,12301,12304],{"className":12248},[68],[56,12250],{"className":12251,"style":770},[72],[56,12253,12255,12258],{"className":12254},[77],[56,12256,548],{"className":12257},[77,78],[56,12259,12261],{"className":12260},[236],[56,12262,12264,12290],{"className":12263},[240,241],[56,12265,12267,12287],{"className":12266},[245],[56,12268,12270],{"className":12269,"style":789},[249],[56,12271,12272,12275],{"style":316},[56,12273],{"className":12274,"style":258},[257],[56,12276,12278],{"className":12277},[262,263,264,265],[56,12279,12281],{"className":12280},[77,265],[56,12282,12284],{"className":12283},[77,590,265],[56,12285,594],{"className":12286},[77,265],[56,12288,273],{"className":12289},[272],[56,12291,12293],{"className":12292},[245],[56,12294,12296],{"className":12295,"style":280},[249],[56,12297],{},[56,12299],{"className":12300,"style":188},[187],[56,12302,193],{"className":12303},[192],[56,12305],{"className":12306,"style":188},[187],[56,12308,12310,12313],{"className":12309},[68],[56,12311],{"className":12312,"style":138},[72],[56,12314,6865],{"className":12315},[77]," (the base configuration) into the table to see\nthe actual per-layer budget:",[3344,12318,12319,12367],{},[3347,12320,12321],{},[3350,12322,12323,12326,12329,12364],{},[3353,12324,12325],{},"Component",[3353,12327,12328],{},"Formula",[3353,12330,12331],{},[56,12332,12334],{"className":12333},[59],[56,12335,12337,12355],{"className":12336,"ariaHidden":64},[63],[56,12338,12340,12343,12346,12349,12352],{"className":12339},[68],[56,12341],{"className":12342,"style":833},[72],[56,12344,548],{"className":12345},[77,78],[56,12347],{"className":12348,"style":188},[187],[56,12350,193],{"className":12351},[192],[56,12353],{"className":12354,"style":188},[187],[56,12356,12358,12361],{"className":12357},[68],[56,12359],{"className":12360,"style":138},[72],[56,12362,6655],{"className":12363},[77],[3353,12365,12366],{},"Share",[3363,12368,12369,12664,12946,13062],{},[3350,12370,12371,12564,12610,12646],{},[3368,12372,12373,12374],{},"Attention ",[56,12375,12377],{"className":12376},[59],[56,12378,12380],{"className":12379,"ariaHidden":64},[63],[56,12381,12383,12386,12426,12429,12432,12472,12475,12478,12518,12521,12524],{"className":12382},[68],[56,12384],{"className":12385,"style":6140},[72],[56,12387,12389,12392],{"className":12388},[77],[56,12390,232],{"className":12391,"style":231},[77,78],[56,12393,12395],{"className":12394},[236],[56,12396,12398,12418],{"className":12397},[240,241],[56,12399,12401,12415],{"className":12400},[245],[56,12402,12404],{"className":12403,"style":3578},[249],[56,12405,12406,12409],{"style":253},[56,12407],{"className":12408,"style":258},[257],[56,12410,12412],{"className":12411},[262,263,264,265],[56,12413,7099],{"className":12414},[77,78,265],[56,12416,273],{"className":12417},[272],[56,12419,12421],{"className":12420},[245],[56,12422,12424],{"className":12423,"style":6189},[249],[56,12425],{},[56,12427,447],{"className":12428},[446],[56,12430],{"className":12431,"style":346},[187],[56,12433,12435,12438],{"className":12434},[77],[56,12436,232],{"className":12437,"style":231},[77,78],[56,12439,12441],{"className":12440},[236],[56,12442,12444,12464],{"className":12443},[240,241],[56,12445,12447,12461],{"className":12446},[245],[56,12448,12450],{"className":12449,"style":3578},[249],[56,12451,12452,12455],{"style":253},[56,12453],{"className":12454,"style":258},[257],[56,12456,12458],{"className":12457},[262,263,264,265],[56,12459,7110],{"className":12460,"style":7109},[77,78,265],[56,12462,273],{"className":12463},[272],[56,12465,12467],{"className":12466},[245],[56,12468,12470],{"className":12469,"style":280},[249],[56,12471],{},[56,12473,447],{"className":12474},[446],[56,12476],{"className":12477,"style":346},[187],[56,12479,12481,12484],{"className":12480},[77],[56,12482,232],{"className":12483,"style":231},[77,78],[56,12485,12487],{"className":12486},[236],[56,12488,12490,12510],{"className":12489},[240,241],[56,12491,12493,12507],{"className":12492},[245],[56,12494,12496],{"className":12495,"style":3578},[249],[56,12497,12498,12501],{"style":253},[56,12499],{"className":12500,"style":258},[257],[56,12502,12504],{"className":12503},[262,263,264,265],[56,12505,7120],{"className":12506,"style":286},[77,78,265],[56,12508,273],{"className":12509},[272],[56,12511,12513],{"className":12512},[245],[56,12514,12516],{"className":12515,"style":280},[249],[56,12517],{},[56,12519,447],{"className":12520},[446],[56,12522],{"className":12523,"style":346},[187],[56,12525,12527,12530],{"className":12526},[77],[56,12528,232],{"className":12529,"style":231},[77,78],[56,12531,12533],{"className":12532},[236],[56,12534,12536,12556],{"className":12535},[240,241],[56,12537,12539,12553],{"className":12538},[245],[56,12540,12542],{"className":12541,"style":3578},[249],[56,12543,12544,12547],{"style":253},[56,12545],{"className":12546,"style":258},[257],[56,12548,12550],{"className":12549},[262,263,264,265],[56,12551,7445],{"className":12552,"style":7444},[77,78,265],[56,12554,273],{"className":12555},[272],[56,12557,12559],{"className":12558},[245],[56,12560,12562],{"className":12561,"style":280},[249],[56,12563],{},[3368,12565,12566],{},[56,12567,12569],{"className":12568},[59],[56,12570,12572],{"className":12571,"ariaHidden":64},[63],[56,12573,12575,12578,12581],{"className":12574},[68],[56,12576],{"className":12577,"style":3237},[72],[56,12579,142],{"className":12580},[77],[56,12582,12584,12587],{"className":12583},[77],[56,12585,548],{"className":12586},[77,78],[56,12588,12590],{"className":12589},[236],[56,12591,12593],{"className":12592},[240],[56,12594,12596],{"className":12595},[245],[56,12597,12599],{"className":12598,"style":3237},[249],[56,12600,12601,12604],{"style":2239},[56,12602],{"className":12603,"style":258},[257],[56,12605,12607],{"className":12606},[262,263,264,265],[56,12608,376],{"className":12609},[77,265],[3368,12611,12612],{},[56,12613,12615],{"className":12614},[59],[56,12616,12618,12630],{"className":12617,"ariaHidden":64},[63],[56,12619,12621,12624,12627],{"className":12620},[68],[56,12622],{"className":12623,"style":3217},[72],[56,12625,3227],{"className":12626},[192],[56,12628],{"className":12629,"style":188},[187],[56,12631,12633,12636,12640],{"className":12632},[68],[56,12634],{"className":12635,"style":73},[72],[56,12637,12639],{"className":12638},[77],"1.05",[56,12641,12643],{"className":12642},[77,590],[56,12644,8152],{"className":12645},[77],[3368,12647,12648],{},[56,12649,12651],{"className":12650},[59],[56,12652,12654],{"className":12653,"ariaHidden":64},[63],[56,12655,12657,12660],{"className":12656},[68],[56,12658],{"className":12659,"style":160},[72],[56,12661,12663],{"className":12662},[77],"1\u002F3",[3350,12665,12666,12846,12892,12928],{},[3368,12667,12668,12669,12171,12767,183],{},"Feed-forward ",[56,12670,12672],{"className":12671},[59],[56,12673,12675],{"className":12674,"ariaHidden":64},[63],[56,12676,12678,12681,12721,12724,12727],{"className":12677},[68],[56,12679],{"className":12680,"style":2058},[72],[56,12682,12684,12687],{"className":12683},[77],[56,12685,232],{"className":12686,"style":231},[77,78],[56,12688,12690],{"className":12689},[236],[56,12691,12693,12713],{"className":12692},[240,241],[56,12694,12696,12710],{"className":12695},[245],[56,12697,12699],{"className":12698,"style":250},[249],[56,12700,12701,12704],{"style":253},[56,12702],{"className":12703,"style":258},[257],[56,12705,12707],{"className":12706},[262,263,264,265],[56,12708,43],{"className":12709},[77,265],[56,12711,273],{"className":12712},[272],[56,12714,12716],{"className":12715},[245],[56,12717,12719],{"className":12718,"style":280},[249],[56,12720],{},[56,12722,447],{"className":12723},[446],[56,12725],{"className":12726,"style":346},[187],[56,12728,12730,12733],{"className":12729},[77],[56,12731,232],{"className":12732,"style":231},[77,78],[56,12734,12736],{"className":12735},[236],[56,12737,12739,12759],{"className":12738},[240,241],[56,12740,12742,12756],{"className":12741},[245],[56,12743,12745],{"className":12744,"style":250},[249],[56,12746,12747,12750],{"style":253},[56,12748],{"className":12749,"style":258},[257],[56,12751,12753],{"className":12752},[262,263,264,265],[56,12754,376],{"className":12755},[77,265],[56,12757,273],{"className":12758},[272],[56,12760,12762],{"className":12761},[245],[56,12763,12765],{"className":12764,"style":280},[249],[56,12766],{},[56,12768,12770],{"className":12769},[59],[56,12771,12773,12834],{"className":12772,"ariaHidden":64},[63],[56,12774,12776,12779,12825,12828,12831],{"className":12775},[68],[56,12777],{"className":12778,"style":770},[72],[56,12780,12782,12785],{"className":12781},[77],[56,12783,548],{"className":12784},[77,78],[56,12786,12788],{"className":12787},[236],[56,12789,12791,12817],{"className":12790},[240,241],[56,12792,12794,12814],{"className":12793},[245],[56,12795,12797],{"className":12796,"style":789},[249],[56,12798,12799,12802],{"style":316},[56,12800],{"className":12801,"style":258},[257],[56,12803,12805],{"className":12804},[262,263,264,265],[56,12806,12808],{"className":12807},[77,265],[56,12809,12811],{"className":12810},[77,590,265],[56,12812,594],{"className":12813},[77,265],[56,12815,273],{"className":12816},[272],[56,12818,12820],{"className":12819},[245],[56,12821,12823],{"className":12822,"style":280},[249],[56,12824],{},[56,12826],{"className":12827,"style":188},[187],[56,12829,193],{"className":12830},[192],[56,12832],{"className":12833,"style":188},[187],[56,12835,12837,12840,12843],{"className":12836},[68],[56,12838],{"className":12839,"style":833},[72],[56,12841,142],{"className":12842},[77],[56,12844,548],{"className":12845},[77,78],[3368,12847,12848],{},[56,12849,12851],{"className":12850},[59],[56,12852,12854],{"className":12853,"ariaHidden":64},[63],[56,12855,12857,12860,12863],{"className":12856},[68],[56,12858],{"className":12859,"style":3237},[72],[56,12861,6691],{"className":12862},[77],[56,12864,12866,12869],{"className":12865},[77],[56,12867,548],{"className":12868},[77,78],[56,12870,12872],{"className":12871},[236],[56,12873,12875],{"className":12874},[240],[56,12876,12878],{"className":12877},[245],[56,12879,12881],{"className":12880,"style":3237},[249],[56,12882,12883,12886],{"style":2239},[56,12884],{"className":12885,"style":258},[257],[56,12887,12889],{"className":12888},[262,263,264,265],[56,12890,376],{"className":12891},[77,265],[3368,12893,12894],{},[56,12895,12897],{"className":12896},[59],[56,12898,12900,12912],{"className":12899,"ariaHidden":64},[63],[56,12901,12903,12906,12909],{"className":12902},[68],[56,12904],{"className":12905,"style":3217},[72],[56,12907,3227],{"className":12908},[192],[56,12910],{"className":12911,"style":188},[187],[56,12913,12915,12918,12922],{"className":12914},[68],[56,12916],{"className":12917,"style":73},[72],[56,12919,12921],{"className":12920},[77],"2.10",[56,12923,12925],{"className":12924},[77,590],[56,12926,8152],{"className":12927},[77],[3368,12929,12930],{},[56,12931,12933],{"className":12932},[59],[56,12934,12936],{"className":12935,"ariaHidden":64},[63],[56,12937,12939,12942],{"className":12938},[68],[56,12940],{"className":12941,"style":160},[72],[56,12943,12945],{"className":12944},[77],"2\u002F3",[3350,12947,12948,12976,12996,13031],{},[3368,12949,12950,12951,12975],{},"LayerNorm (",[56,12952,12954],{"className":12953},[59],[56,12955,12957],{"className":12956,"ariaHidden":64},[63],[56,12958,12960,12963,12966,12969,12972],{"className":12959},[68],[56,12961],{"className":12962,"style":106},[72],[56,12964,2830],{"className":12965,"style":2829},[77,78],[56,12967,447],{"className":12968},[446],[56,12970],{"className":12971,"style":346},[187],[56,12973,3038],{"className":12974,"style":3037},[77,78],", two per layer)",[3368,12977,12978],{},[56,12979,12981],{"className":12980},[59],[56,12982,12984],{"className":12983,"ariaHidden":64},[63],[56,12985,12987,12990,12993],{"className":12986},[68],[56,12988],{"className":12989,"style":833},[72],[56,12991,142],{"className":12992},[77],[56,12994,548],{"className":12995},[77,78],[3368,12997,12998],{},[56,12999,13001],{"className":13000},[59],[56,13002,13004,13016],{"className":13003,"ariaHidden":64},[63],[56,13005,13007,13010,13013],{"className":13006},[68],[56,13008],{"className":13009,"style":3217},[72],[56,13011,3227],{"className":13012},[192],[56,13014],{"className":13015,"style":188},[187],[56,13017,13019,13022,13025],{"className":13018},[68],[56,13020],{"className":13021,"style":833},[72],[56,13023,376],{"className":13024},[77],[56,13026,13028],{"className":13027},[77,590],[56,13029,2414],{"className":13030},[77],[3368,13032,13033],{},[56,13034,13036],{"className":13035},[59],[56,13037,13039,13051],{"className":13038,"ariaHidden":64},[63],[56,13040,13042,13045,13048],{"className":13041},[68],[56,13043],{"className":13044,"style":2199},[72],[56,13046,7996],{"className":13047},[192],[56,13049],{"className":13050,"style":188},[187],[56,13052,13054,13058],{"className":13053},[68],[56,13055],{"className":13056,"style":13057},[72],"height:0.8056em;vertical-align:-0.0556em;",[56,13059,13061],{"className":13060},[77],"0.1%",[3350,13063,13064,13069,13127,13163],{},[3368,13065,13066],{},[51,13067,13068],{},"Per layer total",[3368,13070,13071],{},[56,13072,13074],{"className":13073},[59],[56,13075,13077,13089],{"className":13076,"ariaHidden":64},[63],[56,13078,13080,13083,13086],{"className":13079},[68],[56,13081],{"className":13082,"style":3217},[72],[56,13084,3227],{"className":13085},[192],[56,13087],{"className":13088,"style":188},[187],[56,13090,13092,13095,13098],{"className":13091},[68],[56,13093],{"className":13094,"style":3237},[72],[56,13096,11735],{"className":13097},[77],[56,13099,13101,13104],{"className":13100},[77],[56,13102,548],{"className":13103},[77,78],[56,13105,13107],{"className":13106},[236],[56,13108,13110],{"className":13109},[240],[56,13111,13113],{"className":13112},[245],[56,13114,13116],{"className":13115,"style":3237},[249],[56,13117,13118,13121],{"style":2239},[56,13119],{"className":13120,"style":258},[257],[56,13122,13124],{"className":13123},[262,263,264,265],[56,13125,376],{"className":13126},[77,265],[3368,13128,13129],{},[56,13130,13132],{"className":13131},[59],[56,13133,13135,13147],{"className":13134,"ariaHidden":64},[63],[56,13136,13138,13141,13144],{"className":13137},[68],[56,13139],{"className":13140,"style":3217},[72],[56,13142,3227],{"className":13143},[192],[56,13145],{"className":13146,"style":188},[187],[56,13148,13150,13153,13157],{"className":13149},[68],[56,13151],{"className":13152,"style":73},[72],[56,13154,13156],{"className":13155},[77],"3.15",[56,13158,13160],{"className":13159},[77,590],[56,13161,8152],{"className":13162},[77],[3368,13164,13165],{},[56,13166,13168],{"className":13167},[59],[56,13169,13171],{"className":13170,"ariaHidden":64},[63],[56,13172,13174,13177],{"className":13173},[68],[56,13175],{"className":13176,"style":138},[72],[56,13178,43],{"className":13179},[77],[11,13181,13182,13183,13198,13199,13233,13234,13267,13268,13290,13291,13325],{},"A ",[56,13184,13186],{"className":13185},[59],[56,13187,13189],{"className":13188,"ariaHidden":64},[63],[56,13190,13192,13195],{"className":13191},[68],[56,13193],{"className":13194,"style":138},[72],[56,13196,7521],{"className":13197},[77],"-layer encoder of this width holds ",[56,13200,13202],{"className":13201},[59],[56,13203,13205,13217],{"className":13204,"ariaHidden":64},[63],[56,13206,13208,13211,13214],{"className":13207},[68],[56,13209],{"className":13210,"style":3217},[72],[56,13212,3227],{"className":13213},[192],[56,13215],{"className":13216,"style":188},[187],[56,13218,13220,13223,13227],{"className":13219},[68],[56,13221],{"className":13222,"style":73},[72],[56,13224,13226],{"className":13225},[77],"19",[56,13228,13230],{"className":13229},[77,590],[56,13231,8152],{"className":13232},[77]," weights in its\nblocks; the token embedding and output projection add ",[56,13235,13237],{"className":13236},[59],[56,13238,13240],{"className":13239,"ariaHidden":64},[63],[56,13241,13243,13246,13249,13252,13255,13258,13261,13264],{"className":13242},[68],[56,13244],{"className":13245,"style":160},[72],[56,13247,376],{"className":13248},[77],[56,13250],{"className":13251,"style":346},[187],[56,13253,9010],{"className":13254},[77],[56,13256,7120],{"className":13257,"style":286},[77,78],[56,13259,9010],{"className":13260},[77],[56,13262],{"className":13263,"style":346},[187],[56,13265,548],{"className":13266},[77,78]," on top,\nwhich for a ",[56,13269,13271],{"className":13270},[59],[56,13272,13274],{"className":13273,"ariaHidden":64},[63],[56,13275,13277,13280,13284],{"className":13276},[68],[56,13278],{"className":13279,"style":833},[72],[56,13281,13283],{"className":13282},[77],"30",[56,13285,13287],{"className":13286},[77,590],[56,13288,2414],{"className":13289},[77]," vocabulary is another ",[56,13292,13294],{"className":13293},[59],[56,13295,13297,13309],{"className":13296,"ariaHidden":64},[63],[56,13298,13300,13303,13306],{"className":13299},[68],[56,13301],{"className":13302,"style":3217},[72],[56,13304,3227],{"className":13305},[192],[56,13307],{"className":13308,"style":188},[187],[56,13310,13312,13315,13319],{"className":13311},[68],[56,13313],{"className":13314,"style":73},[72],[56,13316,13318],{"className":13317},[77],"31",[56,13320,13322],{"className":13321},[77,590],[56,13323,8152],{"className":13324},[77]," — a reminder\nthat at small depth the vocabulary table, not the blocks, can dominate the count.",[11,13327,13328,13331,13332,13401],{},[51,13329,13330],{},"Compute."," The cost split is reversed. The FFN is linear in sequence\nlength — ",[56,13333,13335],{"className":13334},[59],[56,13336,13338,13362],{"className":13337,"ariaHidden":64},[63],[56,13339,13341,13344,13347,13350,13353,13356,13359],{"className":13340},[68],[56,13342],{"className":13343,"style":160},[72],[56,13345,7445],{"className":13346,"style":7444},[77,78],[56,13348,174],{"className":13349},[173],[56,13351,1104],{"className":13352},[77,78],[56,13354],{"className":13355,"style":286},[187],[56,13357,1007],{"className":13358},[290],[56,13360],{"className":13361,"style":286},[187],[56,13363,13365,13369,13398],{"className":13364},[68],[56,13366],{"className":13367,"style":13368},[72],"height:1.0641em;vertical-align:-0.25em;",[56,13370,13372,13375],{"className":13371},[77],[56,13373,548],{"className":13374},[77,78],[56,13376,13378],{"className":13377},[236],[56,13379,13381],{"className":13380},[240],[56,13382,13384],{"className":13383},[245],[56,13385,13387],{"className":13386,"style":3237},[249],[56,13388,13389,13392],{"style":2239},[56,13390],{"className":13391,"style":258},[257],[56,13393,13395],{"className":13394},[262,263,264,265],[56,13396,376],{"className":13397},[77,265],[56,13399,183],{"className":13400},[182]," per layer — but the attention matrix is quadratic.",[45,13403,13404],{"type":3519},[11,13405,13406,13409,13410,13425,13426,13441,13442,13495,13496,13546],{},[51,13407,13408],{},"Theorem (Quadratic attention cost)."," Computing self-attention over a\nsequence of length ",[56,13411,13413],{"className":13412},[59],[56,13414,13416],{"className":13415,"ariaHidden":64},[63],[56,13417,13419,13422],{"className":13418},[68],[56,13420],{"className":13421,"style":1100},[72],[56,13423,1104],{"className":13424},[77,78]," with model width ",[56,13427,13429],{"className":13428},[59],[56,13430,13432],{"className":13431,"ariaHidden":64},[63],[56,13433,13435,13438],{"className":13434},[68],[56,13436],{"className":13437,"style":833},[72],[56,13439,548],{"className":13440},[77,78]," costs ",[56,13443,13445],{"className":13444},[59],[56,13446,13448],{"className":13447,"ariaHidden":64},[63],[56,13449,13451,13454,13457,13460,13489,13492],{"className":13450},[68],[56,13452],{"className":13453,"style":13368},[72],[56,13455,7445],{"className":13456,"style":7444},[77,78],[56,13458,174],{"className":13459},[173],[56,13461,13463,13466],{"className":13462},[77],[56,13464,1104],{"className":13465},[77,78],[56,13467,13469],{"className":13468},[236],[56,13470,13472],{"className":13471},[240],[56,13473,13475],{"className":13474},[245],[56,13476,13478],{"className":13477,"style":3237},[249],[56,13479,13480,13483],{"style":2239},[56,13481],{"className":13482,"style":258},[257],[56,13484,13486],{"className":13485},[262,263,264,265],[56,13487,376],{"className":13488},[77,265],[56,13490,548],{"className":13491},[77,78],[56,13493,183],{"className":13494},[182]," time and ",[56,13497,13499],{"className":13498},[59],[56,13500,13502],{"className":13501,"ariaHidden":64},[63],[56,13503,13505,13508,13511,13514,13543],{"className":13504},[68],[56,13506],{"className":13507,"style":13368},[72],[56,13509,7445],{"className":13510,"style":7444},[77,78],[56,13512,174],{"className":13513},[173],[56,13515,13517,13520],{"className":13516},[77],[56,13518,1104],{"className":13519},[77,78],[56,13521,13523],{"className":13522},[236],[56,13524,13526],{"className":13525},[240],[56,13527,13529],{"className":13528},[245],[56,13530,13532],{"className":13531,"style":3237},[249],[56,13533,13534,13537],{"style":2239},[56,13535],{"className":13536,"style":258},[257],[56,13538,13540],{"className":13539},[262,263,264,265],[56,13541,376],{"className":13542},[77,265],[56,13544,183],{"className":13545},[182],"\nmemory for the attention matrix, independent of how the heads are split.",[45,13548,13549],{"type":4048},[11,13550,13551,13553,13554,13599,13600,13633,13634,13667,13668,13721,13722,13755,13756,13806,13807,13840,13841,13874,13875,13928,13929,13944,13945,13966,13967,13982,13983,14057,14058,14111,14112,14145,14146,14196,14197],{},[51,13552,4053],{}," Forming the scores ",[56,13555,13557],{"className":13556},[59],[56,13558,13560],{"className":13559,"ariaHidden":64},[63],[56,13561,13563,13567,13570],{"className":13562},[68],[56,13564],{"className":13565,"style":13566},[72],"height:1.0435em;vertical-align:-0.1944em;",[56,13568,7099],{"className":13569},[77,78],[56,13571,13573,13576],{"className":13572},[77],[56,13574,7110],{"className":13575,"style":7109},[77,78],[56,13577,13579],{"className":13578},[236],[56,13580,13582],{"className":13581},[240],[56,13583,13585],{"className":13584},[245],[56,13586,13588],{"className":13587,"style":2218},[249],[56,13589,13590,13593],{"style":2239},[56,13591],{"className":13592,"style":258},[257],[56,13594,13596],{"className":13595},[262,263,264,265],[56,13597,7242],{"className":13598},[77,265]," multiplies an ",[56,13601,13603],{"className":13602},[59],[56,13604,13606,13624],{"className":13605,"ariaHidden":64},[63],[56,13607,13609,13612,13615,13618,13621],{"className":13608},[68],[56,13610],{"className":13611,"style":3453},[72],[56,13613,1104],{"className":13614},[77,78],[56,13616],{"className":13617,"style":286},[187],[56,13619,552],{"className":13620},[290],[56,13622],{"className":13623,"style":286},[187],[56,13625,13627,13630],{"className":13626},[68],[56,13628],{"className":13629,"style":833},[72],[56,13631,548],{"className":13632},[77,78]," matrix by a\n",[56,13635,13637],{"className":13636},[59],[56,13638,13640,13658],{"className":13639,"ariaHidden":64},[63],[56,13641,13643,13646,13649,13652,13655],{"className":13642},[68],[56,13644],{"className":13645,"style":10846},[72],[56,13647,548],{"className":13648},[77,78],[56,13650],{"className":13651,"style":286},[187],[56,13653,552],{"className":13654},[290],[56,13656],{"className":13657,"style":286},[187],[56,13659,13661,13664],{"className":13660},[68],[56,13662],{"className":13663,"style":1100},[72],[56,13665,1104],{"className":13666},[77,78]," matrix, costing ",[56,13669,13671],{"className":13670},[59],[56,13672,13674],{"className":13673,"ariaHidden":64},[63],[56,13675,13677,13680,13683,13686,13715,13718],{"className":13676},[68],[56,13678],{"className":13679,"style":13368},[72],[56,13681,7445],{"className":13682,"style":7444},[77,78],[56,13684,174],{"className":13685},[173],[56,13687,13689,13692],{"className":13688},[77],[56,13690,1104],{"className":13691},[77,78],[56,13693,13695],{"className":13694},[236],[56,13696,13698],{"className":13697},[240],[56,13699,13701],{"className":13700},[245],[56,13702,13704],{"className":13703,"style":3237},[249],[56,13705,13706,13709],{"style":2239},[56,13707],{"className":13708,"style":258},[257],[56,13710,13712],{"className":13711},[262,263,264,265],[56,13713,376],{"className":13714},[77,265],[56,13716,548],{"className":13717},[77,78],[56,13719,183],{"className":13720},[182]," and producing an ",[56,13723,13725],{"className":13724},[59],[56,13726,13728,13746],{"className":13727,"ariaHidden":64},[63],[56,13729,13731,13734,13737,13740,13743],{"className":13730},[68],[56,13732],{"className":13733,"style":3453},[72],[56,13735,1104],{"className":13736},[77,78],[56,13738],{"className":13739,"style":286},[187],[56,13741,552],{"className":13742},[290],[56,13744],{"className":13745,"style":286},[187],[56,13747,13749,13752],{"className":13748},[68],[56,13750],{"className":13751,"style":1100},[72],[56,13753,1104],{"className":13754},[77,78]," matrix.\nThe softmax is ",[56,13757,13759],{"className":13758},[59],[56,13760,13762],{"className":13761,"ariaHidden":64},[63],[56,13763,13765,13768,13771,13774,13803],{"className":13764},[68],[56,13766],{"className":13767,"style":13368},[72],[56,13769,7445],{"className":13770,"style":7444},[77,78],[56,13772,174],{"className":13773},[173],[56,13775,13777,13780],{"className":13776},[77],[56,13778,1104],{"className":13779},[77,78],[56,13781,13783],{"className":13782},[236],[56,13784,13786],{"className":13785},[240],[56,13787,13789],{"className":13788},[245],[56,13790,13792],{"className":13791,"style":3237},[249],[56,13793,13794,13797],{"style":2239},[56,13795],{"className":13796,"style":258},[257],[56,13798,13800],{"className":13799},[262,263,264,265],[56,13801,376],{"className":13802},[77,265],[56,13804,183],{"className":13805},[182],". Multiplying the ",[56,13808,13810],{"className":13809},[59],[56,13811,13813,13831],{"className":13812,"ariaHidden":64},[63],[56,13814,13816,13819,13822,13825,13828],{"className":13815},[68],[56,13817],{"className":13818,"style":3453},[72],[56,13820,1104],{"className":13821},[77,78],[56,13823],{"className":13824,"style":286},[187],[56,13826,552],{"className":13827},[290],[56,13829],{"className":13830,"style":286},[187],[56,13832,13834,13837],{"className":13833},[68],[56,13835],{"className":13836,"style":1100},[72],[56,13838,1104],{"className":13839},[77,78]," weights by the ",[56,13842,13844],{"className":13843},[59],[56,13845,13847,13865],{"className":13846,"ariaHidden":64},[63],[56,13848,13850,13853,13856,13859,13862],{"className":13849},[68],[56,13851],{"className":13852,"style":3453},[72],[56,13854,1104],{"className":13855},[77,78],[56,13857],{"className":13858,"style":286},[187],[56,13860,552],{"className":13861},[290],[56,13863],{"className":13864,"style":286},[187],[56,13866,13868,13871],{"className":13867},[68],[56,13869],{"className":13870,"style":833},[72],[56,13872,548],{"className":13873},[77,78]," values is again ",[56,13876,13878],{"className":13877},[59],[56,13879,13881],{"className":13880,"ariaHidden":64},[63],[56,13882,13884,13887,13890,13893,13922,13925],{"className":13883},[68],[56,13885],{"className":13886,"style":13368},[72],[56,13888,7445],{"className":13889,"style":7444},[77,78],[56,13891,174],{"className":13892},[173],[56,13894,13896,13899],{"className":13895},[77],[56,13897,1104],{"className":13898},[77,78],[56,13900,13902],{"className":13901},[236],[56,13903,13905],{"className":13904},[240],[56,13906,13908],{"className":13907},[245],[56,13909,13911],{"className":13910,"style":3237},[249],[56,13912,13913,13916],{"style":2239},[56,13914],{"className":13915,"style":258},[257],[56,13917,13919],{"className":13918},[262,263,264,265],[56,13920,376],{"className":13921},[77,265],[56,13923,548],{"className":13924},[77,78],[56,13926,183],{"className":13927},[182],". Splitting into ",[56,13930,13932],{"className":13931},[59],[56,13933,13935],{"className":13934,"ariaHidden":64},[63],[56,13936,13938,13941],{"className":13937},[68],[56,13939],{"className":13940,"style":833},[72],[56,13942,6672],{"className":13943},[77,78]," heads of width ",[56,13946,13948],{"className":13947},[59],[56,13949,13951],{"className":13950,"ariaHidden":64},[63],[56,13952,13954,13957,13960,13963],{"className":13953},[68],[56,13955],{"className":13956,"style":160},[72],[56,13958,548],{"className":13959},[77,78],[56,13961,3985],{"className":13962},[77],[56,13964,6672],{"className":13965},[77,78]," gives\n",[56,13968,13970],{"className":13969},[59],[56,13971,13973],{"className":13972,"ariaHidden":64},[63],[56,13974,13976,13979],{"className":13975},[68],[56,13977],{"className":13978,"style":833},[72],[56,13980,6672],{"className":13981},[77,78]," products of cost ",[56,13984,13986],{"className":13985},[59],[56,13987,13989,14039],{"className":13988,"ariaHidden":64},[63],[56,13990,13992,13995,13998,14001,14030,14033,14036],{"className":13991},[68],[56,13993],{"className":13994,"style":13368},[72],[56,13996,7445],{"className":13997,"style":7444},[77,78],[56,13999,174],{"className":14000},[173],[56,14002,14004,14007],{"className":14003},[77],[56,14005,1104],{"className":14006},[77,78],[56,14008,14010],{"className":14009},[236],[56,14011,14013],{"className":14012},[240],[56,14014,14016],{"className":14015},[245],[56,14017,14019],{"className":14018,"style":3237},[249],[56,14020,14021,14024],{"style":2239},[56,14022],{"className":14023,"style":258},[257],[56,14025,14027],{"className":14026},[262,263,264,265],[56,14028,376],{"className":14029},[77,265],[56,14031],{"className":14032,"style":286},[187],[56,14034,1007],{"className":14035},[290],[56,14037],{"className":14038,"style":286},[187],[56,14040,14042,14045,14048,14051,14054],{"className":14041},[68],[56,14043],{"className":14044,"style":160},[72],[56,14046,548],{"className":14047},[77,78],[56,14049,3985],{"className":14050},[77],[56,14052,6672],{"className":14053},[77,78],[56,14055,183],{"className":14056},[182],", summing back to ",[56,14059,14061],{"className":14060},[59],[56,14062,14064],{"className":14063,"ariaHidden":64},[63],[56,14065,14067,14070,14073,14076,14105,14108],{"className":14066},[68],[56,14068],{"className":14069,"style":13368},[72],[56,14071,7445],{"className":14072,"style":7444},[77,78],[56,14074,174],{"className":14075},[173],[56,14077,14079,14082],{"className":14078},[77],[56,14080,1104],{"className":14081},[77,78],[56,14083,14085],{"className":14084},[236],[56,14086,14088],{"className":14087},[240],[56,14089,14091],{"className":14090},[245],[56,14092,14094],{"className":14093,"style":3237},[249],[56,14095,14096,14099],{"style":2239},[56,14097],{"className":14098,"style":258},[257],[56,14100,14102],{"className":14101},[262,263,264,265],[56,14103,376],{"className":14104},[77,265],[56,14106,548],{"className":14107},[77,78],[56,14109,183],{"className":14110},[182],". The\n",[56,14113,14115],{"className":14114},[59],[56,14116,14118,14136],{"className":14117,"ariaHidden":64},[63],[56,14119,14121,14124,14127,14130,14133],{"className":14120},[68],[56,14122],{"className":14123,"style":3453},[72],[56,14125,1104],{"className":14126},[77,78],[56,14128],{"className":14129,"style":286},[187],[56,14131,552],{"className":14132},[290],[56,14134],{"className":14135,"style":286},[187],[56,14137,14139,14142],{"className":14138},[68],[56,14140],{"className":14141,"style":1100},[72],[56,14143,1104],{"className":14144},[77,78]," score matrix dominates memory at ",[56,14147,14149],{"className":14148},[59],[56,14150,14152],{"className":14151,"ariaHidden":64},[63],[56,14153,14155,14158,14161,14164,14193],{"className":14154},[68],[56,14156],{"className":14157,"style":13368},[72],[56,14159,7445],{"className":14160,"style":7444},[77,78],[56,14162,174],{"className":14163},[173],[56,14165,14167,14170],{"className":14166},[77],[56,14168,1104],{"className":14169},[77,78],[56,14171,14173],{"className":14172},[236],[56,14174,14176],{"className":14175},[240],[56,14177,14179],{"className":14178},[245],[56,14180,14182],{"className":14181,"style":3237},[249],[56,14183,14184,14187],{"style":2239},[56,14185],{"className":14186,"style":258},[257],[56,14188,14190],{"className":14189},[262,263,264,265],[56,14191,376],{"className":14192},[77,265],[56,14194,183],{"className":14195},[182],". ",[56,14198,14200],{"className":14199},[59],[56,14201,14203],{"className":14202,"ariaHidden":64},[63],[56,14204,14206,14209],{"className":14205},[68],[56,14207],{"className":14208,"style":4918},[72],[56,14210,14212],{"className":14211},[4922,4923],[56,14213,4928],{"className":14214},[77,4927],[11,14216,14217,14218,14251,14252,14285,14286,14339,14340,14375,14376,14429,14430,14471],{},"The crossover is at ",[56,14219,14221],{"className":14220},[59],[56,14222,14224,14242],{"className":14223,"ariaHidden":64},[63],[56,14225,14227,14230,14233,14236,14239],{"className":14226},[68],[56,14228],{"className":14229,"style":3217},[72],[56,14231,1104],{"className":14232},[77,78],[56,14234],{"className":14235,"style":188},[187],[56,14237,3227],{"className":14238},[192],[56,14240],{"className":14241,"style":188},[187],[56,14243,14245,14248],{"className":14244},[68],[56,14246],{"className":14247,"style":833},[72],[56,14249,548],{"className":14250},[77,78],": for ",[56,14253,14255],{"className":14254},[59],[56,14256,14258,14276],{"className":14257,"ariaHidden":64},[63],[56,14259,14261,14264,14267,14270,14273],{"className":14260},[68],[56,14262],{"className":14263,"style":2199},[72],[56,14265,1104],{"className":14266},[77,78],[56,14268],{"className":14269,"style":188},[187],[56,14271,7996],{"className":14272},[192],[56,14274],{"className":14275,"style":188},[187],[56,14277,14279,14282],{"className":14278},[68],[56,14280],{"className":14281,"style":833},[72],[56,14283,548],{"className":14284},[77,78]," the per-layer cost is dominated by\nthe ",[56,14287,14289],{"className":14288},[59],[56,14290,14292],{"className":14291,"ariaHidden":64},[63],[56,14293,14295,14298,14301,14304,14307,14336],{"className":14294},[68],[56,14296],{"className":14297,"style":13368},[72],[56,14299,7445],{"className":14300,"style":7444},[77,78],[56,14302,174],{"className":14303},[173],[56,14305,1104],{"className":14306},[77,78],[56,14308,14310,14313],{"className":14309},[77],[56,14311,548],{"className":14312},[77,78],[56,14314,14316],{"className":14315},[236],[56,14317,14319],{"className":14318},[240],[56,14320,14322],{"className":14321},[245],[56,14323,14325],{"className":14324,"style":3237},[249],[56,14326,14327,14330],{"style":2239},[56,14328],{"className":14329,"style":258},[257],[56,14331,14333],{"className":14332},[262,263,264,265],[56,14334,376],{"className":14335},[77,265],[56,14337,183],{"className":14338},[182]," projection and FFN work, but once ",[56,14341,14343],{"className":14342},[59],[56,14344,14346,14366],{"className":14345,"ariaHidden":64},[63],[56,14347,14349,14353,14356,14359,14363],{"className":14348},[68],[56,14350],{"className":14351,"style":14352},[72],"height:0.9592em;vertical-align:-0.2296em;",[56,14354,1104],{"className":14355},[77,78],[56,14357],{"className":14358,"style":188},[187],[56,14360,14362],{"className":14361},[192,4927],"≳",[56,14364],{"className":14365,"style":188},[187],[56,14367,14369,14372],{"className":14368},[68],[56,14370],{"className":14371,"style":833},[72],[56,14373,548],{"className":14374},[77,78]," the ",[56,14377,14379],{"className":14378},[59],[56,14380,14382],{"className":14381,"ariaHidden":64},[63],[56,14383,14385,14388,14391,14394,14423,14426],{"className":14384},[68],[56,14386],{"className":14387,"style":13368},[72],[56,14389,7445],{"className":14390,"style":7444},[77,78],[56,14392,174],{"className":14393},[173],[56,14395,14397,14400],{"className":14396},[77],[56,14398,1104],{"className":14399},[77,78],[56,14401,14403],{"className":14402},[236],[56,14404,14406],{"className":14405},[240],[56,14407,14409],{"className":14408},[245],[56,14410,14412],{"className":14411,"style":3237},[249],[56,14413,14414,14417],{"style":2239},[56,14415],{"className":14416,"style":258},[257],[56,14418,14420],{"className":14419},[262,263,264,265],[56,14421,376],{"className":14422},[77,265],[56,14424,548],{"className":14425},[77,78],[56,14427,183],{"className":14428},[182],"\nattention term takes over and grows quadratically. This single ",[56,14431,14433],{"className":14432},[59],[56,14434,14436],{"className":14435,"ariaHidden":64},[63],[56,14437,14439,14442],{"className":14438},[68],[56,14440],{"className":14441,"style":3237},[72],[56,14443,14445,14448],{"className":14444},[77],[56,14446,1104],{"className":14447},[77,78],[56,14449,14451],{"className":14450},[236],[56,14452,14454],{"className":14453},[240],[56,14455,14457],{"className":14456},[245],[56,14458,14460],{"className":14459,"style":3237},[249],[56,14461,14462,14465],{"style":2239},[56,14463],{"className":14464,"style":258},[257],[56,14466,14468],{"className":14467},[262,263,264,265],[56,14469,376],{"className":14470},[77,265]," is the\nreason context windows are expensive and the target of nearly every\nefficient-attention variant.",[4953,14473],{"hash":14474},"38040bac6fd1de2d5f8ae650fb1326d4806fae00522338df1a790bff3914a4ac",[11,14476,14477,14478,14481,14482,2042],{},"That is the architecture and its cost model. The same design turns out to be\nindifferent to what a token ",[21,14479,14480],{},"is"," — image patches, DNA bases, or program tokens\nall work — and the decoder-only half of it scaled into the large language models\nthat dominate current practice. Those applications, and the empirical scaling\nlaws that make scale pay off so reliably, continue in\n",[15,14483,14485],{"href":14484},"\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice","Transformers in Practice",[83,14487,14489],{"id":14488},"takeaways","Takeaways",[6011,14491,14492,14502,14615,14621,14640,14655,14852,14857],{},[6014,14493,5793,14494,14497,14498,14501],{},[51,14495,14496],{},"Transformer"," is attention plus position-wise feed-forward layers,\nstacked with ",[51,14499,14500],{},"residual + LayerNorm"," wrappers, with no recurrence or\nconvolution anywhere.",[6014,14503,14504,12171,14507,14558,14559,14562,14563,14614],{},[51,14505,14506],{},"Pre-norm",[56,14508,14510],{"className":14509},[59],[56,14511,14513,14531],{"className":14512,"ariaHidden":64},[63],[56,14514,14516,14519,14522,14525,14528],{"className":14515},[68],[56,14517],{"className":14518,"style":3453},[72],[56,14520,178],{"className":14521},[77,78],[56,14523],{"className":14524,"style":286},[187],[56,14526,291],{"className":14527},[290],[56,14529],{"className":14530,"style":286},[187],[56,14532,14534,14537,14540,14543,14549,14552,14555],{"className":14533},[68],[56,14535],{"className":14536,"style":160},[72],[56,14538,111],{"className":14539,"style":110},[77,78],[56,14541,174],{"className":14542},[173],[56,14544,14546],{"className":14545},[164],[56,14547,2800],{"className":14548},[77,168],[56,14550,174],{"className":14551},[173],[56,14553,178],{"className":14554},[77,78],[56,14556,4291],{"className":14557},[182],") leaves a clean identity path up\nthe stack, so deep Transformers train stably; ",[51,14560,14561],{},"post-norm","\n(",[56,14564,14566],{"className":14565},[59],[56,14567,14569,14596],{"className":14568,"ariaHidden":64},[63],[56,14570,14572,14575,14581,14584,14587,14590,14593],{"className":14571},[68],[56,14573],{"className":14574,"style":160},[72],[56,14576,14578],{"className":14577},[164],[56,14579,2800],{"className":14580},[77,168],[56,14582,174],{"className":14583},[173],[56,14585,178],{"className":14586},[77,78],[56,14588],{"className":14589,"style":286},[187],[56,14591,291],{"className":14592},[290],[56,14594],{"className":14595,"style":286},[187],[56,14597,14599,14602,14605,14608,14611],{"className":14598},[68],[56,14600],{"className":14601,"style":160},[72],[56,14603,111],{"className":14604,"style":110},[77,78],[56,14606,174],{"className":14607},[173],[56,14609,178],{"className":14610},[77,78],[56,14612,4291],{"className":14613},[182],") squeezes every residual through a norm and\nneeds warmup.",[6014,14616,14617,14620],{},[51,14618,14619],{},"Sinusoidal positional encoding"," gives each position a unique fingerprint\nacross a geometric band of frequencies, makes relative offsets a linear map,\nand extrapolates past the training length; learned tables and rotary (RoPE)\nencodings are the modern alternatives.",[6014,14622,5793,14623,14625,14626,14628,14629,14632,14633,14636,14637,2042],{},[51,14624,6561],{}," attends bidirectionally; the ",[51,14627,8049],{}," adds ",[51,14630,14631],{},"masked\nself-attention"," (causal, lower-triangular) and ",[51,14634,14635],{},"cross-attention"," to the\nencoder output, and reads out through ",[51,14638,14639],{},"linear + softmax",[6014,14641,5793,14642,14645,14646,14648,14649,14651,14652,14654],{},[51,14643,14644],{},"three families"," specialize the design: ",[51,14647,9960],{}," (BERT, masked\nLM, understanding), ",[51,14650,9968],{}," (GPT, causal LM, generation),\n",[51,14653,9976],{}," (T5, seq2seq, transduction).",[6014,14656,14657,14658,14851],{},"Causal masking realizes the autoregressive factorization ",[56,14659,14661],{"className":14660},[59],[56,14662,14664,14691,14796],{"className":14663,"ariaHidden":64},[63],[56,14665,14667,14670,14673,14676,14679,14682,14685,14688],{"className":14666},[68],[56,14668],{"className":14669,"style":160},[72],[56,14671,11],{"className":14672},[77,78],[56,14674,174],{"className":14675},[173],[56,14677,178],{"className":14678},[77,78],[56,14680,183],{"className":14681},[182],[56,14683],{"className":14684,"style":188},[187],[56,14686,193],{"className":14687},[192],[56,14689],{"className":14690,"style":188},[187],[56,14692,14694,14697,14738,14741,14744,14747,14787,14790,14793],{"className":14693},[68],[56,14695],{"className":14696,"style":4464},[72],[56,14698,14700,14703],{"className":14699},[164],[56,14701,9254],{"className":14702,"style":4472},[164,2432,4471],[56,14704,14706],{"className":14705},[236],[56,14707,14709,14730],{"className":14708},[240,241],[56,14710,14712,14727],{"className":14711},[245],[56,14713,14716],{"className":14714,"style":14715},[249],"height:0.1308em;",[56,14717,14718,14721],{"style":4488},[56,14719],{"className":14720,"style":258},[257],[56,14722,14724],{"className":14723},[262,263,264,265],[56,14725,7979],{"className":14726},[77,78,265],[56,14728,273],{"className":14729},[272],[56,14731,14733],{"className":14732},[245],[56,14734,14736],{"className":14735,"style":4510},[249],[56,14737],{},[56,14739],{"className":14740,"style":346},[187],[56,14742,11],{"className":14743},[77,78],[56,14745,174],{"className":14746},[173],[56,14748,14750,14753],{"className":14749},[77],[56,14751,178],{"className":14752},[77,78],[56,14754,14756],{"className":14755},[236],[56,14757,14759,14779],{"className":14758},[240,241],[56,14760,14762,14776],{"className":14761},[245],[56,14763,14765],{"className":14764,"style":8981},[249],[56,14766,14767,14770],{"style":316},[56,14768],{"className":14769,"style":258},[257],[56,14771,14773],{"className":14772},[262,263,264,265],[56,14774,7979],{"className":14775},[77,78,265],[56,14777,273],{"className":14778},[272],[56,14780,14782],{"className":14781},[245],[56,14783,14785],{"className":14784,"style":280},[249],[56,14786],{},[56,14788],{"className":14789,"style":188},[187],[56,14791,9010],{"className":14792},[192],[56,14794],{"className":14795,"style":188},[187],[56,14797,14799,14802,14848],{"className":14798},[68],[56,14800],{"className":14801,"style":160},[72],[56,14803,14805,14808],{"className":14804},[77],[56,14806,178],{"className":14807},[77,78],[56,14809,14811],{"className":14810},[236],[56,14812,14814,14840],{"className":14813},[240,241],[56,14815,14817,14837],{"className":14816},[245],[56,14818,14820],{"className":14819,"style":8981},[249],[56,14821,14822,14825],{"style":316},[56,14823],{"className":14824,"style":258},[257],[56,14826,14828],{"className":14827},[262,263,264,265],[56,14829,14831,14834],{"className":14830},[77,265],[56,14832,7996],{"className":14833},[192,265],[56,14835,7979],{"className":14836},[77,78,265],[56,14838,273],{"className":14839},[272],[56,14841,14843],{"className":14842},[245],[56,14844,14846],{"className":14845,"style":9064},[249],[56,14847],{},[56,14849,183],{"className":14850},[182]," in a single parallel forward pass.",[6014,14853,5793,14854,14856],{},[51,14855,10001],{}," view reads the stack as a fixed-width bus each sublayer\nreads from and adds back into, never overwriting — which is why contributions\ncompose so cleanly.",[6014,14858,14859,14862,14863,14907,14908,14952,14953,15008],{},[51,14860,14861],{},"Two-thirds"," of the parameters live in the FFN (",[56,14864,14866],{"className":14865},[59],[56,14867,14869],{"className":14868,"ariaHidden":64},[63],[56,14870,14872,14875,14878],{"className":14871},[68],[56,14873],{"className":14874,"style":3237},[72],[56,14876,6691],{"className":14877},[77],[56,14879,14881,14884],{"className":14880},[77],[56,14882,548],{"className":14883},[77,78],[56,14885,14887],{"className":14886},[236],[56,14888,14890],{"className":14889},[240],[56,14891,14893],{"className":14892},[245],[56,14894,14896],{"className":14895,"style":3237},[249],[56,14897,14898,14901],{"style":2239},[56,14899],{"className":14900,"style":258},[257],[56,14902,14904],{"className":14903},[262,263,264,265],[56,14905,376],{"className":14906},[77,265]," vs ",[56,14909,14911],{"className":14910},[59],[56,14912,14914],{"className":14913,"ariaHidden":64},[63],[56,14915,14917,14920,14923],{"className":14916},[68],[56,14918],{"className":14919,"style":3237},[72],[56,14921,142],{"className":14922},[77],[56,14924,14926,14929],{"className":14925},[77],[56,14927,548],{"className":14928},[77,78],[56,14930,14932],{"className":14931},[236],[56,14933,14935],{"className":14934},[240],[56,14936,14938],{"className":14937},[245],[56,14939,14941],{"className":14940,"style":3237},[249],[56,14942,14943,14946],{"style":2239},[56,14944],{"className":14945,"style":258},[257],[56,14947,14949],{"className":14948},[262,263,264,265],[56,14950,376],{"className":14951},[77,265]," per layer),\nwhile compute is dominated by the ",[51,14954,14955],{},[56,14956,14958],{"className":14957},[59],[56,14959,14961],{"className":14960,"ariaHidden":64},[63],[56,14962,14964,14967,14970,14973,15002,15005],{"className":14963},[68],[56,14965],{"className":14966,"style":13368},[72],[56,14968,7445],{"className":14969,"style":7444},[77,78],[56,14971,174],{"className":14972},[173],[56,14974,14976,14979],{"className":14975},[77],[56,14977,1104],{"className":14978},[77,78],[56,14980,14982],{"className":14981},[236],[56,14983,14985],{"className":14984},[240],[56,14986,14988],{"className":14987},[245],[56,14989,14991],{"className":14990,"style":3237},[249],[56,14992,14993,14996],{"style":2239},[56,14994],{"className":14995,"style":258},[257],[56,14997,14999],{"className":14998},[262,263,264,265],[56,15000,376],{"className":15001},[77,265],[56,15003,548],{"className":15004},[77,78],[56,15006,183],{"className":15007},[182]," attention term — the\nquadratic cost that bounds context length.",[15010,15011,15014,15019],"section",{"className":15012,"dataFootnotes":6},[15013],"footnotes",[83,15015,15018],{"className":15016,"id":41},[15017],"sr-only","Footnotes",[15020,15021,15022,15039,15062,15075,15088],"ol",{},[6014,15023,15025,6656,15028,15031,15032],{"id":15024},"user-content-fn-chollet-transformer",[51,15026,15027],{},"Chollet",[21,15029,15030],{},"Deep Learning with Python",", Ch. 11 — The Transformer Architecture: assembling embeddings, positional encoding, stacked attention + FFN sublayers, and the read-out head into the full model. ",[15,15033,15038],{"href":15034,"ariaLabel":15035,"className":15036,"dataFootnoteBackref":6},"#user-content-fnref-chollet-transformer","Back to reference 1",[15037],"data-footnote-backref","↩",[6014,15040,15042,6656,15045,15048,15049,15054,15055],{"id":15041},"user-content-fn-gf-norm",[51,15043,15044],{},"Goodfellow",[21,15046,15047],{},"Deep Learning",", §8.7.1 — Batch\u002Fnormalization and §8.7.5 residual connections: why a clean identity path (here pre-norm) stabilizes optimization of very deep stacks. ",[15,15050,15038],{"href":15051,"ariaLabel":15052,"className":15053,"dataFootnoteBackref":6},"#user-content-fnref-gf-norm","Back to reference 2",[15037]," ",[15,15056,15038,15060],{"href":15057,"ariaLabel":15058,"className":15059,"dataFootnoteBackref":6},"#user-content-fnref-gf-norm-2","Back to reference 2-2",[15037],[35,15061,376],{},[6014,15063,15065,6656,15067,15069,15070],{"id":15064},"user-content-fn-chollet-decoder",[51,15066,15027],{},[21,15068,15030],{},", Ch. 11 — The Transformer decoder: causal (masked) self-attention plus cross-attention to the encoder output for sequence-to-sequence generation. ",[15,15071,15038],{"href":15072,"ariaLabel":15073,"className":15074,"dataFootnoteBackref":6},"#user-content-fnref-chollet-decoder","Back to reference 3",[15037],[6014,15076,15078,6656,15080,15082,15083],{"id":15077},"user-content-fn-chollet-families",[51,15079,15027],{},[21,15081,15030],{},", Ch. 11 — encoder-only vs. decoder-only vs. encoder–decoder usage: how the masking and objective pick out BERT-style, GPT-style, and T5-style models. ",[15,15084,15038],{"href":15085,"ariaLabel":15086,"className":15087,"dataFootnoteBackref":6},"#user-content-fnref-chollet-families","Back to reference 4",[15037],[6014,15089,15091,6656,15093,15095,15096],{"id":15090},"user-content-fn-gf-attention-mem",[51,15092,15044],{},[21,15094,15047],{},", §10.11 — Explicit Memory & attention: the content-addressed read whose cost scales quadratically in sequence length, the bottleneck behind efficient-attention work. ",[15,15097,15038],{"href":15098,"ariaLabel":15099,"className":15100,"dataFootnoteBackref":6},"#user-content-fnref-gf-attention-mem","Back to reference 5",[15037],[15102,15103,15104],"style",{},"html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark-mode .shiki span {color: var(--shiki-dark-mode);background: var(--shiki-dark-mode-bg);font-style: var(--shiki-dark-mode-font-style);font-weight: var(--shiki-dark-mode-font-weight);text-decoration: var(--shiki-dark-mode-text-decoration);}html.dark-mode .shiki span {color: var(--shiki-dark-mode);background: var(--shiki-dark-mode-bg);font-style: var(--shiki-dark-mode-font-style);font-weight: var(--shiki-dark-mode-font-weight);text-decoration: var(--shiki-dark-mode-text-decoration);}",{"title":6,"searchDepth":9835,"depth":9835,"links":15106},[15107,15108,15109,15110,15111,15112,15113,15114,15115,15116,15117],{"id":85,"depth":9835,"text":86},{"id":4958,"depth":9835,"text":4959},{"id":6353,"depth":9835,"text":6354},{"id":7807,"depth":9835,"text":7808},{"id":8082,"depth":9835,"text":8083},{"id":8131,"depth":9835,"text":8132},{"id":9877,"depth":9835,"text":9878},{"id":9994,"depth":9835,"text":9995},{"id":10625,"depth":9835,"text":10626},{"id":14488,"depth":9835,"text":14489},{"id":41,"depth":9835,"text":15018},[],"computer-science","The previous lesson built the\nattention mechanism:\nscaled dot-product attention, multi-head projection, and the positional\nencoding that restores order to a permutation-equivariant operation. That is the\noperation. This lesson assembles the architecture: how those operations\nstack into the encoder–decoder of Attention Is All You Need, how the stack\nsplits into the three families that dominate modern practice, and where its\nparameters and its quadratic cost actually live.1",false,"md",{"moduleNumber":9853,"lessonNumber":9859,"order":15124},506,"Architectures",true,"\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture",[],"---\ntitle: The Transformer Architecture\nmodule: Architectures\nmoduleNumber: 5\nlessonNumber: 6\norder: 506\nsummary: >\n  The Transformer is the architecture built around the attention\n  mechanism. This first part assembles the full encoder–decoder of \"Attention Is\n  All You Need\" — embeddings and positional encoding, stacked self-attention and\n  feed-forward sublayers wrapped in residual connections and LayerNorm, masked\n  decoding and cross-attention — works through causal masking and the three modern\n  families (encoder-only, decoder-only, encoder–decoder), and accounts for where\n  the parameters and the $O(n^2)$ compute actually go.\ntopics: [Architectures]\nsources:\n  - book: Goodfellow\n    ref: \"§10.11 — Explicit Memory & Attention (the Transformer postdates the 2016 text)\"\n  - book: Chollet\n    ref: \"Ch. 11 — Deep Learning for Text; The Transformer Architecture\"\n---\n\nThe previous lesson built the\n[attention mechanism](\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers):\nscaled dot-product attention, multi-head projection, and the positional\nencoding that restores order to a permutation-equivariant operation. That is the\n_operation_. This lesson assembles the _architecture_: how those operations\nstack into the encoder–decoder of \"Attention Is All You Need,\" how the stack\nsplits into the three families that dominate modern practice, and where its\nparameters and its quadratic cost actually live.[^chollet-transformer]\n> **Definition (Transformer).** A sequence model built entirely from attention\n> and position-wise feed-forward layers, with no recurrence or convolution.\n> Token embeddings plus positional encodings feed a stack of $N$ identical\n> layers; each layer interleaves multi-head attention with a position-wise MLP,\n> and wraps every sublayer in a residual connection followed by layer\n> normalization. A linear projection and softmax read the top of the stack out\n> to a distribution over the vocabulary.\n\n## The sublayer wrapper\n\nThe atom of the architecture is not a layer but a **sublayer wrapper**: a\nresidual skip around a function $f$, followed by\n[layer normalization](\u002Fdeep-learning\u002Fregularization\u002Fnormalization). Every\nattention block and every feed-forward block in the entire model is wrapped this\nway, so we fix the convention before stacking anything.\n\n> **Definition (Position-wise feed-forward network).** A two-layer MLP applied\n> independently and identically to every position, with an expansion factor of\n> typically $4$:\n> $$\n> \\FFN(x) = \\parens{\\ReLU(x W_1 + b_1)} W_2 + b_2,\n> \\qquad W_1 \\in \\mathbb{R}^{d \\times d_{\\text{ff}}},\\; W_2 \\in \\mathbb{R}^{d_{\\text{ff}} \\times d},\n> $$\n> with $d_{\\text{ff}} = 4d$ the standard inner width. Attention mixes\n> _across_ positions; the FFN is the only nonlinearity acting _within_ a\n> position. Because its weights are shared across positions, it amounts to a\n> $1 \\times 1$ convolution over the sequence.\n\nThe expansion is not arbitrary. The FFN takes each token's $d$-vector, projects\nit _up_ into a wider $4d$ space, applies a pointwise nonlinearity there, and\nprojects _back down_ to $d$. The wide hidden layer is where the per-token\ncomputation happens: it gives the nonlinearity enough room to compute many\nindependent features of the token before compressing the result. The original\npaper used $\\ReLU$; most modern stacks swap in $\\GELU$\n(a smooth gate $x \\cdot \\Phi(x)$, with $\\Phi$ the standard-normal CDF) or a gated\nvariant like $\\SwiGLU$, which lowers loss at fixed width\nfor reasons that remain partly empirical.\n\nTrack the shapes explicitly. A batch of $B$ sequences of length $n$ enters as a\ntensor of shape $(B, n, d)$. Every operation below preserves the batch and\nsequence axes and acts only on the last (feature) axis:\n\n$$\n\\underbrace{(B, n, d)}_{\\text{input}}\n\\;\\xrightarrow{\\,W_1 \\in \\mathbb{R}^{d \\times 4d}\\,}\\;\n\\underbrace{(B, n, 4d)}_{\\text{hidden}}\n\\;\\xrightarrow{\\,\\ReLU\\,}\\;\n(B, n, 4d)\n\\;\\xrightarrow{\\,W_2 \\in \\mathbb{R}^{4d \\times d}\\,}\\;\n\\underbrace{(B, n, d)}_{\\text{output}} .\n$$\n\nThe same $W_1, W_2$ apply at every one of the $B \\times n$ positions — the FFN\ncarries no positional index and no cross-token interaction, which is what makes it\na position-wise map.\n\n**Layer normalization** is the other half of the wrapper, so its statistics\nmatter for what follows. Given a single token vector $x \\in \\mathbb{R}^{d}$,\nLayerNorm computes the mean and variance _over the $d$ feature entries of that one\ntoken_ — not over the batch, not over the sequence — and standardizes:\n\n$$\n\\mu = \\frac{1}{d}\\sum_{k=1}^{d} x_k,\n\\qquad\n\\sigma^2 = \\frac{1}{d}\\sum_{k=1}^{d} (x_k - \\mu)^2,\n\\qquad\n\\LN(x) = \\gamma \\odot \\frac{x - \\mu}{\\sqrt{\\sigma^2 + \\epsilon}} + \\beta,\n$$\n\nwith learned per-feature scale $\\gamma \\in \\mathbb{R}^{d}$ and shift\n$\\beta \\in \\mathbb{R}^{d}$ (initialized to $1$ and $0$), and $\\epsilon \\approx\n10^{-5}$ for numerical safety. Because the reduction is per-token, LayerNorm is\nindependent of batch size and of the other positions — it behaves identically at\ntraining and inference and needs no running statistics — the reason it\nreplaced BatchNorm for variable-length sequence models.[^gf-norm] The single\naddition it contributes is $2d$ parameters ($\\gamma$ and $\\beta$) per LayerNorm.\n\nThe two wrapper styles differ only in **where** the normalization sits relative\nto the residual sum.\n\n| Style | Sublayer formula | Residual path |\n| --- | --- | --- |\n| Post-norm (original) | $\\LN\\!\\parens{x + f(x)}$ | passes through LN at every layer |\n| Pre-norm (modern) | $x + f\\!\\parens{\\LN(x)}$ | clean identity, never normalized |\n\nThe distinction looks cosmetic but governs whether a deep stack trains at all.[^gf-norm]\n\n> **Theorem (Pre-norm residual identity).** Under pre-norm wrapping, the output\n> of an $N$-layer stack expands as\n> $$\n> z_N = z_0 + \\sum_{\\ell=1}^{N} f_\\ell\\!\\parens{\\LN(z_{\\ell-1})},\n> $$\n> so the input $z_0$ reaches the top through an unbroken identity path, and the\n> gradient $\\partial z_N \u002F \\partial z_0$ contains a term equal to $1$\n> independent of depth.\n\n> **Proof.** Pre-norm defines $z_\\ell = z_{\\ell-1} + f_\\ell(\\LN(z_{\\ell-1}))$.\n> Unrolling the recurrence from $\\ell = 1$ to $N$ telescopes the residual sums,\n> giving $z_N = z_0 + \\sum_{\\ell} f_\\ell(\\LN(z_{\\ell-1}))$.\n> Differentiating, $\\partial z_N\u002F\\partial z_0 = I + \\sum_\\ell \\partial\n> f_\\ell\u002F\\partial z_0$; the leading $I$ is a depth-independent identity, so no\n> product of Jacobians can drive the gradient to zero on the skip path. $\\qed$\n\nPost-norm breaks that identity: each residual sum is squeezed back through a\nLayerNorm, so the gradient path is a _product_ of $N$ normalization Jacobians and\ncan vanish or explode with depth, which is why post-norm Transformers need a\nlearning-rate warmup and pre-norm ones largely do not.\n\n$$\n% caption: Post-norm (left) routes every skip through LayerNorm; pre-norm (right) normalizes only\n% the branch input, leaving a clean identity highway (blue) up the stack.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize,\n  blk\u002F.style={draw, minimum width=24mm, minimum height=8mm, align=center},\n  op\u002F.style={draw, circle, inner sep=0pt, minimum size=6mm}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\definecolor{green}{HTML}{1F9D4D}\n  % ---- post-norm ----\n  \\node (pin)  at (0,0)   {\\texttt{input x}};\n  \\node[blk] (pf) at (0,1.5) {\\texttt{sublayer f}};\n  \\node[op]  (pa) at (0,3.0) {$+$};\n  \\node[blk, draw=green, text=green] (pn) at (0,4.5) {\\texttt{LayerNorm}};\n  \\node (pout) at (0,6.0) {\\texttt{output}};\n  \\draw[->, thick] (pin) -- (pf);\n  \\draw[->, thick] (pf) -- (pa);\n  \\draw[->, thick] (pa) -- (pn);\n  \\draw[->, thick] (pn) -- (pout);\n  \\draw[->, acc, thick] (1.3,0.2) .. controls (2.4,1.0) and (2.4,2.2) .. (1.3,3.0)\n    node[pos=0.5, right, text=acc] {\\texttt{skip}};\n  \\node[font=\\footnotesize] at (0,-0.8) {\\texttt{post-norm}};\n  % ---- pre-norm ----\n  \\begin{scope}[xshift=6.6cm]\n  \\node (qin)  at (0,0)   {\\texttt{input x}};\n  \\node[blk, draw=green, text=green] (qn) at (0,1.5) {\\texttt{LayerNorm}};\n  \\node[blk] (qf) at (0,3.0) {\\texttt{sublayer f}};\n  \\node[op]  (qa) at (0,4.5) {$+$};\n  \\node (qout) at (0,6.0) {\\texttt{output}};\n  \\draw[->, thick] (qin) -- (qn);\n  \\draw[->, thick] (qn) -- (qf);\n  \\draw[->, thick] (qf) -- (qa);\n  \\draw[->, thick] (qa) -- (qout);\n  \\draw[->, acc, thick] (1.3,0.2) .. controls (2.6,1.6) and (2.6,3.0) .. (1.3,4.5)\n    node[pos=0.5, right, text=acc] {\\texttt{identity}};\n  \\node[font=\\footnotesize] at (0,-0.8) {\\texttt{pre-norm}};\n  \\end{scope}\n\\end{tikzpicture}\n$$\n\n## Positional encoding\n\nAttention is **permutation-equivariant**: shuffle the input tokens and the output\nset is the same, merely reordered. That is fatal for language, where \"dog bites\nman\" and \"man bites dog\" are different sentences built from identical tokens. The\nattention operator has no notion of position, so order has to be injected into the\ninputs before the first layer. The original Transformer adds a fixed **sinusoidal\npositional encoding** to the token embeddings.\n\n> **Definition (Sinusoidal positional encoding).** For position $\\text{pos} \\in\n> \\{0, 1, \\dots, n-1\\}$ and feature index $i \\in \\{0, \\dots, d\u002F2 - 1\\}$, the\n> encoding fills even and odd feature slots with a sine\u002Fcosine pair whose\n> frequency decreases geometrically across the width:\n> $$\n> \\PE(\\text{pos}, 2i) = \\sin\\!\\parens{\\frac{\\text{pos}}{10000^{\\,2i\u002Fd}}},\n> \\qquad\n> \\PE(\\text{pos}, 2i+1) = \\cos\\!\\parens{\\frac{\\text{pos}}{10000^{\\,2i\u002Fd}}}.\n> $$\n> The vector $\\PE(\\text{pos}) \\in \\mathbb{R}^{d}$ is added to the\n> token embedding at that position, giving the layer-$0$ input $z_0 = \\text{Embed}(x) +\n> \\PE$.\n\nThe $10000^{2i\u002Fd}$ denominator sets the **wavelength** of each feature: the lowest\nfeature ($i = 0$) oscillates with period $2\\pi$ tokens, and the highest ($i =\nd\u002F2-1$) with period $2\\pi \\cdot 10000$ tokens. Low-frequency channels change slowly\nand encode coarse, long-range position; high-frequency channels distinguish\nadjacent tokens. Together they give each position a unique fingerprint across a\ngeometric band of scales, the same multi-resolution idea a place-value numeral uses\nto name any integer with a fixed set of digits.\n\n$$\n% caption: Sinusoidal positional encoding as a frequency band. Each feature slot $i$ carries a\n% sine\u002Fcosine of period $2\\pi\\cdot 10000^{2i\u002Fd}$: low-$i$ channels (top) oscillate fast and separate\n% adjacent tokens; high-$i$ channels (bottom) oscillate slowly and encode coarse position.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize, x=1cm, y=1cm]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\draw[->, thick] (0,-3.0) -- (7.2,-3.0) node[below right, font=\\footnotesize] {\\texttt{position}};\n  % high frequency (small i)\n  \\draw[thick] plot[domain=0:6.6, samples=120] (\\x, {0.45*sin(\\x*260)});\n  \\node[anchor=west, font=\\footnotesize] at (6.7,0) {\\texttt{i small (fast)}};\n  % mid frequency\n  \\draw[thick] plot[domain=0:6.6, samples=120] (\\x, {-1.2+0.45*sin(\\x*90)});\n  \\node[anchor=west, font=\\footnotesize] at (6.7,-1.2) {\\texttt{i mid}};\n  % low frequency (large i)\n  \\draw[thick] plot[domain=0:6.6, samples=120] (\\x, {-2.4+0.45*sin(\\x*30)});\n  \\node[anchor=west, font=\\footnotesize] at (6.7,-2.4) {\\texttt{i large (slow)}};\n\\end{tikzpicture}\n$$\n\nTwo properties make the sinusoidal choice more than a lookup table:\n\n- **Relative position is linear.** For any fixed offset $k$, the encoding at\n  $\\text{pos} + k$ is a fixed linear function (a rotation, from the angle-sum\n  identities) of the encoding at $\\text{pos}$. A single learned projection inside\n  an attention head can therefore read _relative_ distance, not just absolute\n  index, which is what a language model actually needs.\n- **Length extrapolation.** Because the formula is defined for every real\n  $\\text{pos}$, a model can be evaluated on sequences longer than any it saw in\n  training without a new parameter — the encoding simply continues.\n\nThe alternative is a **learned positional embedding**: a trainable table\n$E_{\\text{pos}} \\in \\mathbb{R}^{n_{\\max} \\times d}$ with one row per position, added\njust like a word embedding. Learned embeddings match or slightly beat sinusoids on\nin-distribution data and are the common choice for encoder-only models (BERT) and\nViT, but they cap the context at the table's row count $n_{\\max}$ and cannot\nextrapolate past it. Modern decoder-only models mostly use neither and instead\nrotate the queries and keys inside attention (rotary embeddings, RoPE), which keeps\nthe linear-relative property while removing the additive table entirely.\n\n## One encoder layer\n\nAn encoder layer is two wrapped sublayers in series: multi-head self-attention,\nthen a position-wise FFN. With pre-norm wrapping and an input $x$,\n\n$$\na = x + \\MHA\\!\\parens{\\LN(x)},\n\\qquad\ny = a + \\FFN\\!\\parens{\\LN(a)}.\n$$\n\nThe self-attention is _unrestricted_: every position attends to every other,\nso each output position is a content-weighted summary of the whole input. This\nis the right behavior for an _encoder_: the entire sequence is available and\nthere is no causality constraint.\n\nEvery tensor in the block has the same shape $(B, n, d)$: the width $d$ is the\ninvariant of the residual stream, so a layer's output plugs into the next layer's\ninput without any reshaping. Trace one block for a concrete configuration\n$d = 512$, $h = 8$ heads (so head width $d_k = d\u002Fh = 64$), $d_{\\text{ff}} = 2048$,\ninput $(B, n, 512)$:\n\n| Step | Operation | Output shape |\n| --- | --- | --- |\n| 0 | input $x$ | $(B, n, 512)$ |\n| 1 | $\\LN(x)$ (per-token, over the $512$ features) | $(B, n, 512)$ |\n| 2 | project to $Q, K, V$, split into $8$ heads | $(B, 8, n, 64)$ each |\n| 3 | scores $QK^\\top\u002F\\sqrt{64}$, softmax over keys | $(B, 8, n, n)$ |\n| 4 | weighted values, concat heads | $(B, n, 512)$ |\n| 5 | output projection $W_O$, add residual $x +$ | $(B, n, 512)$ |\n| 6 | $\\LN$, up-project to $d_{\\text{ff}}$ | $(B, n, 2048)$ |\n| 7 | ReLU, down-project, add residual | $(B, n, 512)$ |\n\nThe only place the shape swells is the $(B, 8, n, n)$ score tensor in step 3 and\nthe $(B, n, 2048)$ FFN hidden in step 6 — the two costs, quadratic-in-$n$ and\nwide-FFN, that the accounting section makes precise.\n\n$$\n% caption: Shapes through one pre-norm encoder block ($d=512$, $h=8$, $d_k=64$, $d_{ff}=2048$). The\n% width $d$ is the residual-stream invariant; only the attention scores ($n\\times n$) and FFN hidden\n% ($4d$ wide) inflate before collapsing back to $(B,n,d)$.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize,\n  bus\u002F.style={draw=acc, text=acc, thick, minimum width=22mm, minimum height=7mm, align=center},\n  wide\u002F.style={draw, minimum width=22mm, minimum height=7mm, align=center, fill=black!8},\n  sh\u002F.style={font=\\scriptsize, text=black}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node[bus] (x)  at (0,0)   {\\texttt{input}};\n  \\node[wide] (sc) at (0,1.7) {\\texttt{attn scores}};\n  \\node[bus] (a)  at (0,3.4) {\\texttt{+ residual}};\n  \\node[wide] (ff) at (0,5.1) {\\texttt{FFN hidden}};\n  \\node[bus] (y)  at (0,6.8) {\\texttt{+ residual}};\n  \\draw[->, thick] (x) -- (sc);\n  \\draw[->, thick] (sc) -- (a);\n  \\draw[->, thick] (a) -- (ff);\n  \\draw[->, thick] (ff) -- (y);\n  \\node[sh, anchor=west] at (1.5,0)   {\\texttt{(B, n, 512)}};\n  \\node[sh, anchor=west] at (1.5,1.7) {\\texttt{(B, 8, n, n)}};\n  \\node[sh, anchor=west] at (1.5,3.4) {\\texttt{(B, n, 512)}};\n  \\node[sh, anchor=west] at (1.5,5.1) {\\texttt{(B, n, 2048)}};\n  \\node[sh, anchor=west] at (1.5,6.8) {\\texttt{(B, n, 512)}};\n\\end{tikzpicture}\n$$\n\n$$\n% caption: One encoder layer: multi-head self-attention then a position-wise FFN, each wrapped in\n% add-and-norm. The blue arcs are the residual connections around each sublayer.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize,\n  blk\u002F.style={draw, minimum width=44mm, minimum height=9mm, align=center},\n  an\u002F.style={draw, minimum width=44mm, minimum height=7mm, align=center, fill=black!8}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\node (in)  at (0,0)   {\\texttt{input (embeddings)}};\n  \\node[blk, draw=acc, text=acc, thick] (mha) at (0,1.5) {\\texttt{multi-head self-attention}};\n  \\node[an]  (an1) at (0,2.9) {\\texttt{add \\& norm}};\n  \\node[blk, draw=acc, text=acc, thick] (ffn) at (0,4.4) {\\texttt{feed-forward (FFN)}};\n  \\node[an]  (an2) at (0,5.8) {\\texttt{add \\& norm}};\n  \\node (out) at (0,7.1) {\\texttt{output (to next layer)}};\n  \\draw[->, thick] (in) -- (mha);\n  \\draw[->, thick] (mha) -- (an1);\n  \\draw[->, thick] (an1) -- (ffn);\n  \\draw[->, thick] (ffn) -- (an2);\n  \\draw[->, thick] (an2) -- (out);\n  \\draw[->, acc, thick] (2.5,0.25) .. controls (3.9,1.0) and (3.9,2.2) .. (2.5,2.9)\n    node[pos=0.5, right, text=acc] {residual};\n  \\draw[->, acc, thick] (2.5,3.15) .. controls (3.9,3.9) and (3.9,5.1) .. (2.5,5.8)\n    node[pos=0.5, right, text=acc] {residual};\n\\end{tikzpicture}\n$$\n\n## One decoder layer\n\nA decoder layer has _three_ wrapped sublayers. It must generate one token at a\ntime without access to tokens it has not yet produced, and it must read the\nencoder. Two additions handle these requirements.\n\n- **Masked self-attention.** Before the softmax, the decoder sets the score\n  $S_{ij} = -\\infty$ for every $j > i$, forbidding position $i$ from attending\n  to any later position. Generation stays **causal**: token $t$ depends only on\n  tokens $\u003C t$.\n- **Cross-attention.** A middle sublayer draws its queries from the decoder\n  state but its keys and values from the encoder's output. This is the channel\n  through which a generated token reads the entire source sequence; in\n  translation it is how each output word reads the sentence being translated.[^chollet-decoder]\n\n| Sublayer | Queries from | Keys \u002F values from | Mask |\n| --- | --- | --- | --- |\n| Masked self-attention | decoder | decoder | causal (lower-triangular) |\n| Cross-attention | decoder | encoder output | none |\n| Feed-forward | — | — | — |\n\n## The full encoder–decoder\n\nThe complete Transformer stacks $N$ encoder layers and $N$ decoder layers, feeds\nboth stacks token embeddings plus positional encodings, and routes the encoder's\nfinal output into the cross-attention sublayer of _every_ decoder layer. A linear\nprojection and softmax convert the decoder's top state into a distribution over\nthe vocabulary.\n\n$$\n% caption: The full encoder–decoder Transformer. The encoder (left) reads the source; its output\n% feeds cross-attention (green) in every decoder layer, which masks self-attention and reads out\n% through linear-plus-softmax.\n\\begin{tikzpicture}[>=stealth, font=\\scriptsize,\n  sub\u002F.style={draw, minimum width=30mm, minimum height=6mm, align=center},\n  an\u002F.style={draw, minimum width=30mm, minimum height=5mm, align=center, fill=black!8},\n  emb\u002F.style={draw, minimum width=30mm, minimum height=6mm, align=center}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\definecolor{green}{HTML}{1F9D4D}\n  \\definecolor{red}{HTML}{C0392B}\n  % ===================== ENCODER (left) =====================\n  \\draw[black, dashed] (-1.85,2.0) rectangle (1.85,6.1);\n  \\node[emb] (esrc) at (0,0) {\\texttt{source tokens}};\n  \\node[emb, draw=acc, text=acc] (eemb) at (0,1.0) {\\texttt{embedding + pos. enc.}};\n  \\node[sub, draw=acc, text=acc, thick] (esa) at (0,2.5) {\\texttt{self-attention}};\n  \\node[an] (ean1) at (0,3.5) {\\texttt{add \\& norm}};\n  \\node[sub, draw=acc, text=acc, thick] (eff) at (0,4.6) {\\texttt{feed-forward}};\n  \\node[an] (ean2) at (0,5.6) {\\texttt{add \\& norm}};\n  \\node[black] (etop) at (0,6.6) {\\texttt{N layers (encoder)}};\n  \\draw[->, thick] (esrc) -- (eemb);\n  \\draw[->, thick] (eemb) -- (esa);\n  \\draw[->, thick] (esa) -- (ean1);\n  \\draw[->, thick] (ean1) -- (eff);\n  \\draw[->, thick] (eff) -- (ean2);\n  \\draw[->, thick] (ean2) -- (etop);\n  % ===================== DECODER (right) =====================\n  \\begin{scope}[xshift=6.6cm]\n  \\draw[black, dashed] (-1.85,2.0) rectangle (1.85,8.2);\n  \\node[emb] (dtgt) at (0,0) {\\texttt{target (shifted)}};\n  \\node[emb, draw=acc, text=acc] (demb) at (0,1.0) {\\texttt{embedding + pos. enc.}};\n  \\node[sub, draw=red, text=red, thick] (dsa) at (0,2.5) {\\texttt{masked self-attention}};\n  \\node[an] (dan1) at (0,3.5) {\\texttt{add \\& norm}};\n  \\node[sub, draw=green, text=green, thick] (dca) at (0,4.6) {\\texttt{cross-attention}};\n  \\node[an] (dan2) at (0,5.6) {\\texttt{add \\& norm}};\n  \\node[sub, draw=acc, text=acc, thick] (dff) at (0,6.7) {\\texttt{feed-forward}};\n  \\node[an] (dan3) at (0,7.7) {\\texttt{add \\& norm}};\n  \\node[sub, draw=acc, text=acc] (lin) at (0,8.9) {\\texttt{linear + softmax}};\n  \\node (dout) at (0,9.9) {\\texttt{output probabilities}};\n  \\draw[->, thick] (dtgt) -- (demb);\n  \\draw[->, thick] (demb) -- (dsa);\n  \\draw[->, thick] (dsa) -- (dan1);\n  \\draw[->, thick] (dan1) -- (dca);\n  \\draw[->, thick] (dca) -- (dan2);\n  \\draw[->, thick] (dan2) -- (dff);\n  \\draw[->, thick] (dff) -- (dan3);\n  \\draw[->, thick] (dan3) -- (lin);\n  \\draw[->, thick] (lin) -- (dout);\n  \\node[black, anchor=west] at (1.95,8.5) {\\texttt{N layers (decoder)}};\n  \\end{scope}\n  % ===================== CROSS-ATTENTION ROUTING =====================\n  \\draw[->, green, thick] (1.85,5.9) .. controls (3.0,5.9) and (3.7,4.6) .. (4.75,4.6)\n    node[pos=0.5, above, text=green, font=\\footnotesize] {\\texttt{keys, values}};\n\\end{tikzpicture}\n$$\n\nThe asymmetry is the whole point. The encoder reads bidirectionally because it\nsees the input all at once; the decoder reads causally because it produces the\noutput left to right. Cross-attention is the only place the two streams meet.\n\n## Causal masking in detail\n\nMasking is implemented additively, before the softmax. Define a mask matrix\n$M \\in \\mathbb{R}^{n \\times n}$ with $M_{ij} = 0$ for $j \\le i$ and $M_{ij} =\n-\\infty$ for $j > i$, and add it to the raw scores:\n\n$$\nA = \\softmax\\!\\parens{\\frac{QK^\\top}{\\sqrt{d_k}} + M},\n\\qquad\nA_{ij} = 0 \\text{ for all } j > i .\n$$\n\nThe $-\\infty$ entries become $e^{-\\infty} = 0$ after exponentiation, so the\nsoftmax renormalizes over only the allowed (lower-triangular) positions. The\nresult is **row-causal**: row $i$ of $A$ has support only on columns $1$ through\n$i$.\n\n> **Theorem (Autoregressive factorization).** With causal masking, the decoder\n> computes $p(x_t \\mid x_{\u003Ct})$ at every position $t$ using only inputs $x_1,\n> \\dots, x_{t-1}$, so a single forward pass yields every factor of the chain rule\n> $p(x) = \\prod_{t=1}^{n} p(x_t \\mid x_{\u003Ct})$ in parallel.\n\n> **Proof.** Each decoder output at position $t$ is a function of the masked\n> self-attention output at $t$, whose attention row has zero weight on all\n> $j > t$ by construction of $M$. By induction over the stacked layers, every\n> intermediate representation at position $t$ depends only on positions $\\le t$;\n> the read-out head at $t-1$ therefore depends only on $x_{\u003Ct}$, giving exactly\n> the conditional $p(x_t \\mid x_{\u003Ct})$. All $n$ positions are computed in one\n> pass because the dependencies are encoded in the mask, not in sequential\n> evaluation. $\\qed$\n\n$$\n% caption: The causal mask. Query row $i$ attends only to key columns $j \\le i$: the lower triangle\n% (blue) is kept, the upper triangle (shaded, $-\\infty$) is blocked before the softmax.\n\\begin{tikzpicture}[font=\\scriptsize, x=0.92cm, y=0.92cm]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\def\\n{6}\n  % cells\n  \\foreach \\r in {1,...,6}{\n    \\foreach \\c in {1,...,6}{\n      \\pgfmathparse{\\c\u003C=\\r ? 1 : 0}\n      \\ifnum\\pgfmathresult=1\n        \\fill[acc!18] (\\c-1,\\n-\\r) rectangle (\\c,\\n-\\r+1);\n      \\else\n        \\fill[black] (\\c-1,\\n-\\r) rectangle (\\c,\\n-\\r+1);\n      \\fi\n    }\n  }\n  % grid\n  \\draw[black] (0,0) grid (\\n,\\n);\n  % labels\n  \\foreach \\c in {1,...,6} \\node[anchor=south] at (\\c-0.5,\\n+0.1) {key \\c};\n  \\foreach \\r in {1,...,6} \\node[anchor=east] at (-0.1,\\n-\\r+0.5) {query \\r};\n  \\node[acc, anchor=west] at (\\n+0.4,4.2) {\\texttt{kept (past)}};\n  \\node[black, anchor=west] at (\\n+0.4,3.2) {\\texttt{blocked (future)}};\n\\end{tikzpicture}\n$$\n\n```algorithm\ncaption: $\\textsc{MaskedSelfAttention}(X)$ — causal scaled dot-product attention\n$Q \\gets X W_Q$; $K \\gets X W_K$; $V \\gets X W_V$\n$S \\gets Q K^{T} \u002F \\sqrt{d_k}$ \u002F\u002F $n \\times n$ raw scores\nfor each $i, j$ with $j > i$ do\n  $S_{ij} \\gets -\\infty$ \u002F\u002F forbid attending to the future\nfor each row $i$ do\n  $A_{i} \\gets \\softmax(S_{i})$ \u002F\u002F mass only on $j \\le i$\nreturn $A V$ \u002F\u002F each row blends past values only\n```\n\n## The three families\n\nThe encoder and decoder were designed to work as a pair, but each half is a\ncomplete model on its own. Modern practice splits the architecture into three\nfamilies, distinguished by which stack they keep, how they mask attention, and\nwhat objective they train against.\n\n| Family | Structure | Attention masking | Training objective | Examples |\n| --- | --- | --- | --- | --- |\n| Encoder-only | encoder stack, bidirectional | none (full self-attention) | masked language modeling (predict held-out tokens) | BERT, RoBERTa |\n| Decoder-only | decoder stack, no cross-attention | causal (lower-triangular) | autoregressive LM (next-token prediction) | GPT, LLaMA |\n| Encoder–decoder | both stacks, cross-attention | encoder full, decoder causal | seq2seq (conditional generation) | original Transformer, T5 |\n\nThe split follows directly from the masking. An **encoder-only** model sees the\nwhole sequence, so it is built for _understanding_ (classification, retrieval,\ntoken tagging) and is trained by corrupting input tokens and reconstructing\nthem. A **decoder-only** model masks causally, so each position predicts the\nnext token, making it a pure _generator_; this is the family that scaled into\nlarge language models. An **encoder–decoder** keeps both and is built for\n_transduction_: mapping one sequence to another, as in translation or\nsummarization.[^chollet-families]\n\n$$\n% caption: The three families. Encoder-only (BERT) attends bidirectionally; decoder-only (GPT)\n% masks causally; encoder–decoder (T5) joins both halves by cross-attention (green).\n\\begin{tikzpicture}[>=stealth, font=\\scriptsize,\n  e\u002F.style={draw, draw=acc, text=acc, minimum width=20mm, minimum height=6mm, align=center},\n  d\u002F.style={draw, draw=red, text=red, minimum width=20mm, minimum height=6mm, align=center},\n  io\u002F.style={font=\\scriptsize, text=black}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\definecolor{red}{HTML}{C0392B}\n  \\definecolor{green}{HTML}{1F9D4D}\n  % ---- encoder-only ----\n  \\node[io] (ei) at (0,-0.7) {\\texttt{tokens}};\n  \\node[e] (e1) at (0,0.2) {\\texttt{encoder}};\n  \\node[e] (e2) at (0,1.1) {\\texttt{encoder}};\n  \\node[io] (eo) at (0,1.9) {\\texttt{features}};\n  \\draw[->, thick] (ei) -- (e1);\n  \\draw[->, thick] (e1) -- (e2);\n  \\draw[->, thick] (e2) -- (eo);\n  \\node[font=\\footnotesize] at (0,-1.5) {\\texttt{encoder-only}};\n  \\node[io] at (0,-2.0) {\\texttt{(BERT, bidirectional)}};\n  % ---- decoder-only ----\n  \\begin{scope}[xshift=3.6cm]\n  \\node[io] (di) at (0,-0.7) {\\texttt{tokens}};\n  \\node[d] (g1) at (0,0.2) {\\texttt{decoder}};\n  \\node[d] (g2) at (0,1.1) {\\texttt{decoder}};\n  \\node[io] (do) at (0,1.9) {\\texttt{next token}};\n  \\draw[->, thick] (di) -- (g1);\n  \\draw[->, thick] (g1) -- (g2);\n  \\draw[->, thick] (g2) -- (do);\n  \\node[font=\\footnotesize] at (0,-1.5) {\\texttt{decoder-only}};\n  \\node[io] at (0,-2.0) {\\texttt{(GPT, causal)}};\n  \\end{scope}\n  % ---- encoder-decoder ----\n  \\begin{scope}[xshift=8.4cm]\n  \\node[io] (xi) at (-1.3,-0.7) {\\texttt{source}};\n  \\node[e] (x1) at (-1.3,0.2) {\\texttt{encoder}};\n  \\node[e] (x2) at (-1.3,1.1) {\\texttt{encoder}};\n  \\node[io] (yi) at (2.1,-0.7) {\\texttt{target}};\n  \\node[d] (y1) at (2.1,0.2) {\\texttt{decoder}};\n  \\node[d] (y2) at (2.1,1.1) {\\texttt{decoder}};\n  \\node[io] (yo) at (2.1,1.9) {\\texttt{output}};\n  \\draw[->, thick] (xi) -- (x1);\n  \\draw[->, thick] (x1) -- (x2);\n  \\draw[->, thick] (yi) -- (y1);\n  \\draw[->, thick] (y1) -- (y2);\n  \\draw[->, thick] (y2) -- (yo);\n  % cross-attention: the encoder output feeds every decoder layer through a clean\n  % vertical bus in the gap, one horizontal feeder per decoder layer.\n  \\draw[->, green, thick] (x2.east) -- (0.4,1.1) -- (y2.west);\n  \\draw[->, green, thick] (0.4,1.1) -- (0.4,0.2) -- (y1.west);\n  \\node[font=\\footnotesize] at (0.4,-1.5) {\\texttt{encoder-decoder}};\n  \\node[io] at (0.4,-2.0) {\\texttt{(T5, seq2seq)}};\n  \\end{scope}\n\\end{tikzpicture}\n$$\n\n## The residual stream\n\nA productive way to read the stack is as a **residual stream**: a fixed-width\n$d$-dimensional bus running from the embeddings to the output head. Each sublayer\n_reads_ a normalized copy of the stream, computes an update, and _writes_ that\nupdate back by addition. No sublayer overwrites the stream; they only accumulate\ninto it.\n\n$$\nz_\\ell = z_{\\ell-1} + \\Delta_\\ell, \\qquad \\Delta_\\ell = f_\\ell\\!\\parens{\\LN(z_{\\ell-1})},\n\\qquad z_N = z_0 + \\sum_{\\ell=1}^{N} \\Delta_\\ell .\n$$\n\nThis linear-accumulation view explains why Transformers are so editable: because\ncontributions add, an attention head and an FFN can read each other's writes, and\nthe final representation is literally the embedding plus every increment the\nsublayers added.\n\n$$\n% caption: The residual stream. A fixed-width bus (black) runs up the stack; each block reads a\n% normalized view (black) and writes an additive update back (green), never overwriting it.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize,\n  blk\u002F.style={draw, minimum width=24mm, minimum height=8mm, align=center}]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\definecolor{green}{HTML}{1F9D4D}\n  % the bus\n  \\draw[black, line width=2.6mm] (0,-0.4) -- (0,8.4);\n  \\node[black, anchor=south, rotate=90] at (-0.6,4.0) {\\texttt{residual stream (width d)}};\n  \\node[anchor=north] at (0,-0.55) {\\texttt{embed + pos}};\n  \\node[anchor=south] at (0,8.55) {\\texttt{to output head}};\n  % blocks on the right, reading and writing\n  \\node[blk, draw=acc, text=acc] (b1) at (3.6,1.2) {\\texttt{self-attention}};\n  \\node[blk, draw=acc, text=acc] (b2) at (3.6,3.2) {\\texttt{feed-forward}};\n  \\node[blk, draw=acc, text=acc] (b3) at (3.6,5.2) {\\texttt{self-attention}};\n  \\node[blk, draw=acc, text=acc] (b4) at (3.6,7.2) {\\texttt{feed-forward}};\n  \\foreach \\b\u002F\\y in {b1\u002F1.2, b2\u002F3.2, b3\u002F5.2, b4\u002F7.2}{\n    \\draw[->, black, thick] (0.16,\\y-0.55) -- (\\b.west |- 0,\\y-0.55);\n    \\draw[->, green, thick] (\\b.west |- 0,\\y+0.55) -- (0.16,\\y+0.55);\n  }\n  \\node[black, anchor=south, font=\\footnotesize] at (1.9,0.7) {\\texttt{read}};\n  \\node[green, anchor=south, font=\\footnotesize] at (1.9,7.85) {\\texttt{write (add)}};\n\\end{tikzpicture}\n$$\n\n## Where the parameters and the compute live\n\nTwo accounting questions decide how a Transformer scales: where do its weights\nsit, and what dominates its runtime. Both have clean closed forms.[^gf-attention-mem]\n\n**Parameters.** Per layer, attention contributes the four projection matrices\n$W_Q, W_K, W_V, W_O$, each $d \\times d$, for $4d^2$. The FFN contributes\n$W_1 \\in \\mathbb{R}^{d \\times d_{\\text{ff}}}$ and $W_2 \\in \\mathbb{R}^{d_{\\text{ff}}\n\\times d}$; with $d_{\\text{ff}} = 4d$ that is $2 \\cdot 4d^2 = 8d^2$. So per layer,\n\n$$\n\\underbrace{4d^2}_{\\text{attention}} + \\underbrace{8d^2}_{\\text{FFN}} = 12d^2,\n\\qquad\n\\frac{\\text{FFN params}}{\\text{layer params}} = \\frac{8d^2}{12d^2} = \\frac{2}{3}.\n$$\n\nTwo-thirds of a Transformer's weights live in the feed-forward networks, not the\nattention — a fact that motivates much of the work on sparsifying or scaling the\nFFN (mixture-of-experts) rather than attention.\n\nThe $12d^2$ count ignores the small additive terms — the biases ($\\sim 5d$ per\nlayer) and the two LayerNorms' $\\gamma, \\beta$ ($4d$ per layer) — which are\nlinear in $d$ and vanish against the quadratic weights for any real width. Put\n$d = 512$, $d_{\\text{ff}} = 2048$ (the base configuration) into the table to see\nthe actual per-layer budget:\n\n| Component | Formula | $d = 512$ | Share |\n| --- | --- | --- | --- |\n| Attention $W_Q, W_K, W_V, W_O$ | $4d^2$ | $\\approx 1.05\\text{M}$ | $1\u002F3$ |\n| Feed-forward $W_1, W_2$ ($d_{\\text{ff}} = 4d$) | $8d^2$ | $\\approx 2.10\\text{M}$ | $2\u002F3$ |\n| LayerNorm ($\\gamma, \\beta$, two per layer) | $4d$ | $\\approx 2\\text{k}$ | $\u003C 0.1\\%$ |\n| **Per layer total** | $\\approx 12d^2$ | $\\approx 3.15\\text{M}$ | $1$ |\n\nA $6$-layer encoder of this width holds $\\approx 19\\text{M}$ weights in its\nblocks; the token embedding and output projection add $2 \\, |V| \\, d$ on top,\nwhich for a $30\\text{k}$ vocabulary is another $\\approx 31\\text{M}$ — a reminder\nthat at small depth the vocabulary table, not the blocks, can dominate the count.\n\n**Compute.** The cost split is reversed. The FFN is linear in sequence\nlength — $O(n \\cdot d^2)$ per layer — but the attention matrix is quadratic.\n\n> **Theorem (Quadratic attention cost).** Computing self-attention over a\n> sequence of length $n$ with model width $d$ costs $O(n^2 d)$ time and $O(n^2)$\n> memory for the attention matrix, independent of how the heads are split.\n\n> **Proof.** Forming the scores $QK^\\top$ multiplies an $n \\times d$ matrix by a\n> $d \\times n$ matrix, costing $O(n^2 d)$ and producing an $n \\times n$ matrix.\n> The softmax is $O(n^2)$. Multiplying the $n \\times n$ weights by the $n \\times\n> d$ values is again $O(n^2 d)$. Splitting into $h$ heads of width $d\u002Fh$ gives\n> $h$ products of cost $O(n^2 \\cdot d\u002Fh)$, summing back to $O(n^2 d)$. The\n> $n \\times n$ score matrix dominates memory at $O(n^2)$. $\\qed$\n\nThe crossover is at $n \\approx d$: for $n \u003C d$ the per-layer cost is dominated by\nthe $O(n d^2)$ projection and FFN work, but once $n \\gtrsim d$ the $O(n^2 d)$\nattention term takes over and grows quadratically. This single $n^2$ is the\nreason context windows are expensive and the target of nearly every\nefficient-attention variant.\n\n$$\n% caption: Per-layer cost vs. sequence length $n$ (log–log). The projection\u002FFFN term is linear\n% (black); attention is quadratic (blue). They cross near $n \\approx d$, after which attention dominates.\n\\begin{tikzpicture}[>=stealth, font=\\footnotesize, x=1.0cm, y=1.0cm]\n  \\definecolor{acc}{HTML}{2348F2}\n  \\draw[->, thick] (0,0) -- (7.0,0) node[right, font=\\scriptsize] {log n};\n  \\draw[->, thick] (0,0) -- (0,4.6) node[above, font=\\scriptsize] {log cost};\n  % linear term: slope 1\n  \\draw[black, very thick] (0.3,0.6) -- (6.4,2.6) node[right, text=black, font=\\scriptsize] {linear};\n  % quadratic term: slope 2\n  \\draw[acc, very thick] (0.3,-0.1) -- (6.4,4.1) node[right, text=acc, font=\\scriptsize] {quadratic};\n  % crossover marker (lines meet near x=2.24, y=1.24)\n  \\draw[black, dashed] (2.24,0) -- (2.24,1.24);\n  \\node[anchor=north, font=\\scriptsize] at (2.24,0) {n near d};\n  \\fill[acc] (2.24,1.24) circle (1.6pt);\n\\end{tikzpicture}\n$$\n\n\nThat is the architecture and its cost model. The same design turns out to be\nindifferent to what a token _is_ — image patches, DNA bases, or program tokens\nall work — and the decoder-only half of it scaled into the large language models\nthat dominate current practice. Those applications, and the empirical scaling\nlaws that make scale pay off so reliably, continue in\n[Transformers in Practice](\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice).\n\n## Takeaways\n\n- The **Transformer** is attention plus position-wise feed-forward layers,\n  stacked with **residual + LayerNorm** wrappers, with no recurrence or\n  convolution anywhere.\n- **Pre-norm** ($x + f(\\LN(x))$) leaves a clean identity path up\n  the stack, so deep Transformers train stably; **post-norm**\n  ($\\LN(x + f(x))$) squeezes every residual through a norm and\n  needs warmup.\n- **Sinusoidal positional encoding** gives each position a unique fingerprint\n  across a geometric band of frequencies, makes relative offsets a linear map,\n  and extrapolates past the training length; learned tables and rotary (RoPE)\n  encodings are the modern alternatives.\n- The **encoder** attends bidirectionally; the **decoder** adds **masked\n  self-attention** (causal, lower-triangular) and **cross-attention** to the\n  encoder output, and reads out through **linear + softmax**.\n- The **three families** specialize the design: **encoder-only** (BERT, masked\n  LM, understanding), **decoder-only** (GPT, causal LM, generation),\n  **encoder–decoder** (T5, seq2seq, transduction).\n- Causal masking realizes the autoregressive factorization $p(x) = \\prod_t\n  p(x_t \\mid x_{\u003Ct})$ in a single parallel forward pass.\n- The **residual stream** view reads the stack as a fixed-width bus each sublayer\n  reads from and adds back into, never overwriting — which is why contributions\n  compose so cleanly.\n- **Two-thirds** of the parameters live in the FFN ($8d^2$ vs $4d^2$ per layer),\n  while compute is dominated by the **$O(n^2 d)$** attention term — the\n  quadratic cost that bounds context length.\n\n[^chollet-transformer]: **Chollet**, _Deep Learning with Python_, Ch. 11 — The Transformer Architecture: assembling embeddings, positional encoding, stacked attention + FFN sublayers, and the read-out head into the full model.\n[^gf-norm]: **Goodfellow**, _Deep Learning_, §8.7.1 — Batch\u002Fnormalization and §8.7.5 residual connections: why a clean identity path (here pre-norm) stabilizes optimization of very deep stacks.\n[^chollet-decoder]: **Chollet**, _Deep Learning with Python_, Ch. 11 — The Transformer decoder: causal (masked) self-attention plus cross-attention to the encoder output for sequence-to-sequence generation.\n[^chollet-families]: **Chollet**, _Deep Learning with Python_, Ch. 11 — encoder-only vs. decoder-only vs. encoder–decoder usage: how the masking and objective pick out BERT-style, GPT-style, and T5-style models.\n[^gf-attention-mem]: **Goodfellow**, _Deep Learning_, §10.11 — Explicit Memory & attention: the content-addressed read whose cost scales quadratically in sequence length, the bottleneck behind efficient-attention work.\n",{"text":15131,"minutes":15132,"time":15133,"words":15134},"13 min read",12.815,768900,2563,{"title":5,"description":15120},[15137,15139],{"book":15044,"ref":15138},"§10.11 — Explicit Memory & Attention (the Transformer postdates the 2016 text)",{"book":15027,"ref":15140},"Ch. 11 — Deep Learning for Text; The Transformer Architecture","available","06.deep-learning\u002F05.architectures\u002F06.the-transformer-architecture","The Transformer is the architecture built around the attention mechanism. This first part assembles the full encoder–decoder of \"Attention Is All You Need\" — embeddings and positional encoding, stacked self-attention and feed-forward sublayers wrapped in residual connections and LayerNorm, masked decoding and cross-attention — works through causal masking and the three modern families (encoder-only, decoder-only, encoder–decoder), and accounts for where the parameters and the $O(n^2)$ compute actually go.\n",[15125],"hnoQEj4T1pgso8JnSeDbpFeyg-gpHh2jnCJdnwG0cJY",{"\u002Falgorithms\u002Ffoundations\u002Fwhat-is-an-algorithm":15147,"\u002Falgorithms\u002Ffoundations\u002Fproof-techniques":15148,"\u002Falgorithms\u002Ffoundations\u002Fasymptotic-analysis":15149,"\u002Falgorithms\u002Ffoundations\u002Fgrowth-rates-and-loop-analysis":15150,"\u002Falgorithms\u002Ffoundations\u002Frecurrences":15151,"\u002Falgorithms\u002Ffoundations\u002Famortized-analysis":15152,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fmergesort":15153,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fquicksort":15154,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fselection":15155,"\u002Falgorithms\u002Fdivide-and-conquer\u002Ffast-multiplication":15156,"\u002Falgorithms\u002Fsorting\u002Fheaps-and-heapsort":15157,"\u002Falgorithms\u002Fsorting\u002Fsorting-lower-bounds":15158,"\u002Falgorithms\u002Fsorting\u002Flinear-time-sorting":15159,"\u002Falgorithms\u002Fsorting\u002Fexternal-sorting":15160,"\u002Falgorithms\u002Fdata-structures\u002Felementary-structures":15161,"\u002Falgorithms\u002Fdata-structures\u002Fhash-tables":15162,"\u002Falgorithms\u002Fdata-structures\u002Fbinary-search-trees":15163,"\u002Falgorithms\u002Fdata-structures\u002Favl-trees":15164,"\u002Falgorithms\u002Fdata-structures\u002Fbalanced-trees":15165,"\u002Falgorithms\u002Fdata-structures\u002Funion-find":15166,"\u002Falgorithms\u002Fdata-structures\u002Ffenwick-and-segment-trees":15167,"\u002Falgorithms\u002Fdata-structures\u002Fspatial-data-structures":15168,"\u002Falgorithms\u002Fdata-structures\u002Fskip-lists-and-probabilistic-structures":15169,"\u002Falgorithms\u002Fdata-structures\u002Fb-trees":15170,"\u002Falgorithms\u002Fdata-structures\u002Fdata-stream-algorithms":15171,"\u002Falgorithms\u002Fdata-structures\u002Fstreaming-sketches":15172,"\u002Falgorithms\u002Fsequences\u002Ftwo-pointers-and-windows":15173,"\u002Falgorithms\u002Fsequences\u002Fprefix-sums":15174,"\u002Falgorithms\u002Fsequences\u002Fmonotonic-stacks":15175,"\u002Falgorithms\u002Fsequences\u002Fbinary-search-on-the-answer":15176,"\u002Falgorithms\u002Fsequences\u002Fstring-matching":15177,"\u002Falgorithms\u002Fsequences\u002Fkmp-and-z-function":15178,"\u002Falgorithms\u002Fsequences\u002Ftries":15179,"\u002Falgorithms\u002Fsequences\u002Fsuffix-arrays-and-aho-corasick":15180,"\u002Falgorithms\u002Fgraphs\u002Frepresentations-and-traversal":15181,"\u002Falgorithms\u002Fgraphs\u002Fdepth-first-search":15182,"\u002Falgorithms\u002Fgraphs\u002Ftopological-sort-and-scc":15183,"\u002Falgorithms\u002Fgraphs\u002Fminimum-spanning-trees":15184,"\u002Falgorithms\u002Fgraphs\u002Fkruskal-and-prim":15185,"\u002Falgorithms\u002Fgraphs\u002Fshortest-paths":15186,"\u002Falgorithms\u002Fgraphs\u002Fall-pairs-and-negative-weights":15187,"\u002Falgorithms\u002Fgraphs\u002Fnetwork-flow":15188,"\u002Falgorithms\u002Fgraphs\u002Fmax-flow-min-cut":15189,"\u002Falgorithms\u002Fgraphs\u002Fbridges-and-articulation-points":15190,"\u002Falgorithms\u002Fgraphs\u002Flowest-common-ancestor":15191,"\u002Falgorithms\u002Fgraphs\u002Ftwo-sat":15192,"\u002Falgorithms\u002Fgraphs\u002Feulerian-tours":15193,"\u002Falgorithms\u002Fgraphs\u002Fbipartite-matching":15194,"\u002Falgorithms\u002Fgreedy\u002Fthe-greedy-method":15195,"\u002Falgorithms\u002Fgreedy\u002Fscheduling-and-intervals":15196,"\u002Falgorithms\u002Fgreedy\u002Fhuffman-codes":15197,"\u002Falgorithms\u002Fgreedy\u002Fmatroids":15198,"\u002Falgorithms\u002Fgreedy\u002Fstable-matching":15199,"\u002Falgorithms\u002Fdynamic-programming\u002Fprinciples":15200,"\u002Falgorithms\u002Fdynamic-programming\u002Fsequence-dp":15201,"\u002Falgorithms\u002Fdynamic-programming\u002Flongest-increasing-subsequence":15202,"\u002Falgorithms\u002Fdynamic-programming\u002Fknapsack":15203,"\u002Falgorithms\u002Fdynamic-programming\u002Fcoin-change-and-unbounded":15204,"\u002Falgorithms\u002Fdynamic-programming\u002Finterval-dp":15205,"\u002Falgorithms\u002Fdynamic-programming\u002Ftree-dp":15206,"\u002Falgorithms\u002Fdynamic-programming\u002Fbitmask-dp":15207,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-optimizations":15208,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-on-graphs":15209,"\u002Falgorithms\u002Fdynamic-programming\u002Fdigit-and-probability-dp":15210,"\u002Falgorithms\u002Fbacktracking\u002Fbacktracking-fundamentals":15211,"\u002Falgorithms\u002Fbacktracking\u002Fconstraint-search":15212,"\u002Falgorithms\u002Fbacktracking\u002Fbranch-and-bound":15213,"\u002Falgorithms\u002Fbacktracking\u002Fgraph-backtracking":15214,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fnumber-theory-basics":15215,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmodular-exponentiation-and-primality":15216,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fsieve-and-factorization":15217,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fcombinatorics":15218,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmatrix-exponentiation":15219,"\u002Falgorithms\u002Fmathematical-algorithms\u002Ffast-fourier-transform":15220,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fgradient-descent":15221,"\u002Falgorithms\u002Fcomputational-geometry\u002Fgeometric-primitives":15222,"\u002Falgorithms\u002Fcomputational-geometry\u002Fconvex-hull":15223,"\u002Falgorithms\u002Fcomputational-geometry\u002Fsweep-line":15224,"\u002Falgorithms\u002Fcomputational-geometry\u002Fpolygons-and-proximity":15225,"\u002Falgorithms\u002Fintractability\u002Fp-np-reductions":15226,"\u002Falgorithms\u002Fintractability\u002Fnp-completeness":15227,"\u002Falgorithms\u002Fintractability\u002Fcoping-with-hardness":15228,"\u002Falgorithms\u002Fintractability\u002Fapproximation-algorithms":15229,"\u002Falgorithms":15230,"\u002Fcalculus\u002Flimits-and-continuity\u002Ffunctions-and-models":15231,"\u002Fcalculus\u002Flimits-and-continuity\u002Fthe-limit-of-a-function":15232,"\u002Fcalculus\u002Flimits-and-continuity\u002Flimit-laws-and-the-precise-definition":15233,"\u002Fcalculus\u002Flimits-and-continuity\u002Fcontinuity":15234,"\u002Fcalculus\u002Fderivatives\u002Fthe-derivative-and-rates-of-change":15235,"\u002Fcalculus\u002Fderivatives\u002Fdifferentiation-rules-and-the-chain-rule":15236,"\u002Fcalculus\u002Fderivatives\u002Fimplicit-differentiation-and-related-rates":15237,"\u002Fcalculus\u002Fderivatives\u002Flinear-approximations-and-differentials":15238,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fextrema-and-the-mean-value-theorem":15239,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fhow-derivatives-shape-a-graph":15240,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fcurve-sketching-and-optimization":15241,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fnewtons-method-and-antiderivatives":15242,"\u002Fcalculus\u002Fintegrals\u002Farea-and-the-definite-integral":15243,"\u002Fcalculus\u002Fintegrals\u002Fthe-fundamental-theorem-of-calculus":15244,"\u002Fcalculus\u002Fintegrals\u002Fthe-substitution-rule":15245,"\u002Fcalculus\u002Fapplications-of-integration\u002Fareas-and-volumes":15246,"\u002Fcalculus\u002Fapplications-of-integration\u002Fwork-average-value-and-arc-length":15247,"\u002Fcalculus\u002Fapplications-of-integration\u002Fphysics-economics-and-probability":15248,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Finverse-functions-logarithms-and-exponentials":15249,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Fgrowth-decay-inverse-trig-and-hyperbolic-functions":15250,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Flhospitals-rule":15251,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fintegration-by-parts":15252,"\u002Fcalculus\u002Ftechniques-of-integration\u002Ftrigonometric-integrals-and-substitution":15253,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fpartial-fractions-and-integration-strategy":15254,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fapproximate-and-improper-integrals":15255,"\u002Fcalculus\u002Fparametric-and-polar\u002Fparametric-curves-and-their-calculus":15256,"\u002Fcalculus\u002Fparametric-and-polar\u002Fpolar-coordinates":15257,"\u002Fcalculus\u002Fparametric-and-polar\u002Fconic-sections":15258,"\u002Fcalculus\u002Fsequences-and-series\u002Fsequences":15259,"\u002Fcalculus\u002Fsequences-and-series\u002Fseries-and-the-integral-test":15260,"\u002Fcalculus\u002Fsequences-and-series\u002Fthe-convergence-tests":15261,"\u002Fcalculus\u002Fsequences-and-series\u002Fpower-series":15262,"\u002Fcalculus\u002Fsequences-and-series\u002Ftaylor-and-maclaurin-series":15263,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvectors-and-the-dot-product":15264,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fthe-cross-product-lines-and-planes":15245,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fcylinders-and-quadric-surfaces":15265,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvector-functions-and-space-curves":15266,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Farc-length-curvature-and-motion":15267,"\u002Fcalculus\u002Fpartial-derivatives\u002Ffunctions-of-several-variables":15235,"\u002Fcalculus\u002Fpartial-derivatives\u002Fpartial-derivatives":15268,"\u002Fcalculus\u002Fpartial-derivatives\u002Ftangent-planes-and-the-chain-rule":15269,"\u002Fcalculus\u002Fpartial-derivatives\u002Fdirectional-derivatives-and-the-gradient":15270,"\u002Fcalculus\u002Fpartial-derivatives\u002Foptimization-and-lagrange-multipliers":15271,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fdouble-integrals":15272,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Ftriple-integrals-and-coordinate-systems":15273,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fvector-fields-and-line-integrals":15274,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fgreens-theorem-curl-and-divergence":15275,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fsurface-integrals":15276,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fstokes-and-the-divergence-theorem":15277,"\u002Fcalculus":15278,"\u002Fmechanics\u002Ffoundations\u002Fmeasurement-and-dimensions":15279,"\u002Fmechanics\u002Ffoundations\u002Fvector-algebra":15280,"\u002Fmechanics\u002Fkinematics\u002Fone-dimensional-motion":15281,"\u002Fmechanics\u002Fkinematics\u002Fmotion-graphs":15282,"\u002Fmechanics\u002Fkinematics\u002Fprojectile-motion":15283,"\u002Fmechanics\u002Fkinematics\u002Frelative-motion":15284,"\u002Fmechanics\u002Fkinematics\u002Fcircular-motion":15285,"\u002Fmechanics\u002Fdynamics\u002Fnewtons-laws":15286,"\u002Fmechanics\u002Fdynamics\u002Ffree-body-diagrams":15287,"\u002Fmechanics\u002Fdynamics\u002Ffriction-and-curved-motion":15288,"\u002Fmechanics\u002Fdynamics\u002Fnumerical-dynamics":15289,"\u002Fmechanics\u002Fdynamics\u002Fcenter-of-mass-systems":15290,"\u002Fmechanics\u002Fenergy\u002Fwork-and-kinetic-energy":15291,"\u002Fmechanics\u002Fenergy\u002Fpotential-energy":15292,"\u002Fmechanics\u002Fenergy\u002Fmultiparticle-work":15293,"\u002Fmechanics\u002Fenergy\u002Fmass-energy-and-binding":15294,"\u002Fmechanics\u002Fenergy\u002Fphotons-and-quantization":15295,"\u002Fmechanics\u002Fmomentum\u002Fmomentum-and-collisions":15296,"\u002Fmechanics\u002Fmomentum\u002Fcenter-of-mass-collisions":15297,"\u002Fmechanics\u002Fmomentum\u002Frocket-propulsion":15298,"\u002Fmechanics\u002Frotation\u002Frotational-inertia":15299,"\u002Fmechanics\u002Frotation\u002Frotational-dynamics":15300,"\u002Fmechanics\u002Frotation\u002Frolling-motion":15301,"\u002Fmechanics\u002Frotation\u002Fangular-momentum":15302,"\u002Fmechanics\u002Frotation\u002Frolling-resistance":15303,"\u002Fmechanics\u002Frotation\u002Fgyroscopic-precession":15304,"\u002Fmechanics\u002Fgravity-and-matter\u002Fkeplerian-orbits":15305,"\u002Fmechanics\u002Fgravity-and-matter\u002Fgravitational-fields":15306,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstatic-equilibrium":15307,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-statics":15308,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-flow":15309,"\u002Fmechanics\u002Fgravity-and-matter\u002Forbital-motion":15310,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstress-and-elasticity":15311,"\u002Fmechanics\u002Foscillations-waves\u002Fdamped-oscillators":15312,"\u002Fmechanics\u002Foscillations-waves\u002Ftravelling-waves":15313,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-superposition":15314,"\u002Fmechanics\u002Foscillations-waves\u002Fstanding-waves":15315,"\u002Fmechanics\u002Foscillations-waves\u002Fsound-waves":15316,"\u002Fmechanics\u002Foscillations-waves\u002Fdoppler-effect":15317,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-packets":15318,"\u002Fmechanics\u002Foscillations-waves\u002Fbeats-and-coupling":15319,"\u002Fmechanics\u002Foscillations-waves\u002Fsimple-harmonic-motion":15320,"\u002Fmechanics\u002Foscillations-waves\u002Fpendulum-motion":15321,"\u002Fmechanics\u002Foscillations-waves\u002Fdriven-oscillators":15322,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-boundaries":15323,"\u002Fmechanics\u002Fthermodynamics\u002Fkinetic-theory-of-ideal-gases":15324,"\u002Fmechanics\u002Fthermodynamics\u002Ffirst-law-of-thermodynamics":15325,"\u002Fmechanics\u002Fthermodynamics\u002Fentropy-and-the-second-law":15326,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-processes":15327,"\u002Fmechanics\u002Fthermodynamics\u002Fphase-changes":15328,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-machines":15329,"\u002Fmechanics":15330,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcharge-and-conductors":15331,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcoulombs-law":15332,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-and-force":15333,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-maps":15334,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-dipoles":15335,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fcontinuous-charge-fields":15336,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fgauss-law-and-conductors":15337,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpoint-charge-potential":15338,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpotential-gradients-and-equipotentials":15339,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Felectrostatic-energy-and-pressure":15340,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Flaplace-boundary-problems":15341,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fcontinuous-charge-potentials":15342,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitance-fundamentals":15319,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-networks":15343,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-energy-and-force":15344,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fdielectric-polarization-and-breakdown":15345,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fcurrent-and-resistance":15315,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fkirchhoff-network-analysis":15180,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Frc-transients":15346,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-trajectories":15306,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fhall-effect":15347,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-force-on-conductors":15348,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-dipoles":15349,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmass-spectrometry":15350,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmoving-charge-fields":15351,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fbiot-savart-law":15352,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fcircular-current-loops":15353,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Famperes-law":15354,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fgauss-law-for-magnetism":15355,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmagnetic-materials":15280,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-flux":15356,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Ffaradays-law":15357,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Flenzs-law":15358,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmotional-emf":15359,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Feddy-currents":15360,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fself-inductance":15361,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-energy":15362,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Frl-circuits":15363,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-fundamentals":15298,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Freactance":15297,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Frlc-resonance":15364,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-power":15365,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Ftransformers":15366,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdisplacement-current":15367,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-waves":15368,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-momentum":15369,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdipole-radiation":15370,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fpolarization":15371,"\u002Felectricity-and-magnetism\u002Foptics\u002Freflection-and-refraction":15372,"\u002Felectricity-and-magnetism\u002Foptics\u002Fthin-lenses":15324,"\u002Felectricity-and-magnetism\u002Foptics\u002Fspherical-mirrors":15322,"\u002Felectricity-and-magnetism":15373,"\u002Flinear-algebra\u002Flinear-systems\u002Fsystems-and-echelon-forms":15374,"\u002Flinear-algebra\u002Flinear-systems\u002Fvector-and-matrix-equations":15375,"\u002Flinear-algebra\u002Flinear-systems\u002Fsolution-sets-and-applications":15376,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-independence":15377,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-transformations":15378,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-operations":15379,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-inverse-and-invertibility":15380,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fpartitioned-matrices-and-lu":15381,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fsubspaces-dimension-rank":15382,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fapplications-leontief-and-graphics":15232,"\u002Flinear-algebra\u002Fdeterminants\u002Fdeterminants-and-cofactors":15383,"\u002Flinear-algebra\u002Fdeterminants\u002Fproperties-of-determinants":15384,"\u002Flinear-algebra\u002Fdeterminants\u002Fcramer-volume-and-area":15236,"\u002Flinear-algebra\u002Fvector-spaces\u002Fvector-spaces-and-subspaces":15385,"\u002Flinear-algebra\u002Fvector-spaces\u002Fnull-and-column-spaces":15386,"\u002Flinear-algebra\u002Fvector-spaces\u002Fbases-and-independent-sets":15387,"\u002Flinear-algebra\u002Fvector-spaces\u002Fcoordinate-systems":15388,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdimension-and-rank":15389,"\u002Flinear-algebra\u002Fvector-spaces\u002Fchange-of-basis":15390,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdifference-equations-and-markov":15391,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-eigenvalues":15392,"\u002Flinear-algebra\u002Feigenvalues\u002Fthe-characteristic-equation":15393,"\u002Flinear-algebra\u002Feigenvalues\u002Fdiagonalization":15394,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-linear-transformations":15395,"\u002Flinear-algebra\u002Feigenvalues\u002Fcomplex-eigenvalues":15396,"\u002Flinear-algebra\u002Feigenvalues\u002Fdynamical-systems":15397,"\u002Flinear-algebra\u002Feigenvalues\u002Fpower-method":15398,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-length-orthogonality":15399,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Forthogonal-sets-and-projections":15400,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fgram-schmidt-and-qr":15401,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-problems":15402,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-applications":15403,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-spaces":15404,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fdiagonalizing-symmetric-matrices":15271,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fquadratic-forms":15405,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fconstrained-optimization":15406,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsingular-value-decomposition":15407,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsvd-applications-pca-imaging":15408,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-thinking-and-matrix-computation":15409,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Flu-and-cholesky":15410,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fconditioning-and-floating-point":15411,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fstability-and-error-analysis":15412,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fqr-and-numerical-least-squares":15413,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-eigenvalues-and-svd":15414,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-combinations":15415,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-independence-and-barycentric-coordinates":15416,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fconvex-combinations-and-convex-sets":15417,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fhyperplanes-and-polytopes":15418,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fcurves-and-surfaces":15419,"\u002Flinear-algebra":15420,"\u002Ftheory-of-computation":15421,"\u002Fcomputer-architecture\u002Ffoundations\u002Fbits-bytes-and-words":15422,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-representation":15423,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-arithmetic":15424,"\u002Fcomputer-architecture\u002Ffoundations\u002Ffloating-point":15425,"\u002Fcomputer-architecture\u002Ffoundations\u002Fboolean-algebra-and-bit-manipulation":15426,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fthe-machines-view":15427,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fdata-movement":15428,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farithmetic-and-logic":15429,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fcontrol-flow":15430,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fprocedures":15431,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farrays-structs-and-alignment":15432,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fmemory-layout-and-buffer-overflows":15433,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fwhat-an-isa-is":15434,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Finstruction-formats-and-operands":15435,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Faddressing-modes":15436,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fthe-y86-64-instruction-set":15437,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fy86-64-programming":15438,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Ftransistors-gates-and-boolean-functions":15439,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fcombinational-logic-and-hcl":15440,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmultiplexers-decoders-and-the-alu":15441,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmemory-elements-latches-flip-flops-and-clocking":15442,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fregister-files-and-random-access-memory":15443,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-fetch-decode-execute-cycle":15444,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-seq-stages":15445,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fcontrol-logic-and-sequencing":15446,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fassembling-seq":15447,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Ftracing-a-program":15448,"\u002Fcomputer-architecture\u002Fpipelining\u002Fpipelining-principles":15449,"\u002Fcomputer-architecture\u002Fpipelining\u002Ffrom-seq-to-pipe":15450,"\u002Fcomputer-architecture\u002Fpipelining\u002Fdata-hazards-stalling-and-forwarding":15451,"\u002Fcomputer-architecture\u002Fpipelining\u002Fcontrol-hazards-and-branch-prediction":15452,"\u002Fcomputer-architecture\u002Fpipelining\u002Fthe-complete-pipe-processor":15453,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fstorage-technologies-and-the-latency-gap":15454,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Flocality":15455,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-memories-direct-mapped":15456,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fset-associative-and-write-policies":15457,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-performance-and-cache-friendly-code":15458,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Faddress-spaces-and-translation":15459,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fpage-tables-and-page-faults":15460,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fthe-tlb-and-multi-level-page-tables":15461,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Fexceptional-control-flow":15462,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Finterrupts-and-the-kernel":15463,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fprocesses-threads-and-parallelism":15464,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fhardware-multithreading":15465,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fcache-coherence":15466,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmemory-consistency-and-synchronization":15467,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmulticore-organization":15468,"\u002Fcomputer-architecture\u002Fcapstone\u002Fthe-whole-machine":15469,"\u002Fcomputer-architecture\u002Fcapstone\u002Fassembling-a-complete-cpu":15470,"\u002Fcomputer-architecture":15421,"\u002Fdifferential-equations\u002Ffoundations\u002Fmodels-and-direction-fields":15471,"\u002Fdifferential-equations\u002Ffoundations\u002Fclassification-and-terminology":15472,"\u002Fdifferential-equations\u002Ffirst-order\u002Flinear-first-order-integrating-factors":15473,"\u002Fdifferential-equations\u002Ffirst-order\u002Fseparable-and-exact":15236,"\u002Fdifferential-equations\u002Ffirst-order\u002Fmodeling-first-order":15474,"\u002Fdifferential-equations\u002Ffirst-order\u002Fautonomous-and-population-dynamics":15235,"\u002Fdifferential-equations\u002Ffirst-order\u002Fexistence-uniqueness-euler":15242,"\u002Fdifferential-equations\u002Ffirst-order\u002Ffirst-order-difference-equations":15475,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhomogeneous-constant-coefficients":15476,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fcomplex-and-repeated-roots":15276,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fnonhomogeneous-undetermined-coefficients":15477,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fvariation-of-parameters":15478,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fmechanical-electrical-vibrations":15479,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhigher-order-linear":15480,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fpower-series-ordinary-points":15481,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fregular-singular-frobenius":15482,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fbessel-and-special-functions":15483,"\u002Fdifferential-equations\u002Flaplace\u002Flaplace-definition-ivps":15484,"\u002Fdifferential-equations\u002Flaplace\u002Fstep-impulse-convolution":15485,"\u002Fdifferential-equations\u002Fsystems\u002Fmatrices-eigenvalues-review":15486,"\u002Fdifferential-equations\u002Fsystems\u002Fconstant-coefficient-systems-phase-portraits":15487,"\u002Fdifferential-equations\u002Fsystems\u002Frepeated-eigenvalues-fundamental-matrices":15488,"\u002Fdifferential-equations\u002Fnumerical\u002Feuler-and-runge-kutta":15483,"\u002Fdifferential-equations\u002Fnumerical\u002Fmultistep-systems-stability":15489,"\u002Fdifferential-equations\u002Fnonlinear\u002Fphase-plane-autonomous-stability":15490,"\u002Fdifferential-equations\u002Fnonlinear\u002Flocally-linear-and-liapunov":15491,"\u002Fdifferential-equations\u002Fnonlinear\u002Fcompeting-species-predator-prey-limit-cycles":15492,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Ffourier-series":15493,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fheat-wave-laplace-equations":15494,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fsturm-liouville":15495,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fcalculus-of-variations":15496,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fhistorical-notes":15497,"\u002Fdifferential-equations":15498,"\u002Frelativity\u002Ffoundations\u002Fspecial-relativity-postulates":15499,"\u002Frelativity\u002Ffoundations\u002Florentz-transformation-spacetime":15500,"\u002Frelativity\u002Ffoundations\u002Ftime-dilation-length-contraction":15501,"\u002Frelativity\u002Ffoundations\u002Frelativistic-momentum-energy":15502,"\u002Frelativity\u002Ffoundations\u002Fgeneral-relativity":15381,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fminkowski-spacetime-and-the-interval":15503,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Ffour-vectors-and-index-notation":15504,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fthe-lorentz-group-and-rapidity":15505,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fdoppler-aberration-and-appearance":15506,"\u002Frelativity\u002Frelativistic-dynamics\u002Ffour-momentum-force-and-accelerated-motion":15507,"\u002Frelativity\u002Frelativistic-dynamics\u002Fparticle-decays-and-two-body-kinematics":15508,"\u002Frelativity\u002Frelativistic-dynamics\u002Fcollisions-thresholds-and-the-cm-frame":15251,"\u002Frelativity\u002Frelativistic-dynamics\u002Fmandelstam-variables-and-invariants":15509,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ffour-current-and-the-four-potential":15510,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fthe-electromagnetic-field-tensor":15511,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ftransformation-of-electric-and-magnetic-fields":15512,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fcovariant-maxwell-and-the-stress-energy-tensor":15513,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-equivalence-principle-formalized":15514,"\u002Frelativity\u002Fcurved-spacetime\u002Fmanifolds-vectors-and-the-metric":15515,"\u002Frelativity\u002Fcurved-spacetime\u002Fcovariant-derivative-and-christoffel-symbols":15516,"\u002Frelativity\u002Fcurved-spacetime\u002Fgeodesics-and-the-geodesic-equation":15517,"\u002Frelativity\u002Fcurved-spacetime\u002Fcurvature-riemann-and-geodesic-deviation":15518,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-einstein-field-equations":15473,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fthe-schwarzschild-metric":15519,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fgeodesics-and-orbits-in-schwarzschild":15520,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Flight-bending-and-null-geodesics":15521,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fperihelion-precession-of-mercury":15522,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fdeflection-of-light-and-gravitational-lensing":15523,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fgravitational-redshift-and-shapiro-delay":15402,"\u002Frelativity\u002Ftests-of-general-relativity\u002Frelativity-in-technology-gps":15524,"\u002Frelativity\u002Fblack-holes\u002Fhorizons-and-coordinate-singularities":15525,"\u002Frelativity\u002Fblack-holes\u002Frotating-and-charged-black-holes":15412,"\u002Frelativity\u002Fblack-holes\u002Fblack-hole-thermodynamics":15526,"\u002Frelativity\u002Fgravitational-waves\u002Flinearized-gravity-and-wave-solutions":15527,"\u002Frelativity\u002Fgravitational-waves\u002Fgeneration-and-the-quadrupole-formula":15528,"\u002Frelativity\u002Fgravitational-waves\u002Fdetection-ligo-and-the-first-events":15529,"\u002Frelativity\u002Fcosmological-bridge\u002Fthe-cosmological-principle-and-flrw-metric":15530,"\u002Frelativity\u002Fcosmological-bridge\u002Ffriedmann-equations-and-cosmic-dynamics":15531,"\u002Frelativity":15532,"\u002Fphysical-computing":15421,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fblackbody-radiation-and-the-planck-quantum":15533,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-photoelectric-effect-and-the-photon":15512,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fx-rays-and-the-compton-effect":15534,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-old-quantum-theory-bohr-and-sommerfeld":15535,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fde-broglie-waves-and-electron-diffraction":15536,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fwave-packets-and-the-probability-interpretation":15537,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fthe-uncertainty-principle":15538,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-schrodinger-equation-in-one-dimension":15539,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-free-particle-and-wave-packet-dynamics":15540,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fparticle-in-infinite-and-finite-square-wells":15488,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Foperators-expectation-values-and-the-harmonic-oscillator":15412,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-dirac-delta-potential":15541,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fbarrier-penetration-and-quantum-tunneling":15542,"\u002Fquantum-mechanics\u002Fformalism\u002Fhilbert-space-and-dirac-notation":15543,"\u002Fquantum-mechanics\u002Fformalism\u002Fobservables-hermitian-operators-and-eigenvalues":15544,"\u002Fquantum-mechanics\u002Fformalism\u002Fthe-postulates-and-quantum-measurement":15540,"\u002Fquantum-mechanics\u002Fformalism\u002Fposition-momentum-and-continuous-spectra":15545,"\u002Fquantum-mechanics\u002Fformalism\u002Fcommutators-and-the-generalized-uncertainty-principle":15520,"\u002Fquantum-mechanics\u002Fformalism\u002Ftime-evolution-schrodinger-and-heisenberg-pictures":15273,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fladder-operators-and-the-number-states":15546,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fcoherent-and-squeezed-states":15547,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fsymmetries-generators-and-conservation-laws":15253,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fparity-time-reversal-and-discrete-symmetries":15548,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Forbital-angular-momentum-and-spherical-harmonics":15549,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Fthe-angular-momentum-algebra":15550,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Faddition-of-angular-momenta-and-clebsch-gordan":15551,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-schrodinger-equation-in-three-dimensions":15552,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-hydrogen-atom":15553,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-isotropic-oscillator-and-hidden-symmetry":15554,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-half-pauli-matrices-and-stern-gerlach":15555,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-in-a-magnetic-field-precession-and-resonance":15556,"\u002Fquantum-mechanics\u002Fspin\u002Ftwo-level-systems-and-the-bloch-sphere":15512,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fidentical-particles-and-exchange-symmetry":15557,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fthe-pauli-principle-atoms-and-the-periodic-table":15558,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ftime-independent-perturbation-theory":15559,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ffine-structure-and-the-real-hydrogen-atom":15546,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-zeeman-and-stark-effects":15234,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-variational-method":15560,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-wkb-approximation":15561,"\u002Fquantum-mechanics":15562,"\u002Freal-analysis\u002Ffoundations\u002Fsets-logic-functions":15496,"\u002Freal-analysis\u002Ffoundations\u002Fordered-fields-completeness":15563,"\u002Freal-analysis\u002Ffoundations\u002Fabsolute-value-bounds":15564,"\u002Freal-analysis\u002Ffoundations\u002Fintervals-uncountability":15385,"\u002Freal-analysis\u002Fsequences-series\u002Fsequences-limits":15565,"\u002Freal-analysis\u002Fsequences-series\u002Flimit-laws-monotone":15271,"\u002Freal-analysis\u002Fsequences-series\u002Flimsup-bolzano-weierstrass":15566,"\u002Freal-analysis\u002Fsequences-series\u002Fcauchy-completeness":15567,"\u002Freal-analysis\u002Fsequences-series\u002Fseries-convergence":15408,"\u002Freal-analysis\u002Fsequences-series\u002Fabsolute-conditional-rearrangement":15518,"\u002Freal-analysis\u002Fmetric-spaces\u002Fmetric-spaces-norms":15568,"\u002Freal-analysis\u002Fmetric-spaces\u002Fopen-closed-sets":15569,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconvergence-completeness":15570,"\u002Freal-analysis\u002Fmetric-spaces\u002Fcompactness":15571,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconnectedness":15572,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-of-functions":15545,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuous-functions":15573,"\u002Freal-analysis\u002Fcontinuity\u002Fevt-ivt":15378,"\u002Freal-analysis\u002Fcontinuity\u002Funiform-continuity":15574,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuity-metric-spaces":15575,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-infinity-monotone":15232,"\u002Freal-analysis\u002Fdifferentiation\u002Fthe-derivative":15576,"\u002Freal-analysis\u002Fdifferentiation\u002Fmean-value-theorem":15577,"\u002Freal-analysis\u002Fdifferentiation\u002Ftaylors-theorem":15534,"\u002Freal-analysis\u002Fdifferentiation\u002Finverse-function-1d":15261,"\u002Freal-analysis\u002Friemann-integration\u002Fdarboux-integral":15412,"\u002Freal-analysis\u002Friemann-integration\u002Fintegrability-classes":15578,"\u002Freal-analysis\u002Friemann-integration\u002Fproperties-of-the-integral":15579,"\u002Freal-analysis\u002Friemann-integration\u002Ffundamental-theorem":15397,"\u002Freal-analysis\u002Friemann-integration\u002Flog-exp-improper":15522,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpointwise-uniform-convergence":15580,"\u002Freal-analysis\u002Ffunction-sequences\u002Finterchange-of-limits":15581,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpower-series-weierstrass":15582,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpicard-ode":15417,"\u002Freal-analysis\u002Fseveral-variables\u002Fdifferentiability-rn":15583,"\u002Freal-analysis\u002Fseveral-variables\u002Fgradient-chain-rule":15584,"\u002Freal-analysis\u002Fseveral-variables\u002Fhigher-derivatives-taylor-extrema":15585,"\u002Freal-analysis\u002Fseveral-variables\u002Finverse-implicit-theorems":15585,"\u002Freal-analysis\u002Fseveral-variables\u002Fmultiple-integrals":15586,"\u002Freal-analysis":15587,"\u002Fabstract-algebra\u002Ffoundations\u002Fsets-functions-relations":15588,"\u002Fabstract-algebra\u002Ffoundations\u002Fintegers-and-modular-arithmetic":15589,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fgroup-axioms-and-first-examples":15590,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fdihedral-and-symmetric-groups":15591,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fmatrix-and-quaternion-groups":15592,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fhomomorphisms-and-group-actions":15593,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fsubgroups-and-substructures":15594,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcyclic-groups":15595,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fgeneration-and-subgroup-lattices":15596,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcosets-lagrange-and-normal-subgroups":15597,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fisomorphism-theorems":15561,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcomposition-series-and-the-alternating-group":15598,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Factions-and-cayleys-theorem":15590,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fconjugation-and-the-class-equation":15507,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fsylow-theorems":15599,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fautomorphisms-and-simple-groups":15600,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fdirect-products-and-finite-abelian-groups":15601,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fsemidirect-products":15602,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fnilpotent-and-solvable-groups":15603,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fclassifying-small-groups":15604,"\u002Fabstract-algebra\u002Fring-theory\u002Frings-definitions-and-examples":15605,"\u002Fabstract-algebra\u002Fring-theory\u002Fideals-quotients-and-homomorphisms":15606,"\u002Fabstract-algebra\u002Fring-theory\u002Ffractions-and-the-chinese-remainder-theorem":15600,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Feuclidean-domains-pids-ufds":15607,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fpolynomial-rings-over-fields":15576,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fgauss-lemma-and-unique-factorization":15608,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Firreducibility-criteria-and-groebner":15609,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fintroduction-to-modules":15610,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ffree-modules-and-direct-sums":15611,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ftensor-products-and-exact-sequences":15612,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fvector-spaces-and-linear-maps":15613,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fstructure-theorem-over-pids":15614,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Frational-canonical-form":15615,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fjordan-canonical-form":15616,"\u002Fabstract-algebra\u002Ffield-theory\u002Ffield-extensions-and-algebraic-elements":15617,"\u002Fabstract-algebra\u002Ffield-theory\u002Fstraightedge-and-compass-constructions":15250,"\u002Fabstract-algebra\u002Ffield-theory\u002Fsplitting-fields-and-algebraic-closure":15618,"\u002Fabstract-algebra\u002Ffield-theory\u002Fseparable-and-cyclotomic-extensions":15619,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fthe-galois-correspondence":15492,"\u002Fabstract-algebra\u002Fgalois-theory\u002Ffinite-fields":15620,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fcyclotomic-and-abelian-extensions":15621,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fgalois-groups-of-polynomials":15549,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fsolvability-by-radicals-and-the-quintic":15621,"\u002Fabstract-algebra\u002Fcapstone\u002Fcommutative-algebra-and-algebraic-geometry":15622,"\u002Fabstract-algebra\u002Fcapstone\u002Frepresentation-and-character-theory":15623,"\u002Fabstract-algebra":15624,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fatomic-spectra-rutherford":15625,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-model-hydrogen":15626,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fx-ray-spectra-franck-hertz":15627,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-sommerfeld-old-quantum-theory":15628,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fold-quantum-theory-limits-wkb":15629,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fschrodinger-3d-hydrogen":15541,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fhydrogen-wave-functions":15630,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fradial-equation-in-full":15631,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fsymmetry-degeneracy-runge-lenz":15632,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fexpectation-values-virial":15633,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fquantum-defects-alkali-spectra":15634,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Frydberg-atoms":15635,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Frelativistic-kinetic-correction":15636,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fspin-orbit-thomas-precession":15375,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdarwin-term-fine-structure-formula":15504,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdirac-equation-hydrogen":15250,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Flamb-shift-qed":15637,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fhyperfine-structure-21cm":15234,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fnuclear-effects-isotope-shift":15638,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fperiodic-table-atomic-spectra":15639,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fcentral-field-self-consistent":15272,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fidentical-particles-hartree-fock":15566,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhelium-two-electron-atom":15640,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fls-jj-coupling-term-symbols":15641,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhund-rules-ground-terms":15642,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fzeeman-effect":15643,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fpaschen-back-intermediate":15644,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fstark-effect-polarizability":15645,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Ftime-dependent-perturbation-golden-rule":15646,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fdipole-approximation-einstein-coefficients":15647,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fselection-rules-forbidden-transitions":15648,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Flifetimes-and-line-shapes":15649,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Flaser-principles":15650,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fspectroscopy-techniques":15651,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fline-catalog-nist-asd":15652,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Flaser-cooling-doppler":15653,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fsub-doppler-trapping":15597,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fbose-einstein-condensation":15654,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Foptical-clocks-precision":15655,"\u002Fatomic-physics":15656,"\u002Fdatabases":15421,"\u002Fcategory-theory\u002Ffoundations\u002Fwhat-is-a-category":15657,"\u002Fcategory-theory\u002Ffoundations\u002Fexamples-of-categories":15658,"\u002Fcategory-theory\u002Ffoundations\u002Fspecial-morphisms":15659,"\u002Fcategory-theory\u002Ffoundations\u002Ffunctors":15588,"\u002Fcategory-theory\u002Ffoundations\u002Fnatural-transformations":15660,"\u002Fcategory-theory\u002Ffoundations\u002Fsize-and-set-theory":15661,"\u002Fcategory-theory\u002Funiversal-properties\u002Funiversal-properties":15662,"\u002Fcategory-theory\u002Funiversal-properties\u002Fproducts-and-coproducts":15663,"\u002Fcategory-theory\u002Funiversal-properties\u002Fconstructions-on-categories":15664,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Frepresentable-functors":15665,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-lemma":15666,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-consequences":15667,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits":15668,"\u002Fcategory-theory\u002Flimits-colimits\u002Fproducts-equalizers-pullbacks":15669,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcolimits":15670,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcomputing-limits":15671,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits-and-functors":15672,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions":15673,"\u002Fcategory-theory\u002Fadjunctions\u002Funits-and-counits":15674,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions-via-universal-arrows":15675,"\u002Fcategory-theory\u002Fadjunctions\u002Ffree-forgetful-adjunctions":15676,"\u002Fcategory-theory\u002Fadjoints-limits\u002Flimits-via-adjoints":15677,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fpresheaf-limits-colimits":15678,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoints-preserve-limits":15679,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoint-functor-theorem":15670,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fmonads":15680,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-eilenberg-moore":15681,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fkleisli-and-programming":15682,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-for-endofunctors":15683,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Fcartesian-closed-categories":15684,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Flambda-calculus-correspondence":15629,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Ffixed-points-and-recursion":15685,"\u002Fcategory-theory":15686,"\u002Fdeep-learning\u002Fmathematical-background\u002Flinear-algebra-for-deep-learning":15687,"\u002Fdeep-learning\u002Fmathematical-background\u002Fprobability-and-information-theory":15688,"\u002Fdeep-learning\u002Fmathematical-background\u002Fnumerical-computation":15689,"\u002Fdeep-learning\u002Fmathematical-background\u002Fcalculus":15690,"\u002Fdeep-learning\u002Ffoundations\u002Fwhat-is-deep-learning":15691,"\u002Fdeep-learning\u002Ffoundations\u002Fmachine-learning-refresher":15692,"\u002Fdeep-learning\u002Ffoundations\u002Flinear-models-and-the-perceptron":15651,"\u002Fdeep-learning\u002Fneural-networks\u002Fthe-multilayer-perceptron":15693,"\u002Fdeep-learning\u002Fneural-networks\u002Factivation-functions":15694,"\u002Fdeep-learning\u002Fneural-networks\u002Funiversal-approximation":15695,"\u002Fdeep-learning\u002Fneural-networks\u002Fbackpropagation":15696,"\u002Fdeep-learning\u002Fneural-networks\u002Floss-functions-and-output-units":15697,"\u002Fdeep-learning\u002Foptimization\u002Fgradient-descent-and-sgd":15698,"\u002Fdeep-learning\u002Foptimization\u002Fmomentum-and-adaptive-methods":15699,"\u002Fdeep-learning\u002Foptimization\u002Finitialization":15700,"\u002Fdeep-learning\u002Foptimization\u002Fthe-optimization-landscape":15701,"\u002Fdeep-learning\u002Foptimization\u002Fsecond-order-and-approximate-methods":15702,"\u002Fdeep-learning\u002Fregularization\u002Fregularization-overview":15703,"\u002Fdeep-learning\u002Fregularization\u002Fdropout-and-data-augmentation":15704,"\u002Fdeep-learning\u002Fregularization\u002Fearly-stopping-and-parameter-sharing":15705,"\u002Fdeep-learning\u002Fregularization\u002Fnormalization":15706,"\u002Fdeep-learning\u002Farchitectures\u002Fconvolutional-networks":15707,"\u002Fdeep-learning\u002Farchitectures\u002Fcnn-architectures":15708,"\u002Fdeep-learning\u002Farchitectures\u002Frecurrent-networks":15709,"\u002Fdeep-learning\u002Farchitectures\u002Flstm-and-gru":15710,"\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers":15711,"\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture":15134,"\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice":15712,"\u002Fdeep-learning\u002Farchitectures\u002Fgraph-neural-networks":15713,"\u002Fdeep-learning\u002Farchitectures\u002Fstate-space-models":15714,"\u002Fdeep-learning\u002Ftheory\u002Fgeneralization-theory":15715,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-robustness":15716,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-defenses":15717,"\u002Fdeep-learning\u002Ftheory\u002Fbayesian-and-ensemble-methods":15718,"\u002Fdeep-learning\u002Ftheory\u002Fdeep-equilibrium-models":15663,"\u002Fdeep-learning\u002Fgenerative-models\u002Flinear-factor-models":15719,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoencoders":15720,"\u002Fdeep-learning\u002Fgenerative-models\u002Fvariational-autoencoders":15721,"\u002Fdeep-learning\u002Fgenerative-models\u002Fgenerative-adversarial-networks":15722,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoregressive-and-normalizing-flows":15723,"\u002Fdeep-learning\u002Fgenerative-models\u002Fenergy-based-and-boltzmann-machines":15724,"\u002Fdeep-learning\u002Fgenerative-models\u002Fdiffusion-and-score-based-models":15725,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fstructured-probabilistic-models":15215,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fmonte-carlo-and-mcmc":15726,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fapproximate-inference":15727,"\u002Fdeep-learning\u002Fpractical\u002Fpractical-methodology":15451,"\u002Fdeep-learning\u002Fpractical\u002Fhyperparameters-and-debugging":15728,"\u002Fdeep-learning\u002Fpractical\u002Frepresentation-learning":15729,"\u002Fdeep-learning\u002Fpractical\u002Ftransfer-learning":15730,"\u002Fdeep-learning\u002Fpractical\u002Fapplications":15731,"\u002Fdeep-learning\u002Fpractical\u002Fmodel-compression-and-distillation":15732,"\u002Fdeep-learning\u002Fpractical\u002Fmeta-learning-and-few-shot":15733,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Flarge-language-models":15734,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fscaling-inference-and-alignment":15735,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fseq2seq-pretraining-and-bart":15736,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ftext-to-text-transfer-and-conditional-generation":15737,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fspeech-and-audio-models":15738,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fself-supervised-speech-and-synthesis":15739,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fai-agents":15424,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fagent-memory-retrieval-and-orchestration":15740,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmixture-of-experts":15741,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmultimodal-models":15742,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ffusion-and-vision-language-models":15743,"\u002Fdeep-learning\u002Freinforcement-learning\u002Ffoundations-of-reinforcement-learning":15461,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fmodel-free-prediction-and-control":15744,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fdeep-q-networks":15745,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fpolicy-gradients-and-actor-critic":15746,"\u002Fdeep-learning\u002Freinforcement-learning\u002Frl-from-human-feedback":15747,"\u002Fdeep-learning":15421,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fequilibrium-state-variables-zeroth-law":15748,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Ffirst-law-heat-and-work":15546,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fsecond-law-entropy-and-the-carnot-bound":15749,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fthermodynamic-potentials-and-maxwell-relations":15750,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fstability-response-functions-and-the-third-law":15751,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fclassical-statistics-and-equipartition":15752,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fphase-space-and-liouvilles-theorem":15753,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fensembles-and-the-equal-probability-postulate":15754,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fstatistical-entropy-boltzmann-and-gibbs":15755,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fmicrocanonical-ensemble-and-entropy":15756,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fequilibrium-conditions-temperature-pressure-chemical-potential":15593,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fideal-gas-phase-space-and-the-sackur-tetrode-entropy":15757,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Ftwo-state-systems-paramagnets-and-negative-temperature":15758,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fcanonical-ensemble-and-the-boltzmann-distribution":15759,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fpartition-function-and-the-helmholtz-free-energy":15480,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fenergy-fluctuations-and-ensemble-equivalence":15273,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fthe-einstein-solid-and-harmonic-systems":15760,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fparamagnetism-and-the-schottky-anomaly":15761,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fideal-gas-partition-function-and-the-gibbs-paradox":15762,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fequipartition-and-the-virial-theorem":15407,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fmolecular-gases-rotation-and-vibration":15763,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fgrand-canonical-ensemble-and-the-grand-partition-function":15764,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fchemical-potential-fugacity-and-number-fluctuations":15485,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fensemble-summary-and-the-thermodynamic-web":15412,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fquantum-statistics-bose-einstein-and-fermi-dirac":15765,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fderiving-the-quantum-distributions":15381,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fthe-classical-limit-and-quantum-concentration":15251,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fideal-quantum-gases-general-framework":15267,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-and-the-fermion-gas":15766,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthe-photon-gas-and-plancks-radiation-law":15767,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fblackbody-thermodynamics-and-radiation-pressure":15768,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fphonons-and-the-debye-model":15399,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-derived":15769,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthermodynamics-of-the-bose-gas-and-superfluidity":15261,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fthe-ideal-fermi-gas-at-zero-temperature":15770,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fsommerfeld-expansion-and-electrons-in-metals":15771,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":15772,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fneutron-stars-and-nuclear-matter":15773,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-cluster-expansion-and-virial-coefficients":15595,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-van-der-waals-gas-and-liquid-gas-coexistence":15774,"\u002Fstatistical-mechanics\u002Finteractions\u002Fquantum-gases-with-interactions-and-exchange":15775,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fphases-coexistence-and-classification":15776,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-ising-model-and-exact-solutions":15777,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fmean-field-theory-and-the-weiss-model":15541,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fcritical-exponents-and-landau-theory":15778,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-renormalization-group-idea":15519,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fthermodynamic-fluctuations-and-response":15779,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fbrownian-motion-and-the-langevin-equation":15380,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Flinear-response-and-the-fluctuation-dissipation-theorem":15780,"\u002Fstatistical-mechanics":15781,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fbonding-mechanisms":15782,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fmolecular-orbitals-and-h2-plus":15246,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fhydrogen-molecule-and-exchange":15506,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fvan-der-waals-forces":15783,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Frotational-vibrational-spectra":15784,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Fanharmonicity-and-rovibrational-structure":15785,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Framan-and-electronic-bands":15786,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Flasers-and-masers":15787,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fstructure-of-solids":15788,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fbravais-lattices-and-crystal-systems":15379,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Freciprocal-lattice-and-brillouin-zones":15789,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fdiffraction-and-structure-factors":15790,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonon-dispersion":15791,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonons-quantization-and-dos":15792,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fdebye-einstein-heat-capacity":15522,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fanharmonicity-and-thermal-transport":15793,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ffree-electron-gas-and-conduction":15794,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fsommerfeld-model-and-heat-capacity":15795,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ftransport-and-the-hall-effect":15796,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fscreening-and-plasmons":15797,"\u002Fcondensed-matter\u002Fband-theory\u002Fblochs-theorem-and-energy-bands":15577,"\u002Fcondensed-matter\u002Fband-theory\u002Fnearly-free-electron-model":15521,"\u002Fcondensed-matter\u002Fband-theory\u002Ftight-binding-method":15798,"\u002Fcondensed-matter\u002Fband-theory\u002Ffermi-surfaces-and-semiclassical-dynamics":15799,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fsemiconductor-bands-and-junctions":15800,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fintrinsic-and-extrinsic-semiconductors":15801,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fcarrier-transport-and-recombination":15512,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fthe-pn-junction":15802,"\u002Fcondensed-matter\u002Fsemiconductors\u002Ftransistors-and-optoelectronics":15803,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fdielectrics-and-polarization":15748,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fferroelectrics-and-piezoelectrics":15649,"\u002Fcondensed-matter\u002Fmagnetism\u002Fdiamagnetism-and-paramagnetism":15376,"\u002Fcondensed-matter\u002Fmagnetism\u002Fexchange-and-ferromagnetism":15804,"\u002Fcondensed-matter\u002Fmagnetism\u002Fantiferromagnetism-and-domains":15242,"\u002Fcondensed-matter\u002Fmagnetism\u002Fspin-waves-and-magnons":15805,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fsuperconductivity-phenomenology":15806,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Flondon-theory-and-the-meissner-effect":15387,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fginzburg-landau-theory":15807,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fbcs-theory":15642,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fjosephson-and-high-tc":15808,"\u002Fcondensed-matter\u002Fnanostructures\u002Fquantum-wells-wires-and-dots":15234,"\u002Fcondensed-matter\u002Fnanostructures\u002Finteger-quantum-hall-effect":15809,"\u002Fcondensed-matter\u002Fnanostructures\u002Ffractional-quantum-hall-and-topology":15245,"\u002Fcondensed-matter\u002Fnanostructures\u002Fgraphene-and-dirac-materials":15810,"\u002Fcondensed-matter":15562,"\u002Flogic\u002Ffoundations\u002Flogic-as-a-mathematical-model":15811,"\u002Flogic\u002Fsentential-logic\u002Fformal-languages-and-well-formed-formulas":15812,"\u002Flogic\u002Fsentential-logic\u002Ftruth-assignments-and-tautologies":15813,"\u002Flogic\u002Fsentential-logic\u002Funique-readability-and-parsing":15814,"\u002Flogic\u002Fsentential-logic\u002Finduction-and-recursion":15259,"\u002Flogic\u002Fsentential-logic\u002Fexpressive-completeness-and-normal-forms":15815,"\u002Flogic\u002Fsentential-logic\u002Fboolean-circuits":15816,"\u002Flogic\u002Fsentential-logic\u002Fcompactness-and-effectiveness":15259,"\u002Flogic\u002Ffirst-order-languages\u002Ffirst-order-languages":15817,"\u002Flogic\u002Ffirst-order-languages\u002Fstructures-truth-and-satisfaction":15672,"\u002Flogic\u002Ffirst-order-languages\u002Fdefinability-and-elementary-equivalence":15818,"\u002Flogic\u002Ffirst-order-languages\u002Fterms-substitution-and-parsing":15819,"\u002Flogic\u002Fdeductive-calculus\u002Fa-deductive-calculus":15820,"\u002Flogic\u002Fdeductive-calculus\u002Fdeduction-theorem-and-derived-rules":15818,"\u002Flogic\u002Fdeductive-calculus\u002Fsoundness":15821,"\u002Flogic\u002Fdeductive-calculus\u002Fcompleteness-and-consistency":15822,"\u002Flogic\u002Fmodels-and-theories\u002Fcompactness-and-lowenheim-skolem":15823,"\u002Flogic\u002Fmodels-and-theories\u002Ftheories-elementary-classes-and-categoricity":15824,"\u002Flogic\u002Fmodels-and-theories\u002Finterpretations-between-theories":15825,"\u002Flogic\u002Fmodels-and-theories\u002Fnonstandard-analysis":15826,"\u002Flogic\u002Farithmetic-and-definability\u002Fdefinability-in-arithmetic":15827,"\u002Flogic\u002Farithmetic-and-definability\u002Fnatural-numbers-with-successor":15828,"\u002Flogic\u002Farithmetic-and-definability\u002Fpresburger-and-reducts":15749,"\u002Flogic\u002Farithmetic-and-definability\u002Fa-subtheory-and-representability":15829,"\u002Flogic\u002Fincompleteness\u002Farithmetization-of-syntax":15822,"\u002Flogic\u002Fincompleteness\u002Fincompleteness-and-undecidability":15830,"\u002Flogic\u002Fincompleteness\u002Fsecond-incompleteness-theorem":15831,"\u002Flogic\u002Fcomputability-and-representability\u002Frecursive-functions":15465,"\u002Flogic\u002Fcomputability-and-representability\u002Frepresenting-exponentiation":15832,"\u002Flogic\u002Fsecond-order-logic\u002Fsecond-order-languages":15650,"\u002Flogic\u002Fsecond-order-logic\u002Fskolem-functions-and-many-sorted-logic":15833,"\u002Flogic\u002Fsecond-order-logic\u002Fgeneral-structures":15834,"\u002Flogic":15835,"\u002Freinforcement-learning\u002Ffoundations\u002Fwhat-is-reinforcement-learning":15836,"\u002Freinforcement-learning\u002Ffoundations\u002Fa-brief-history-of-rl":15837,"\u002Freinforcement-learning\u002Ffoundations\u002Fmulti-armed-bandits":15451,"\u002Freinforcement-learning\u002Ffoundations\u002Fbandit-exploration-algorithms":15838,"\u002Freinforcement-learning\u002Ffoundations\u002Fmarkov-decision-processes":15839,"\u002Freinforcement-learning\u002Ffoundations\u002Fvalue-functions-and-optimality":15840,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdynamic-programming":15841,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdp-async-and-gpi":15831,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-methods":15842,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-off-policy":15843,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftemporal-difference-learning":15844,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftd-control-sarsa-and-q-learning":15742,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-bootstrapping":15845,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-off-policy-methods":15846,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-and-learning":15847,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-focusing-and-decision-time":15848,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdecision-time-planning":15849,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-tree-search":15468,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-prediction":15850,"\u002Freinforcement-learning\u002Fapproximation\u002Ffeature-construction-and-nonlinear":15851,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-control":15852,"\u002Freinforcement-learning\u002Fapproximation\u002Faverage-reward-control":15853,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-and-the-deadly-triad":15659,"\u002Freinforcement-learning\u002Fapproximation\u002Fbellman-error-and-gradient-td":15854,"\u002Freinforcement-learning\u002Fapproximation\u002Feligibility-traces":15830,"\u002Freinforcement-learning\u002Fapproximation\u002Ftrue-online-and-sarsa-lambda":15855,"\u002Freinforcement-learning\u002Fapproximation\u002Fpolicy-gradient-methods":15856,"\u002Freinforcement-learning\u002Fapproximation\u002Factor-critic-and-continuous-actions":15857,"\u002Freinforcement-learning\u002Fapproximation\u002Fleast-squares-and-memory-based-methods":15479,"\u002Freinforcement-learning\u002Fapproximation\u002Fmemory-and-kernel-methods":15858,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-eligibility-traces":15609,"\u002Freinforcement-learning\u002Fapproximation\u002Fstable-off-policy-traces":15859,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdeep-q-networks":15860,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdqn-improvements":15441,"\u002Freinforcement-learning\u002Fdeep-rl\u002Factor-critic-and-ppo":15861,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fppo-and-continuous-control":15862,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fcase-studies":15863,"\u002Freinforcement-learning\u002Fdeep-rl\u002Frl-beyond-games":15864,"\u002Freinforcement-learning\u002Fdeep-rl\u002Ffrontiers":15865,"\u002Freinforcement-learning\u002Fdeep-rl\u002Freward-design-and-open-problems":15718,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow":15866,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow-part-2":15867,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control":15868,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control-part-2":15753,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl":15869,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl-part-2":15870,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration":15871,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration-part-2":15468,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl":15535,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl-part-2":15872,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl":15873,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl-part-2":15874,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl":15875,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl-part-2":15876,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl":15877,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl-part-2":15878,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Frlhf-and-language-models":15879,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps":15880,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps-part-2":15881,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl":15882,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl-part-2":15883,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmeta-rl-and-generalization":15884,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fpsychology-of-reinforcement":15885,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Finstrumental-conditioning-and-control":15886,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-and-td-error":15887,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-in-the-brain":15888,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fanimal-learning-and-cognition":15889,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fcognitive-maps-and-planning":15890,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fneuroscience-of-reinforcement":15891,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fseveral-learning-systems":15892,"\u002Freinforcement-learning":15421,"\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai":15893,"\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai":15894,"\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents":15895,"\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures":15896,"\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search":15897,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared":15898,"\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search":15899,"\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions":15900,"\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search":15901,"\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search":15902,"\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search":15903,"\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information":15904,"\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction":15905,"\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure":15747,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty":15603,"\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search":15906,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic":15907,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference":15908,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic":15909,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use":15910,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution":15911,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution":15729,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning":15912,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan":15913,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world":15914,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty":15915,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation":15916,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults":15917,"\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes":15918,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes":15919,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks":15920,"\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks":15921,"\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time":15922,"\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association":15923,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions":15662,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes":15913,"\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory":15924,"\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design":15202,"\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples":15925,"\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families":15926,"\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning":15927,"\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization":15928,"\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning":15929,"\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search":15711,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning":15930,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods":15931,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception":15932,"\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world":15933,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics":15934,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control":15935,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai":15936,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech":15937,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future":15938,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future":15939,"\u002Fartificial-intelligence":15421,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart":15678,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions":15940,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy":15238,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula":15236,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles":15771,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview":15941,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron":15264,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering":15574,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin":15942,"\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model":15943,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates":15944,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle":15634,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations":15945,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes":15946,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium":15947,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory":15832,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance":15948,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino":15949,"\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay":15248,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation":15477,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass":15950,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation":15578,"\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers":15951,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer":15952,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections":15473,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances":15561,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model":15953,"\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics":15954,"\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics":15955,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement":15243,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis":15618,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis":15480,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power":15956,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions":15528,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors":15592,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology":15957,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine":15958,"\u002Fnuclear-physics":15959,"\u002Fnatural-language-processing\u002Ffoundations\u002Fwhat-is-nlp":15960,"\u002Fnatural-language-processing\u002Ffoundations\u002Fregex-and-text-normalization":15961,"\u002Fnatural-language-processing\u002Ffoundations\u002Fminimum-edit-distance":15599,"\u002Fnatural-language-processing\u002Ffoundations\u002Fn-gram-language-models":15962,"\u002Fnatural-language-processing\u002Ffoundations\u002Fsmoothing-and-backoff":15963,"\u002Fnatural-language-processing\u002Fclassification\u002Fnaive-bayes-and-sentiment":15964,"\u002Fnatural-language-processing\u002Fclassification\u002Fevaluating-classifiers":15447,"\u002Fnatural-language-processing\u002Fclassification\u002Flogistic-regression":15965,"\u002Fnatural-language-processing\u002Fclassification\u002Fsentiment-and-affect-lexicons":15966,"\u002Fnatural-language-processing\u002Fsemantics\u002Fvector-semantics-and-embeddings":15743,"\u002Fnatural-language-processing\u002Fsemantics\u002Fstatic-word-embeddings":15967,"\u002Fnatural-language-processing\u002Fsemantics\u002Fneural-language-models":15912,"\u002Fnatural-language-processing\u002Fsequences\u002Fsequence-labeling":15968,"\u002Fnatural-language-processing\u002Fsequences\u002Fcrfs-and-neural-taggers":15969,"\u002Fnatural-language-processing\u002Fsequences\u002Frnns-and-lstms":15970,"\u002Fnatural-language-processing\u002Ftransformers\u002Ftransformers-and-attention":15971,"\u002Fnatural-language-processing\u002Ftransformers\u002Fthe-transformer-architecture":15972,"\u002Fnatural-language-processing\u002Ftransformers\u002Flarge-language-models":15973,"\u002Fnatural-language-processing\u002Ftransformers\u002Fllm-pretraining-and-scaling":15974,"\u002Fnatural-language-processing\u002Ftransformers\u002Ffine-tuning-and-prompting":15425,"\u002Fnatural-language-processing\u002Ftransformers\u002Fprompting-and-alignment":15975,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-parsing":15976,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcky-scoring-and-evaluation":15918,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdependency-parsing":15977,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fgraph-based-and-neural-dependency-parsing":15978,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fword-senses-and-wsd":15979,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fwsd-in-practice-and-induction":15980,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-roles-and-information-extraction":15981,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Frelations-events-and-templates":15982,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoreference-and-discourse":15983,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoherence-and-discourse-structure":15984,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Flogical-semantics":15842,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcompositional-semantics-and-description-logics":15985,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-parsing":15986,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fneural-semantic-parsing":15987,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Finformation-extraction":15988,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftimes-events-and-templates":15989,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdiscourse-coherence":15990,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fentity-based-and-global-coherence":15991,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-grammars":15992,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftreebanks-and-lexicalized-grammars":15993,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation":15994,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation-decoding-and-evaluation":15995,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering":15996,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering-knowledge-and-llms":15697,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-and-chatbots":15863,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-systems-and-assistants":15453,"\u002Fnatural-language-processing\u002Fapplications\u002Ftext-summarization":15997,"\u002Fnatural-language-processing\u002Fapplications\u002Fabstractive-summarization-and-evaluation":15998,"\u002Fnatural-language-processing\u002Fspeech\u002Fphonetics":15999,"\u002Fnatural-language-processing\u002Fspeech\u002Facoustic-phonetics":16000,"\u002Fnatural-language-processing\u002Fspeech\u002Fautomatic-speech-recognition":15711,"\u002Fnatural-language-processing\u002Fspeech\u002Fasr-evaluation-and-applications":16001,"\u002Fnatural-language-processing":15421,"\u002Fparticle-physics\u002Ffoundations\u002Fhistorical-overview-particle-zoo":16002,"\u002Fparticle-physics\u002Ffoundations\u002Fparticle-physics-basic-concepts":15619,"\u002Fparticle-physics\u002Ffoundations\u002Ffundamental-interactions-force-carriers":16003,"\u002Fparticle-physics\u002Funits-kinematics\u002Fnatural-units-and-scales":15763,"\u002Fparticle-physics\u002Funits-kinematics\u002Ffour-vectors-invariant-mass":16004,"\u002Fparticle-physics\u002Funits-kinematics\u002Fdecay-scattering-kinematics-mandelstam":16005,"\u002Fparticle-physics\u002Funits-kinematics\u002Fcross-sections-golden-rule":15953,"\u002Fparticle-physics\u002Fsymmetries\u002Fconservation-laws-symmetries":16006,"\u002Fparticle-physics\u002Fsymmetries\u002Fdiscrete-symmetries-cpt":16007,"\u002Fparticle-physics\u002Fsymmetries\u002Fparity-violation-weak":15569,"\u002Fparticle-physics\u002Fsymmetries\u002Fsu2-su3-flavor-symmetry":15271,"\u002Fparticle-physics\u002Fquark-model\u002Feightfold-way-su3":16008,"\u002Fparticle-physics\u002Fquark-model\u002Fmeson-spectroscopy":15523,"\u002Fparticle-physics\u002Fquark-model\u002Fbaryon-spectroscopy":16009,"\u002Fparticle-physics\u002Fquark-model\u002Fcolor-confinement-exotics":15556,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fklein-gordon-equation":16010,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fdirac-equation-spinors":15809,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fantiparticles-hole-theory":16011,"\u002Fparticle-physics\u002Fqed\u002Ffeynman-rules-qed":16012,"\u002Fparticle-physics\u002Fqed\u002Fqed-tree-processes":15778,"\u002Fparticle-physics\u002Fqed\u002Frenormalization-running-coupling":16013,"\u002Fparticle-physics\u002Fqed\u002Felectron-g-2":15242,"\u002Fparticle-physics\u002Fweak-interaction\u002Fva-structure-weak":16014,"\u002Fparticle-physics\u002Fweak-interaction\u002Fw-z-bosons-decays":16015,"\u002Fparticle-physics\u002Fweak-interaction\u002Fckm-matrix":16016,"\u002Fparticle-physics\u002Fweak-interaction\u002Fcp-violation-kaons-b-mesons":15560,"\u002Fparticle-physics\u002Fqcd\u002Fcolor-su3-gluons":15775,"\u002Fparticle-physics\u002Fqcd\u002Fasymptotic-freedom-confinement":16017,"\u002Fparticle-physics\u002Fqcd\u002Fdeep-inelastic-scattering-partons":16018,"\u002Fparticle-physics\u002Fqcd\u002Fjets-hadronization":15635,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Felectroweak-su2-u1":16019,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fspontaneous-symmetry-breaking":15680,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-mechanism":16020,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-boson-discovery":16021,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fstandard-model":15569,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-oscillations":15602,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-mass-pmns":16022,"\u002Fparticle-physics\u002Fneutrinos\u002Fdirac-majorana-experiments":16023,"\u002Fparticle-physics\u002Fexperiment\u002Faccelerators-luminosity":16024,"\u002Fparticle-physics\u002Fexperiment\u002Fdetectors-subsystems":15658,"\u002Fparticle-physics\u002Fexperiment\u002Fhow-discoveries-are-made":16025,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fbeyond-standard-model":15399,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fgrand-unified-theories":16026,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fsupersymmetry":15502,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fhierarchy-problem-naturalness":16027,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fdark-matter-candidates":16028,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fmatter-antimatter-open-questions":15825,"\u002Fparticle-physics":16029,"\u002Fastrophysics-cosmology\u002Forientation\u002Fthe-sun-and-stars":15620,"\u002Fastrophysics-cosmology\u002Forientation\u002Fstellar-death-final-states":15773,"\u002Fastrophysics-cosmology\u002Forientation\u002Fgalaxies-and-cosmology":16030,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fmagnitudes-fluxes-and-the-distance-modulus":15559,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fstellar-spectra-and-spectral-classification":16031,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Ftelescopes-and-detectors-across-the-spectrum":15619,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fthe-cosmic-distance-ladder":15531,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fblackbody-radiation-and-specific-intensity":16032,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fradiative-transfer-and-the-transfer-equation":16033,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fspectral-line-formation-and-broadening":16034,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fopacity-and-the-rosseland-mean":16035,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fhydrostatic-equilibrium-and-the-virial-theorem":16036,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equations-of-stellar-structure":15824,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equation-of-state-and-polytropes":15755,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-standard-solar-model":16037,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fthermonuclear-reaction-rates-and-the-gamow-peak":16038,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhydrogen-burning-pp-chains-and-cno":16039,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhelium-burning-and-the-triple-alpha-process":16040,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fadvanced-burning-and-neutron-capture-nucleosynthesis":15952,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fphases-of-the-interstellar-medium":16041,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fmolecular-clouds-and-gravitational-collapse":15515,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fprotostars-and-the-pre-main-sequence":15578,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-main-sequence-and-its-structure":15560,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fpost-main-sequence-low-mass-evolution":16042,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-evolution-of-massive-stars":15644,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fstellar-pulsation-and-the-instability-strip":15260,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":16043,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fcore-collapse-supernovae":16044,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fthermonuclear-supernovae-type-ia":15774,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fneutron-stars-and-pulsars":16045,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fblack-holes-schwarzschild-and-kerr":16046,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fbinary-systems-and-mass-transfer":16047,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Faccreting-compact-objects":16048,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fgravitational-waves-from-inspiraling-binaries":15241,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fmultimessenger-astronomy-and-gamma-ray-bursts":16049,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fthe-milky-way":16050,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-morphology-and-classification":15502,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-rotation-curves-and-dark-matter":16051,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Factive-galactic-nuclei-and-supermassive-black-holes":16052,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-clusters-and-large-scale-structure":15767,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-expanding-universe-and-hubbles-law":15423,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-frw-metric-and-cosmological-redshift":16053,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-friedmann-equations-and-cosmic-dynamics":16054,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fcosmological-models-and-distances":15680,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fdark-energy-and-the-accelerating-universe":15666,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fthe-thermal-history-of-the-universe":15678,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fbig-bang-nucleosynthesis":15774,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Frecombination-and-the-cosmic-microwave-background":16055,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcmb-anisotropies-and-cosmological-parameters":15240,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcosmic-inflation":15432,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fstructure-formation-and-the-growth-of-perturbations":16056,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fdark-matter-dark-energy-and-open-questions":15519,"\u002Fastrophysics-cosmology":15624,"\u002Fcolophon":16057,"\u002F":15421},4250,4808,3626,2682,4109,4786,3878,3875,3751,3415,4067,3153,3000,4042,5461,5808,3961,3749,4327,5067,4246,4655,4154,5436,2640,4003,3601,2158,4331,4189,2273,3252,4633,4964,4172,3131,5524,3160,4031,2309,4207,3226,2648,4842,5340,3307,5701,4977,4039,2615,3472,4460,3848,4075,4400,3382,3010,3602,3737,3740,3707,3922,5191,4043,3804,4542,4214,5062,2850,4361,3443,3627,4044,3766,4140,3860,4006,5199,4334,5234,3651,5509,5680,153,1375,1073,1093,1125,1146,1014,1132,876,1541,1189,1173,984,1402,1301,950,1268,1063,1107,1408,1161,925,1012,866,964,1090,1142,1085,1020,1207,973,980,728,764,1225,1329,796,929,801,878,774,1044,1488,1175,1130,890,814,870,154,4073,5140,4961,5127,4870,5382,5195,4955,5369,4501,5576,3824,4132,4289,4307,4570,3403,5084,5105,5201,5116,5341,5175,5368,5188,5211,5499,5155,4981,5125,5415,5255,5304,5130,5167,5552,5164,5094,5239,5036,5190,5004,5099,5035,5159,5088,5026,4937,5023,5264,5244,133,5114,5078,5043,5312,5170,5342,5139,5151,5049,5212,5013,5068,5079,5102,5121,5081,5029,5379,5854,5110,2139,3798,5055,5364,4984,4935,4895,4972,5289,5112,5156,4987,5031,5025,5149,5302,5042,5002,4979,4922,4960,5279,126,1877,1180,1129,907,958,1112,1300,1053,1250,1181,1241,1234,966,1050,734,1190,484,1082,926,733,761,571,607,798,804,952,977,731,784,645,771,1017,742,1004,1000,1562,1254,1288,1101,1011,1486,1061,856,992,1169,988,137,0,2037,1782,2384,2254,2123,2332,1643,1714,2089,1751,1367,1660,2511,1998,1892,1854,1791,2438,2487,1917,2375,2525,2266,1845,2275,1810,1631,2310,2166,2233,2113,2505,2347,2672,2112,2473,2592,2380,3013,2513,3256,3218,2194,2173,2205,2326,2081,3342,3152,1799,1670,1027,960,1095,1291,986,897,1209,1055,1817,1801,1593,1465,1196,1464,1201,1230,1435,1684,1461,1926,1500,1409,1284,1774,1869,162,1487,1122,1188,1001,1351,982,1005,979,1325,1046,943,1279,824,1008,989,1798,1277,1025,987,1043,1211,1074,981,939,1002,739,1139,1108,1013,1070,978,1458,1317,157,1357,1077,2355,1116,1037,1178,1637,1314,1109,1056,1702,1474,1071,1158,832,993,1404,1024,1068,1339,1106,1264,1248,913,1848,1328,1633,1224,1143,135,1378,959,1028,998,911,1527,1203,1266,1483,1165,990,938,965,1257,1418,1099,942,1352,956,1035,1398,1003,1094,1292,138,1721,1827,1449,1354,1148,1184,1285,1281,1213,1290,1271,1252,1274,1778,1591,1503,1437,1571,1584,1957,1117,1781,1648,1342,1667,1510,1965,1607,1365,1849,1259,1303,1356,1238,2208,1564,173,1671,1286,1227,1638,1529,668,1078,918,709,865,880,940,1534,1015,874,922,841,794,1194,822,1105,1658,1359,1296,1438,1921,1844,1570,1429,1324,1400,140,1787,1558,1654,1492,1747,2224,2002,2009,1323,1349,1785,1573,1722,1829,1353,1548,1552,1583,1624,1585,1245,1364,1514,1343,1397,1355,2211,1481,1770,160,2388,2293,2256,2552,2569,2478,2039,2496,2578,2814,2519,2461,2587,2492,2714,3278,2654,3050,2447,2849,2238,2369,2061,2214,2602,2186,2985,2749,3364,2038,2282,2409,2126,2573,2206,2176,2268,2182,2402,2705,2633,2414,2213,2801,3313,3410,3195,1952,2017,1509,2537,2645,2027,2415,2838,2356,1906,3184,2950,2807,2954,1683,1316,1034,1138,1763,1822,1705,1246,1701,1097,1104,1187,1032,1083,1228,916,1489,1033,1652,997,692,837,1023,888,864,1089,1231,1214,1675,1156,1075,1520,1309,139,1205,1051,735,1123,1072,915,567,768,825,1253,983,1007,762,1058,861,862,971,1208,1149,1145,1029,1084,927,810,838,857,807,936,949,2321,1622,1069,1113,1057,854,1958,1528,1618,2049,1432,1679,1796,1685,1346,1275,1476,1505,1610,2018,1599,1215,1838,1909,132,3902,2215,2240,3266,3208,3073,2454,2969,2451,1875,2728,1884,2371,2516,2842,1690,1904,2346,3146,1386,2607,1966,2668,1665,2885,1606,2577,3074,2869,2403,2433,2082,1939,1587,2460,2747,2032,2642,1619,3123,1993,2090,2339,3829,1737,2622,2340,2322,3828,4409,2305,3411,2510,4527,3030,3569,3043,2457,1946,2277,2044,2909,1693,1945,2093,2399,2115,2898,2742,2242,3895,3378,3376,2769,2223,3062,3262,2651,2949,2768,3128,2423,1977,2087,2866,3388,2830,2210,2489,2884,3945,2099,2713,3402,1692,2931,4195,3989,3206,4391,3004,3704,3494,2902,999,881,901,919,748,869,1018,1045,1049,1333,954,1092,1019,976,1771,1480,1396,953,1026,161,3533,2495,1818,3007,2595,3427,3537,2216,1895,2304,3396,1739,2073,1962,2203,1767,2666,2264,2276,2852,1807,3735,1560,4144,1669,1676,1972,2418,3291,1525,2040,2766,2337,2220,2800,3001,2078,1759,2836,1896,2026,1758,1543,1047,896,946,1060,1384,1482,815,1414,1322,1440,1240,1468,1098,1133,847,1009,1381,1052,1191,1258,1370,1712,1441,1199,957,1079,150,1262,1417,1368,1219,1136,1064,1463,1636,1059,931,1115,1736,1174,1376,1363,1411,1247,1746,1313,1299,1617,1102,1076,1495,1265,1193,1263,80,{"\u002Falgorithms\u002Ffoundations\u002Fwhat-is-an-algorithm":16059,"\u002Falgorithms\u002Ffoundations\u002Fproof-techniques":16064,"\u002Falgorithms\u002Ffoundations\u002Fasymptotic-analysis":16068,"\u002Falgorithms\u002Ffoundations\u002Fgrowth-rates-and-loop-analysis":16072,"\u002Falgorithms\u002Ffoundations\u002Frecurrences":16076,"\u002Falgorithms\u002Ffoundations\u002Famortized-analysis":16080,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fmergesort":16084,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fquicksort":16089,"\u002Falgorithms\u002Fdivide-and-conquer\u002Fselection":16093,"\u002Falgorithms\u002Fdivide-and-conquer\u002Ffast-multiplication":16097,"\u002Falgorithms\u002Fsorting\u002Fheaps-and-heapsort":16101,"\u002Falgorithms\u002Fsorting\u002Fsorting-lower-bounds":16106,"\u002Falgorithms\u002Fsorting\u002Flinear-time-sorting":16110,"\u002Falgorithms\u002Fsorting\u002Fexternal-sorting":16114,"\u002Falgorithms\u002Fdata-structures\u002Felementary-structures":16118,"\u002Falgorithms\u002Fdata-structures\u002Fhash-tables":16123,"\u002Falgorithms\u002Fdata-structures\u002Fbinary-search-trees":16127,"\u002Falgorithms\u002Fdata-structures\u002Favl-trees":16131,"\u002Falgorithms\u002Fdata-structures\u002Fbalanced-trees":16135,"\u002Falgorithms\u002Fdata-structures\u002Funion-find":16139,"\u002Falgorithms\u002Fdata-structures\u002Ffenwick-and-segment-trees":16143,"\u002Falgorithms\u002Fdata-structures\u002Fspatial-data-structures":16147,"\u002Falgorithms\u002Fdata-structures\u002Fskip-lists-and-probabilistic-structures":16151,"\u002Falgorithms\u002Fdata-structures\u002Fb-trees":16155,"\u002Falgorithms\u002Fdata-structures\u002Fdata-stream-algorithms":16159,"\u002Falgorithms\u002Fdata-structures\u002Fstreaming-sketches":16163,"\u002Falgorithms\u002Fsequences\u002Ftwo-pointers-and-windows":16167,"\u002Falgorithms\u002Fsequences\u002Fprefix-sums":16172,"\u002Falgorithms\u002Fsequences\u002Fmonotonic-stacks":16176,"\u002Falgorithms\u002Fsequences\u002Fbinary-search-on-the-answer":16180,"\u002Falgorithms\u002Fsequences\u002Fstring-matching":16184,"\u002Falgorithms\u002Fsequences\u002Fkmp-and-z-function":16188,"\u002Falgorithms\u002Fsequences\u002Ftries":16192,"\u002Falgorithms\u002Fsequences\u002Fsuffix-arrays-and-aho-corasick":16196,"\u002Falgorithms\u002Fgraphs\u002Frepresentations-and-traversal":16200,"\u002Falgorithms\u002Fgraphs\u002Fdepth-first-search":16205,"\u002Falgorithms\u002Fgraphs\u002Ftopological-sort-and-scc":16209,"\u002Falgorithms\u002Fgraphs\u002Fminimum-spanning-trees":16213,"\u002Falgorithms\u002Fgraphs\u002Fkruskal-and-prim":16217,"\u002Falgorithms\u002Fgraphs\u002Fshortest-paths":16221,"\u002Falgorithms\u002Fgraphs\u002Fall-pairs-and-negative-weights":16225,"\u002Falgorithms\u002Fgraphs\u002Fnetwork-flow":16229,"\u002Falgorithms\u002Fgraphs\u002Fmax-flow-min-cut":16233,"\u002Falgorithms\u002Fgraphs\u002Fbridges-and-articulation-points":16237,"\u002Falgorithms\u002Fgraphs\u002Flowest-common-ancestor":16241,"\u002Falgorithms\u002Fgraphs\u002Ftwo-sat":16245,"\u002Falgorithms\u002Fgraphs\u002Feulerian-tours":16249,"\u002Falgorithms\u002Fgraphs\u002Fbipartite-matching":16253,"\u002Falgorithms\u002Fgreedy\u002Fthe-greedy-method":16257,"\u002Falgorithms\u002Fgreedy\u002Fscheduling-and-intervals":16262,"\u002Falgorithms\u002Fgreedy\u002Fhuffman-codes":16266,"\u002Falgorithms\u002Fgreedy\u002Fmatroids":16270,"\u002Falgorithms\u002Fgreedy\u002Fstable-matching":16274,"\u002Falgorithms\u002Fdynamic-programming\u002Fprinciples":16278,"\u002Falgorithms\u002Fdynamic-programming\u002Fsequence-dp":16283,"\u002Falgorithms\u002Fdynamic-programming\u002Flongest-increasing-subsequence":16287,"\u002Falgorithms\u002Fdynamic-programming\u002Fknapsack":16291,"\u002Falgorithms\u002Fdynamic-programming\u002Fcoin-change-and-unbounded":16295,"\u002Falgorithms\u002Fdynamic-programming\u002Finterval-dp":16299,"\u002Falgorithms\u002Fdynamic-programming\u002Ftree-dp":16303,"\u002Falgorithms\u002Fdynamic-programming\u002Fbitmask-dp":16307,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-optimizations":16311,"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-on-graphs":16315,"\u002Falgorithms\u002Fdynamic-programming\u002Fdigit-and-probability-dp":16319,"\u002Falgorithms\u002Fbacktracking\u002Fbacktracking-fundamentals":16323,"\u002Falgorithms\u002Fbacktracking\u002Fconstraint-search":16328,"\u002Falgorithms\u002Fbacktracking\u002Fbranch-and-bound":16332,"\u002Falgorithms\u002Fbacktracking\u002Fgraph-backtracking":16336,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fnumber-theory-basics":16340,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmodular-exponentiation-and-primality":16345,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fsieve-and-factorization":16349,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fcombinatorics":16353,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmatrix-exponentiation":16357,"\u002Falgorithms\u002Fmathematical-algorithms\u002Ffast-fourier-transform":16361,"\u002Falgorithms\u002Fmathematical-algorithms\u002Fgradient-descent":16365,"\u002Falgorithms\u002Fcomputational-geometry\u002Fgeometric-primitives":16369,"\u002Falgorithms\u002Fcomputational-geometry\u002Fconvex-hull":16374,"\u002Falgorithms\u002Fcomputational-geometry\u002Fsweep-line":16378,"\u002Falgorithms\u002Fcomputational-geometry\u002Fpolygons-and-proximity":16382,"\u002Falgorithms\u002Fintractability\u002Fp-np-reductions":16386,"\u002Falgorithms\u002Fintractability\u002Fnp-completeness":16391,"\u002Falgorithms\u002Fintractability\u002Fcoping-with-hardness":16395,"\u002Falgorithms\u002Fintractability\u002Fapproximation-algorithms":16399,"\u002Falgorithms":16403,"\u002Fcalculus\u002Flimits-and-continuity\u002Ffunctions-and-models":16406,"\u002Fcalculus\u002Flimits-and-continuity\u002Fthe-limit-of-a-function":16411,"\u002Fcalculus\u002Flimits-and-continuity\u002Flimit-laws-and-the-precise-definition":16415,"\u002Fcalculus\u002Flimits-and-continuity\u002Fcontinuity":16419,"\u002Fcalculus\u002Fderivatives\u002Fthe-derivative-and-rates-of-change":16423,"\u002Fcalculus\u002Fderivatives\u002Fdifferentiation-rules-and-the-chain-rule":16428,"\u002Fcalculus\u002Fderivatives\u002Fimplicit-differentiation-and-related-rates":16432,"\u002Fcalculus\u002Fderivatives\u002Flinear-approximations-and-differentials":16436,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fextrema-and-the-mean-value-theorem":16440,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fhow-derivatives-shape-a-graph":16445,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fcurve-sketching-and-optimization":16449,"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fnewtons-method-and-antiderivatives":16453,"\u002Fcalculus\u002Fintegrals\u002Farea-and-the-definite-integral":16457,"\u002Fcalculus\u002Fintegrals\u002Fthe-fundamental-theorem-of-calculus":16462,"\u002Fcalculus\u002Fintegrals\u002Fthe-substitution-rule":16466,"\u002Fcalculus\u002Fapplications-of-integration\u002Fareas-and-volumes":16470,"\u002Fcalculus\u002Fapplications-of-integration\u002Fwork-average-value-and-arc-length":16475,"\u002Fcalculus\u002Fapplications-of-integration\u002Fphysics-economics-and-probability":16479,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Finverse-functions-logarithms-and-exponentials":16483,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Fgrowth-decay-inverse-trig-and-hyperbolic-functions":16488,"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Flhospitals-rule":16492,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fintegration-by-parts":16496,"\u002Fcalculus\u002Ftechniques-of-integration\u002Ftrigonometric-integrals-and-substitution":16501,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fpartial-fractions-and-integration-strategy":16505,"\u002Fcalculus\u002Ftechniques-of-integration\u002Fapproximate-and-improper-integrals":16509,"\u002Fcalculus\u002Fparametric-and-polar\u002Fparametric-curves-and-their-calculus":16513,"\u002Fcalculus\u002Fparametric-and-polar\u002Fpolar-coordinates":16518,"\u002Fcalculus\u002Fparametric-and-polar\u002Fconic-sections":16522,"\u002Fcalculus\u002Fsequences-and-series\u002Fsequences":16526,"\u002Fcalculus\u002Fsequences-and-series\u002Fseries-and-the-integral-test":16531,"\u002Fcalculus\u002Fsequences-and-series\u002Fthe-convergence-tests":16535,"\u002Fcalculus\u002Fsequences-and-series\u002Fpower-series":16539,"\u002Fcalculus\u002Fsequences-and-series\u002Ftaylor-and-maclaurin-series":16543,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvectors-and-the-dot-product":16547,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fthe-cross-product-lines-and-planes":16552,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fcylinders-and-quadric-surfaces":16556,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvector-functions-and-space-curves":16560,"\u002Fcalculus\u002Fvectors-and-space-curves\u002Farc-length-curvature-and-motion":16564,"\u002Fcalculus\u002Fpartial-derivatives\u002Ffunctions-of-several-variables":16568,"\u002Fcalculus\u002Fpartial-derivatives\u002Fpartial-derivatives":16573,"\u002Fcalculus\u002Fpartial-derivatives\u002Ftangent-planes-and-the-chain-rule":16576,"\u002Fcalculus\u002Fpartial-derivatives\u002Fdirectional-derivatives-and-the-gradient":16580,"\u002Fcalculus\u002Fpartial-derivatives\u002Foptimization-and-lagrange-multipliers":16584,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fdouble-integrals":16588,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Ftriple-integrals-and-coordinate-systems":16593,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fvector-fields-and-line-integrals":16597,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fgreens-theorem-curl-and-divergence":16601,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fsurface-integrals":16605,"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fstokes-and-the-divergence-theorem":16609,"\u002Fcalculus":16613,"\u002Fmechanics\u002Ffoundations\u002Fmeasurement-and-dimensions":16616,"\u002Fmechanics\u002Ffoundations\u002Fvector-algebra":16620,"\u002Fmechanics\u002Fkinematics\u002Fone-dimensional-motion":16624,"\u002Fmechanics\u002Fkinematics\u002Fmotion-graphs":16629,"\u002Fmechanics\u002Fkinematics\u002Fprojectile-motion":16633,"\u002Fmechanics\u002Fkinematics\u002Frelative-motion":16637,"\u002Fmechanics\u002Fkinematics\u002Fcircular-motion":16641,"\u002Fmechanics\u002Fdynamics\u002Fnewtons-laws":16645,"\u002Fmechanics\u002Fdynamics\u002Ffree-body-diagrams":16650,"\u002Fmechanics\u002Fdynamics\u002Ffriction-and-curved-motion":16654,"\u002Fmechanics\u002Fdynamics\u002Fnumerical-dynamics":16658,"\u002Fmechanics\u002Fdynamics\u002Fcenter-of-mass-systems":16662,"\u002Fmechanics\u002Fenergy\u002Fwork-and-kinetic-energy":16666,"\u002Fmechanics\u002Fenergy\u002Fpotential-energy":16671,"\u002Fmechanics\u002Fenergy\u002Fmultiparticle-work":16675,"\u002Fmechanics\u002Fenergy\u002Fmass-energy-and-binding":16679,"\u002Fmechanics\u002Fenergy\u002Fphotons-and-quantization":16683,"\u002Fmechanics\u002Fmomentum\u002Fmomentum-and-collisions":16687,"\u002Fmechanics\u002Fmomentum\u002Fcenter-of-mass-collisions":16692,"\u002Fmechanics\u002Fmomentum\u002Frocket-propulsion":16696,"\u002Fmechanics\u002Frotation\u002Frotational-inertia":16700,"\u002Fmechanics\u002Frotation\u002Frotational-dynamics":16705,"\u002Fmechanics\u002Frotation\u002Frolling-motion":16709,"\u002Fmechanics\u002Frotation\u002Fangular-momentum":16713,"\u002Fmechanics\u002Frotation\u002Frolling-resistance":16717,"\u002Fmechanics\u002Frotation\u002Fgyroscopic-precession":16721,"\u002Fmechanics\u002Fgravity-and-matter\u002Fkeplerian-orbits":16725,"\u002Fmechanics\u002Fgravity-and-matter\u002Fgravitational-fields":16730,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstatic-equilibrium":16734,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-statics":16738,"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-flow":16742,"\u002Fmechanics\u002Fgravity-and-matter\u002Forbital-motion":16746,"\u002Fmechanics\u002Fgravity-and-matter\u002Fstress-and-elasticity":16750,"\u002Fmechanics\u002Foscillations-waves\u002Fdamped-oscillators":16754,"\u002Fmechanics\u002Foscillations-waves\u002Ftravelling-waves":16759,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-superposition":16763,"\u002Fmechanics\u002Foscillations-waves\u002Fstanding-waves":16767,"\u002Fmechanics\u002Foscillations-waves\u002Fsound-waves":16771,"\u002Fmechanics\u002Foscillations-waves\u002Fdoppler-effect":16775,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-packets":16779,"\u002Fmechanics\u002Foscillations-waves\u002Fbeats-and-coupling":16783,"\u002Fmechanics\u002Foscillations-waves\u002Fsimple-harmonic-motion":16787,"\u002Fmechanics\u002Foscillations-waves\u002Fpendulum-motion":16791,"\u002Fmechanics\u002Foscillations-waves\u002Fdriven-oscillators":16795,"\u002Fmechanics\u002Foscillations-waves\u002Fwave-boundaries":16799,"\u002Fmechanics\u002Fthermodynamics\u002Fkinetic-theory-of-ideal-gases":16803,"\u002Fmechanics\u002Fthermodynamics\u002Ffirst-law-of-thermodynamics":16808,"\u002Fmechanics\u002Fthermodynamics\u002Fentropy-and-the-second-law":16812,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-processes":16816,"\u002Fmechanics\u002Fthermodynamics\u002Fphase-changes":16820,"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-machines":16824,"\u002Fmechanics":16828,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcharge-and-conductors":16831,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcoulombs-law":16836,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-and-force":16840,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-maps":16844,"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-dipoles":16848,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fcontinuous-charge-fields":16852,"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fgauss-law-and-conductors":16857,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpoint-charge-potential":16861,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpotential-gradients-and-equipotentials":16866,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Felectrostatic-energy-and-pressure":16870,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Flaplace-boundary-problems":16874,"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fcontinuous-charge-potentials":16878,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitance-fundamentals":16882,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-networks":16887,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-energy-and-force":16891,"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fdielectric-polarization-and-breakdown":16895,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fcurrent-and-resistance":16899,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fkirchhoff-network-analysis":16904,"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Frc-transients":16908,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-trajectories":16912,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fhall-effect":16917,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-force-on-conductors":16921,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-dipoles":16925,"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmass-spectrometry":16929,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmoving-charge-fields":16933,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fbiot-savart-law":16938,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fcircular-current-loops":16942,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Famperes-law":16946,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fgauss-law-for-magnetism":16950,"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmagnetic-materials":16954,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-flux":16958,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Ffaradays-law":16963,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Flenzs-law":16967,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmotional-emf":16971,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Feddy-currents":16975,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fself-inductance":16979,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-energy":16983,"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Frl-circuits":16987,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-fundamentals":16991,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Freactance":16996,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Frlc-resonance":17000,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-power":17004,"\u002Felectricity-and-magnetism\u002Falternating-current\u002Ftransformers":17008,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdisplacement-current":17012,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-waves":17017,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-momentum":17021,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdipole-radiation":17025,"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fpolarization":17029,"\u002Felectricity-and-magnetism\u002Foptics\u002Freflection-and-refraction":17033,"\u002Felectricity-and-magnetism\u002Foptics\u002Fthin-lenses":17038,"\u002Felectricity-and-magnetism\u002Foptics\u002Fspherical-mirrors":17042,"\u002Felectricity-and-magnetism":17046,"\u002Flinear-algebra\u002Flinear-systems\u002Fsystems-and-echelon-forms":17049,"\u002Flinear-algebra\u002Flinear-systems\u002Fvector-and-matrix-equations":17054,"\u002Flinear-algebra\u002Flinear-systems\u002Fsolution-sets-and-applications":17058,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-independence":17062,"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-transformations":17066,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-operations":17070,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-inverse-and-invertibility":17075,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fpartitioned-matrices-and-lu":17079,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fsubspaces-dimension-rank":17083,"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fapplications-leontief-and-graphics":17087,"\u002Flinear-algebra\u002Fdeterminants\u002Fdeterminants-and-cofactors":17091,"\u002Flinear-algebra\u002Fdeterminants\u002Fproperties-of-determinants":17096,"\u002Flinear-algebra\u002Fdeterminants\u002Fcramer-volume-and-area":17100,"\u002Flinear-algebra\u002Fvector-spaces\u002Fvector-spaces-and-subspaces":17104,"\u002Flinear-algebra\u002Fvector-spaces\u002Fnull-and-column-spaces":17109,"\u002Flinear-algebra\u002Fvector-spaces\u002Fbases-and-independent-sets":17113,"\u002Flinear-algebra\u002Fvector-spaces\u002Fcoordinate-systems":17117,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdimension-and-rank":17121,"\u002Flinear-algebra\u002Fvector-spaces\u002Fchange-of-basis":17125,"\u002Flinear-algebra\u002Fvector-spaces\u002Fdifference-equations-and-markov":17129,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-eigenvalues":17133,"\u002Flinear-algebra\u002Feigenvalues\u002Fthe-characteristic-equation":17138,"\u002Flinear-algebra\u002Feigenvalues\u002Fdiagonalization":17142,"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-linear-transformations":17146,"\u002Flinear-algebra\u002Feigenvalues\u002Fcomplex-eigenvalues":17150,"\u002Flinear-algebra\u002Feigenvalues\u002Fdynamical-systems":17154,"\u002Flinear-algebra\u002Feigenvalues\u002Fpower-method":17158,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-length-orthogonality":17162,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Forthogonal-sets-and-projections":17167,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fgram-schmidt-and-qr":17171,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-problems":17175,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-applications":17179,"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-spaces":17183,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fdiagonalizing-symmetric-matrices":17187,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fquadratic-forms":17192,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fconstrained-optimization":17196,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsingular-value-decomposition":17200,"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsvd-applications-pca-imaging":17204,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-thinking-and-matrix-computation":17208,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Flu-and-cholesky":17213,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fconditioning-and-floating-point":17217,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fstability-and-error-analysis":17221,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fqr-and-numerical-least-squares":17225,"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-eigenvalues-and-svd":17229,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-combinations":17233,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-independence-and-barycentric-coordinates":17238,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fconvex-combinations-and-convex-sets":17242,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fhyperplanes-and-polytopes":17246,"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fcurves-and-surfaces":17250,"\u002Flinear-algebra":17254,"\u002Ftheory-of-computation":17257,"\u002Fcomputer-architecture\u002Ffoundations\u002Fbits-bytes-and-words":17260,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-representation":17264,"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-arithmetic":17268,"\u002Fcomputer-architecture\u002Ffoundations\u002Ffloating-point":17272,"\u002Fcomputer-architecture\u002Ffoundations\u002Fboolean-algebra-and-bit-manipulation":17276,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fthe-machines-view":17280,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fdata-movement":17285,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farithmetic-and-logic":17289,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fcontrol-flow":17293,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fprocedures":17297,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farrays-structs-and-alignment":17301,"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fmemory-layout-and-buffer-overflows":17305,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fwhat-an-isa-is":17309,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Finstruction-formats-and-operands":17314,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Faddressing-modes":17318,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fthe-y86-64-instruction-set":17322,"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fy86-64-programming":17326,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Ftransistors-gates-and-boolean-functions":17330,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fcombinational-logic-and-hcl":17335,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmultiplexers-decoders-and-the-alu":17339,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmemory-elements-latches-flip-flops-and-clocking":17343,"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fregister-files-and-random-access-memory":17347,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-fetch-decode-execute-cycle":17351,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-seq-stages":17356,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fcontrol-logic-and-sequencing":17360,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fassembling-seq":17364,"\u002Fcomputer-architecture\u002Fprocessor-design\u002Ftracing-a-program":17368,"\u002Fcomputer-architecture\u002Fpipelining\u002Fpipelining-principles":17372,"\u002Fcomputer-architecture\u002Fpipelining\u002Ffrom-seq-to-pipe":17377,"\u002Fcomputer-architecture\u002Fpipelining\u002Fdata-hazards-stalling-and-forwarding":17381,"\u002Fcomputer-architecture\u002Fpipelining\u002Fcontrol-hazards-and-branch-prediction":17385,"\u002Fcomputer-architecture\u002Fpipelining\u002Fthe-complete-pipe-processor":17389,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fstorage-technologies-and-the-latency-gap":17393,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Flocality":17398,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-memories-direct-mapped":17402,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fset-associative-and-write-policies":17406,"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-performance-and-cache-friendly-code":17410,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Faddress-spaces-and-translation":17414,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fpage-tables-and-page-faults":17419,"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fthe-tlb-and-multi-level-page-tables":17423,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Fexceptional-control-flow":17427,"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Finterrupts-and-the-kernel":17432,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fprocesses-threads-and-parallelism":17436,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fhardware-multithreading":17441,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fcache-coherence":17445,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmemory-consistency-and-synchronization":17449,"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmulticore-organization":17453,"\u002Fcomputer-architecture\u002Fcapstone\u002Fthe-whole-machine":17457,"\u002Fcomputer-architecture\u002Fcapstone\u002Fassembling-a-complete-cpu":17462,"\u002Fcomputer-architecture":17466,"\u002Fdifferential-equations\u002Ffoundations\u002Fmodels-and-direction-fields":17469,"\u002Fdifferential-equations\u002Ffoundations\u002Fclassification-and-terminology":17473,"\u002Fdifferential-equations\u002Ffirst-order\u002Flinear-first-order-integrating-factors":17477,"\u002Fdifferential-equations\u002Ffirst-order\u002Fseparable-and-exact":17482,"\u002Fdifferential-equations\u002Ffirst-order\u002Fmodeling-first-order":17486,"\u002Fdifferential-equations\u002Ffirst-order\u002Fautonomous-and-population-dynamics":17490,"\u002Fdifferential-equations\u002Ffirst-order\u002Fexistence-uniqueness-euler":17494,"\u002Fdifferential-equations\u002Ffirst-order\u002Ffirst-order-difference-equations":17498,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhomogeneous-constant-coefficients":17502,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fcomplex-and-repeated-roots":17507,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fnonhomogeneous-undetermined-coefficients":17511,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fvariation-of-parameters":17515,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fmechanical-electrical-vibrations":17519,"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhigher-order-linear":17523,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fpower-series-ordinary-points":17527,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fregular-singular-frobenius":17532,"\u002Fdifferential-equations\u002Fseries-solutions\u002Fbessel-and-special-functions":17536,"\u002Fdifferential-equations\u002Flaplace\u002Flaplace-definition-ivps":17540,"\u002Fdifferential-equations\u002Flaplace\u002Fstep-impulse-convolution":17545,"\u002Fdifferential-equations\u002Fsystems\u002Fmatrices-eigenvalues-review":17549,"\u002Fdifferential-equations\u002Fsystems\u002Fconstant-coefficient-systems-phase-portraits":17554,"\u002Fdifferential-equations\u002Fsystems\u002Frepeated-eigenvalues-fundamental-matrices":17558,"\u002Fdifferential-equations\u002Fnumerical\u002Feuler-and-runge-kutta":17562,"\u002Fdifferential-equations\u002Fnumerical\u002Fmultistep-systems-stability":17567,"\u002Fdifferential-equations\u002Fnonlinear\u002Fphase-plane-autonomous-stability":17571,"\u002Fdifferential-equations\u002Fnonlinear\u002Flocally-linear-and-liapunov":17576,"\u002Fdifferential-equations\u002Fnonlinear\u002Fcompeting-species-predator-prey-limit-cycles":17580,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Ffourier-series":17584,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fheat-wave-laplace-equations":17589,"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fsturm-liouville":17593,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fcalculus-of-variations":17597,"\u002Fdifferential-equations\u002Fhistory-variations\u002Fhistorical-notes":17602,"\u002Fdifferential-equations":17606,"\u002Frelativity\u002Ffoundations\u002Fspecial-relativity-postulates":17609,"\u002Frelativity\u002Ffoundations\u002Florentz-transformation-spacetime":17614,"\u002Frelativity\u002Ffoundations\u002Ftime-dilation-length-contraction":17618,"\u002Frelativity\u002Ffoundations\u002Frelativistic-momentum-energy":17622,"\u002Frelativity\u002Ffoundations\u002Fgeneral-relativity":17626,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fminkowski-spacetime-and-the-interval":17630,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Ffour-vectors-and-index-notation":17635,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fthe-lorentz-group-and-rapidity":17639,"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fdoppler-aberration-and-appearance":17643,"\u002Frelativity\u002Frelativistic-dynamics\u002Ffour-momentum-force-and-accelerated-motion":17647,"\u002Frelativity\u002Frelativistic-dynamics\u002Fparticle-decays-and-two-body-kinematics":17652,"\u002Frelativity\u002Frelativistic-dynamics\u002Fcollisions-thresholds-and-the-cm-frame":17656,"\u002Frelativity\u002Frelativistic-dynamics\u002Fmandelstam-variables-and-invariants":17660,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ffour-current-and-the-four-potential":17664,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fthe-electromagnetic-field-tensor":17669,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ftransformation-of-electric-and-magnetic-fields":17673,"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fcovariant-maxwell-and-the-stress-energy-tensor":17677,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-equivalence-principle-formalized":17681,"\u002Frelativity\u002Fcurved-spacetime\u002Fmanifolds-vectors-and-the-metric":17686,"\u002Frelativity\u002Fcurved-spacetime\u002Fcovariant-derivative-and-christoffel-symbols":17690,"\u002Frelativity\u002Fcurved-spacetime\u002Fgeodesics-and-the-geodesic-equation":17694,"\u002Frelativity\u002Fcurved-spacetime\u002Fcurvature-riemann-and-geodesic-deviation":17698,"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-einstein-field-equations":17702,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fthe-schwarzschild-metric":17706,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fgeodesics-and-orbits-in-schwarzschild":17711,"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Flight-bending-and-null-geodesics":17715,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fperihelion-precession-of-mercury":17719,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fdeflection-of-light-and-gravitational-lensing":17724,"\u002Frelativity\u002Ftests-of-general-relativity\u002Fgravitational-redshift-and-shapiro-delay":17728,"\u002Frelativity\u002Ftests-of-general-relativity\u002Frelativity-in-technology-gps":17732,"\u002Frelativity\u002Fblack-holes\u002Fhorizons-and-coordinate-singularities":17736,"\u002Frelativity\u002Fblack-holes\u002Frotating-and-charged-black-holes":17741,"\u002Frelativity\u002Fblack-holes\u002Fblack-hole-thermodynamics":17745,"\u002Frelativity\u002Fgravitational-waves\u002Flinearized-gravity-and-wave-solutions":17749,"\u002Frelativity\u002Fgravitational-waves\u002Fgeneration-and-the-quadrupole-formula":17754,"\u002Frelativity\u002Fgravitational-waves\u002Fdetection-ligo-and-the-first-events":17758,"\u002Frelativity\u002Fcosmological-bridge\u002Fthe-cosmological-principle-and-flrw-metric":17762,"\u002Frelativity\u002Fcosmological-bridge\u002Ffriedmann-equations-and-cosmic-dynamics":17767,"\u002Frelativity":17771,"\u002Fphysical-computing":17774,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fblackbody-radiation-and-the-planck-quantum":17777,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-photoelectric-effect-and-the-photon":17782,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fx-rays-and-the-compton-effect":17786,"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-old-quantum-theory-bohr-and-sommerfeld":17790,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fde-broglie-waves-and-electron-diffraction":17794,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fwave-packets-and-the-probability-interpretation":17799,"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fthe-uncertainty-principle":17803,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-schrodinger-equation-in-one-dimension":17807,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-free-particle-and-wave-packet-dynamics":17812,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fparticle-in-infinite-and-finite-square-wells":17816,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Foperators-expectation-values-and-the-harmonic-oscillator":17820,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-dirac-delta-potential":17824,"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fbarrier-penetration-and-quantum-tunneling":17828,"\u002Fquantum-mechanics\u002Fformalism\u002Fhilbert-space-and-dirac-notation":17832,"\u002Fquantum-mechanics\u002Fformalism\u002Fobservables-hermitian-operators-and-eigenvalues":17837,"\u002Fquantum-mechanics\u002Fformalism\u002Fthe-postulates-and-quantum-measurement":17841,"\u002Fquantum-mechanics\u002Fformalism\u002Fposition-momentum-and-continuous-spectra":17845,"\u002Fquantum-mechanics\u002Fformalism\u002Fcommutators-and-the-generalized-uncertainty-principle":17849,"\u002Fquantum-mechanics\u002Fformalism\u002Ftime-evolution-schrodinger-and-heisenberg-pictures":17853,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fladder-operators-and-the-number-states":17857,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fcoherent-and-squeezed-states":17862,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fsymmetries-generators-and-conservation-laws":17866,"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fparity-time-reversal-and-discrete-symmetries":17870,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Forbital-angular-momentum-and-spherical-harmonics":17874,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Fthe-angular-momentum-algebra":17878,"\u002Fquantum-mechanics\u002Fangular-momentum\u002Faddition-of-angular-momenta-and-clebsch-gordan":17882,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-schrodinger-equation-in-three-dimensions":17886,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-hydrogen-atom":17891,"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-isotropic-oscillator-and-hidden-symmetry":17895,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-half-pauli-matrices-and-stern-gerlach":17899,"\u002Fquantum-mechanics\u002Fspin\u002Fspin-in-a-magnetic-field-precession-and-resonance":17904,"\u002Fquantum-mechanics\u002Fspin\u002Ftwo-level-systems-and-the-bloch-sphere":17908,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fidentical-particles-and-exchange-symmetry":17912,"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fthe-pauli-principle-atoms-and-the-periodic-table":17917,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ftime-independent-perturbation-theory":17921,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ffine-structure-and-the-real-hydrogen-atom":17926,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-zeeman-and-stark-effects":17930,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-variational-method":17934,"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-wkb-approximation":17938,"\u002Fquantum-mechanics":17942,"\u002Freal-analysis\u002Ffoundations\u002Fsets-logic-functions":17945,"\u002Freal-analysis\u002Ffoundations\u002Fordered-fields-completeness":17950,"\u002Freal-analysis\u002Ffoundations\u002Fabsolute-value-bounds":17954,"\u002Freal-analysis\u002Ffoundations\u002Fintervals-uncountability":17958,"\u002Freal-analysis\u002Fsequences-series\u002Fsequences-limits":17962,"\u002Freal-analysis\u002Fsequences-series\u002Flimit-laws-monotone":17967,"\u002Freal-analysis\u002Fsequences-series\u002Flimsup-bolzano-weierstrass":17971,"\u002Freal-analysis\u002Fsequences-series\u002Fcauchy-completeness":17975,"\u002Freal-analysis\u002Fsequences-series\u002Fseries-convergence":17979,"\u002Freal-analysis\u002Fsequences-series\u002Fabsolute-conditional-rearrangement":17983,"\u002Freal-analysis\u002Fmetric-spaces\u002Fmetric-spaces-norms":17987,"\u002Freal-analysis\u002Fmetric-spaces\u002Fopen-closed-sets":17992,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconvergence-completeness":17996,"\u002Freal-analysis\u002Fmetric-spaces\u002Fcompactness":18000,"\u002Freal-analysis\u002Fmetric-spaces\u002Fconnectedness":18004,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-of-functions":18008,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuous-functions":18012,"\u002Freal-analysis\u002Fcontinuity\u002Fevt-ivt":18016,"\u002Freal-analysis\u002Fcontinuity\u002Funiform-continuity":18020,"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuity-metric-spaces":18024,"\u002Freal-analysis\u002Fcontinuity\u002Flimits-infinity-monotone":18028,"\u002Freal-analysis\u002Fdifferentiation\u002Fthe-derivative":18032,"\u002Freal-analysis\u002Fdifferentiation\u002Fmean-value-theorem":18037,"\u002Freal-analysis\u002Fdifferentiation\u002Ftaylors-theorem":18041,"\u002Freal-analysis\u002Fdifferentiation\u002Finverse-function-1d":18045,"\u002Freal-analysis\u002Friemann-integration\u002Fdarboux-integral":18049,"\u002Freal-analysis\u002Friemann-integration\u002Fintegrability-classes":18054,"\u002Freal-analysis\u002Friemann-integration\u002Fproperties-of-the-integral":18058,"\u002Freal-analysis\u002Friemann-integration\u002Ffundamental-theorem":18062,"\u002Freal-analysis\u002Friemann-integration\u002Flog-exp-improper":18065,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpointwise-uniform-convergence":18069,"\u002Freal-analysis\u002Ffunction-sequences\u002Finterchange-of-limits":18074,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpower-series-weierstrass":18078,"\u002Freal-analysis\u002Ffunction-sequences\u002Fpicard-ode":18082,"\u002Freal-analysis\u002Fseveral-variables\u002Fdifferentiability-rn":18086,"\u002Freal-analysis\u002Fseveral-variables\u002Fgradient-chain-rule":18091,"\u002Freal-analysis\u002Fseveral-variables\u002Fhigher-derivatives-taylor-extrema":18095,"\u002Freal-analysis\u002Fseveral-variables\u002Finverse-implicit-theorems":18099,"\u002Freal-analysis\u002Fseveral-variables\u002Fmultiple-integrals":18103,"\u002Freal-analysis":18107,"\u002Fabstract-algebra\u002Ffoundations\u002Fsets-functions-relations":18110,"\u002Fabstract-algebra\u002Ffoundations\u002Fintegers-and-modular-arithmetic":18114,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fgroup-axioms-and-first-examples":18118,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fdihedral-and-symmetric-groups":18123,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fmatrix-and-quaternion-groups":18127,"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fhomomorphisms-and-group-actions":18131,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fsubgroups-and-substructures":18135,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcyclic-groups":18140,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fgeneration-and-subgroup-lattices":18144,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcosets-lagrange-and-normal-subgroups":18148,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fisomorphism-theorems":18152,"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcomposition-series-and-the-alternating-group":18156,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Factions-and-cayleys-theorem":18160,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fconjugation-and-the-class-equation":18165,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fsylow-theorems":18169,"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fautomorphisms-and-simple-groups":18173,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fdirect-products-and-finite-abelian-groups":18177,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fsemidirect-products":18182,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fnilpotent-and-solvable-groups":18186,"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fclassifying-small-groups":18190,"\u002Fabstract-algebra\u002Fring-theory\u002Frings-definitions-and-examples":18194,"\u002Fabstract-algebra\u002Fring-theory\u002Fideals-quotients-and-homomorphisms":18199,"\u002Fabstract-algebra\u002Fring-theory\u002Ffractions-and-the-chinese-remainder-theorem":18203,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Feuclidean-domains-pids-ufds":18207,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fpolynomial-rings-over-fields":18212,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fgauss-lemma-and-unique-factorization":18216,"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Firreducibility-criteria-and-groebner":18220,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fintroduction-to-modules":18224,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ffree-modules-and-direct-sums":18229,"\u002Fabstract-algebra\u002Fmodule-theory\u002Ftensor-products-and-exact-sequences":18233,"\u002Fabstract-algebra\u002Fmodule-theory\u002Fvector-spaces-and-linear-maps":18237,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fstructure-theorem-over-pids":18241,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Frational-canonical-form":18246,"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fjordan-canonical-form":18250,"\u002Fabstract-algebra\u002Ffield-theory\u002Ffield-extensions-and-algebraic-elements":18254,"\u002Fabstract-algebra\u002Ffield-theory\u002Fstraightedge-and-compass-constructions":18259,"\u002Fabstract-algebra\u002Ffield-theory\u002Fsplitting-fields-and-algebraic-closure":18263,"\u002Fabstract-algebra\u002Ffield-theory\u002Fseparable-and-cyclotomic-extensions":18267,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fthe-galois-correspondence":18271,"\u002Fabstract-algebra\u002Fgalois-theory\u002Ffinite-fields":18276,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fcyclotomic-and-abelian-extensions":18280,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fgalois-groups-of-polynomials":18284,"\u002Fabstract-algebra\u002Fgalois-theory\u002Fsolvability-by-radicals-and-the-quintic":18288,"\u002Fabstract-algebra\u002Fcapstone\u002Fcommutative-algebra-and-algebraic-geometry":18292,"\u002Fabstract-algebra\u002Fcapstone\u002Frepresentation-and-character-theory":18297,"\u002Fabstract-algebra":18301,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fatomic-spectra-rutherford":18304,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-model-hydrogen":18309,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fx-ray-spectra-franck-hertz":18313,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-sommerfeld-old-quantum-theory":18317,"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fold-quantum-theory-limits-wkb":18321,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fschrodinger-3d-hydrogen":18325,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fhydrogen-wave-functions":18330,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fradial-equation-in-full":18334,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fsymmetry-degeneracy-runge-lenz":18338,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fexpectation-values-virial":18342,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fquantum-defects-alkali-spectra":18346,"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Frydberg-atoms":18350,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Frelativistic-kinetic-correction":18354,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fspin-orbit-thomas-precession":18359,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdarwin-term-fine-structure-formula":18363,"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdirac-equation-hydrogen":18367,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Flamb-shift-qed":18371,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fhyperfine-structure-21cm":18376,"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fnuclear-effects-isotope-shift":18380,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fperiodic-table-atomic-spectra":18384,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fcentral-field-self-consistent":18389,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fidentical-particles-hartree-fock":18393,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhelium-two-electron-atom":18397,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fls-jj-coupling-term-symbols":18401,"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhund-rules-ground-terms":18405,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fzeeman-effect":18409,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fpaschen-back-intermediate":18414,"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fstark-effect-polarizability":18418,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Ftime-dependent-perturbation-golden-rule":18422,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fdipole-approximation-einstein-coefficients":18427,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fselection-rules-forbidden-transitions":18431,"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Flifetimes-and-line-shapes":18435,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Flaser-principles":18439,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fspectroscopy-techniques":18444,"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fline-catalog-nist-asd":18448,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Flaser-cooling-doppler":18452,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fsub-doppler-trapping":18457,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fbose-einstein-condensation":18461,"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Foptical-clocks-precision":18465,"\u002Fatomic-physics":18469,"\u002Fdatabases":18472,"\u002Fcategory-theory\u002Ffoundations\u002Fwhat-is-a-category":18475,"\u002Fcategory-theory\u002Ffoundations\u002Fexamples-of-categories":18479,"\u002Fcategory-theory\u002Ffoundations\u002Fspecial-morphisms":18483,"\u002Fcategory-theory\u002Ffoundations\u002Ffunctors":18487,"\u002Fcategory-theory\u002Ffoundations\u002Fnatural-transformations":18491,"\u002Fcategory-theory\u002Ffoundations\u002Fsize-and-set-theory":18495,"\u002Fcategory-theory\u002Funiversal-properties\u002Funiversal-properties":18499,"\u002Fcategory-theory\u002Funiversal-properties\u002Fproducts-and-coproducts":18504,"\u002Fcategory-theory\u002Funiversal-properties\u002Fconstructions-on-categories":18508,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Frepresentable-functors":18512,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-lemma":18517,"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-consequences":18521,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits":18525,"\u002Fcategory-theory\u002Flimits-colimits\u002Fproducts-equalizers-pullbacks":18530,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcolimits":18534,"\u002Fcategory-theory\u002Flimits-colimits\u002Fcomputing-limits":18538,"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits-and-functors":18542,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions":18546,"\u002Fcategory-theory\u002Fadjunctions\u002Funits-and-counits":18551,"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions-via-universal-arrows":18555,"\u002Fcategory-theory\u002Fadjunctions\u002Ffree-forgetful-adjunctions":18559,"\u002Fcategory-theory\u002Fadjoints-limits\u002Flimits-via-adjoints":18563,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fpresheaf-limits-colimits":18568,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoints-preserve-limits":18572,"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoint-functor-theorem":18576,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fmonads":18580,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-eilenberg-moore":18585,"\u002Fcategory-theory\u002Fmonads-algebras\u002Fkleisli-and-programming":18589,"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-for-endofunctors":18593,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Fcartesian-closed-categories":18597,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Flambda-calculus-correspondence":18602,"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Ffixed-points-and-recursion":18606,"\u002Fcategory-theory":18610,"\u002Fdeep-learning\u002Fmathematical-background\u002Flinear-algebra-for-deep-learning":18613,"\u002Fdeep-learning\u002Fmathematical-background\u002Fprobability-and-information-theory":18617,"\u002Fdeep-learning\u002Fmathematical-background\u002Fnumerical-computation":18621,"\u002Fdeep-learning\u002Fmathematical-background\u002Fcalculus":18625,"\u002Fdeep-learning\u002Ffoundations\u002Fwhat-is-deep-learning":18628,"\u002Fdeep-learning\u002Ffoundations\u002Fmachine-learning-refresher":18632,"\u002Fdeep-learning\u002Ffoundations\u002Flinear-models-and-the-perceptron":18636,"\u002Fdeep-learning\u002Fneural-networks\u002Fthe-multilayer-perceptron":18640,"\u002Fdeep-learning\u002Fneural-networks\u002Factivation-functions":18645,"\u002Fdeep-learning\u002Fneural-networks\u002Funiversal-approximation":18649,"\u002Fdeep-learning\u002Fneural-networks\u002Fbackpropagation":18653,"\u002Fdeep-learning\u002Fneural-networks\u002Floss-functions-and-output-units":18657,"\u002Fdeep-learning\u002Foptimization\u002Fgradient-descent-and-sgd":18661,"\u002Fdeep-learning\u002Foptimization\u002Fmomentum-and-adaptive-methods":18666,"\u002Fdeep-learning\u002Foptimization\u002Finitialization":18670,"\u002Fdeep-learning\u002Foptimization\u002Fthe-optimization-landscape":18674,"\u002Fdeep-learning\u002Foptimization\u002Fsecond-order-and-approximate-methods":18678,"\u002Fdeep-learning\u002Fregularization\u002Fregularization-overview":18682,"\u002Fdeep-learning\u002Fregularization\u002Fdropout-and-data-augmentation":18687,"\u002Fdeep-learning\u002Fregularization\u002Fearly-stopping-and-parameter-sharing":18691,"\u002Fdeep-learning\u002Fregularization\u002Fnormalization":18695,"\u002Fdeep-learning\u002Farchitectures\u002Fconvolutional-networks":18698,"\u002Fdeep-learning\u002Farchitectures\u002Fcnn-architectures":18702,"\u002Fdeep-learning\u002Farchitectures\u002Frecurrent-networks":18706,"\u002Fdeep-learning\u002Farchitectures\u002Flstm-and-gru":18710,"\u002Fdeep-learning\u002Farchitectures\u002Fattention-and-transformers":18714,"\u002Fdeep-learning\u002Farchitectures\u002Fthe-transformer-architecture":18717,"\u002Fdeep-learning\u002Farchitectures\u002Ftransformers-in-practice":18718,"\u002Fdeep-learning\u002Farchitectures\u002Fgraph-neural-networks":18720,"\u002Fdeep-learning\u002Farchitectures\u002Fstate-space-models":18724,"\u002Fdeep-learning\u002Ftheory\u002Fgeneralization-theory":18728,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-robustness":18733,"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-defenses":18737,"\u002Fdeep-learning\u002Ftheory\u002Fbayesian-and-ensemble-methods":18741,"\u002Fdeep-learning\u002Ftheory\u002Fdeep-equilibrium-models":18745,"\u002Fdeep-learning\u002Fgenerative-models\u002Flinear-factor-models":18749,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoencoders":18754,"\u002Fdeep-learning\u002Fgenerative-models\u002Fvariational-autoencoders":18758,"\u002Fdeep-learning\u002Fgenerative-models\u002Fgenerative-adversarial-networks":18762,"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoregressive-and-normalizing-flows":18766,"\u002Fdeep-learning\u002Fgenerative-models\u002Fenergy-based-and-boltzmann-machines":18770,"\u002Fdeep-learning\u002Fgenerative-models\u002Fdiffusion-and-score-based-models":18774,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fstructured-probabilistic-models":18778,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fmonte-carlo-and-mcmc":18783,"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fapproximate-inference":18787,"\u002Fdeep-learning\u002Fpractical\u002Fpractical-methodology":18791,"\u002Fdeep-learning\u002Fpractical\u002Fhyperparameters-and-debugging":18796,"\u002Fdeep-learning\u002Fpractical\u002Frepresentation-learning":18800,"\u002Fdeep-learning\u002Fpractical\u002Ftransfer-learning":18804,"\u002Fdeep-learning\u002Fpractical\u002Fapplications":18808,"\u002Fdeep-learning\u002Fpractical\u002Fmodel-compression-and-distillation":18812,"\u002Fdeep-learning\u002Fpractical\u002Fmeta-learning-and-few-shot":18816,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Flarge-language-models":18820,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fscaling-inference-and-alignment":18825,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fseq2seq-pretraining-and-bart":18829,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ftext-to-text-transfer-and-conditional-generation":18833,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fspeech-and-audio-models":18837,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fself-supervised-speech-and-synthesis":18841,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fai-agents":18845,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fagent-memory-retrieval-and-orchestration":18849,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmixture-of-experts":18853,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmultimodal-models":18857,"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ffusion-and-vision-language-models":18861,"\u002Fdeep-learning\u002Freinforcement-learning\u002Ffoundations-of-reinforcement-learning":18865,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fmodel-free-prediction-and-control":18870,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fdeep-q-networks":18874,"\u002Fdeep-learning\u002Freinforcement-learning\u002Fpolicy-gradients-and-actor-critic":18878,"\u002Fdeep-learning\u002Freinforcement-learning\u002Frl-from-human-feedback":18882,"\u002Fdeep-learning":18886,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fequilibrium-state-variables-zeroth-law":18888,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Ffirst-law-heat-and-work":18892,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fsecond-law-entropy-and-the-carnot-bound":18896,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fthermodynamic-potentials-and-maxwell-relations":18900,"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fstability-response-functions-and-the-third-law":18904,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fclassical-statistics-and-equipartition":18908,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fphase-space-and-liouvilles-theorem":18913,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fensembles-and-the-equal-probability-postulate":18917,"\u002Fstatistical-mechanics\u002Ffoundations\u002Fstatistical-entropy-boltzmann-and-gibbs":18921,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fmicrocanonical-ensemble-and-entropy":18925,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fequilibrium-conditions-temperature-pressure-chemical-potential":18930,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fideal-gas-phase-space-and-the-sackur-tetrode-entropy":18934,"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Ftwo-state-systems-paramagnets-and-negative-temperature":18938,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fcanonical-ensemble-and-the-boltzmann-distribution":18942,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fpartition-function-and-the-helmholtz-free-energy":18947,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fenergy-fluctuations-and-ensemble-equivalence":18951,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fthe-einstein-solid-and-harmonic-systems":18955,"\u002Fstatistical-mechanics\u002Fcanonical\u002Fparamagnetism-and-the-schottky-anomaly":18959,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fideal-gas-partition-function-and-the-gibbs-paradox":18963,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fequipartition-and-the-virial-theorem":18968,"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fmolecular-gases-rotation-and-vibration":18972,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fgrand-canonical-ensemble-and-the-grand-partition-function":18976,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fchemical-potential-fugacity-and-number-fluctuations":18981,"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fensemble-summary-and-the-thermodynamic-web":18985,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fquantum-statistics-bose-einstein-and-fermi-dirac":18989,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fderiving-the-quantum-distributions":18994,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fthe-classical-limit-and-quantum-concentration":18998,"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fideal-quantum-gases-general-framework":19002,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-and-the-fermion-gas":19006,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthe-photon-gas-and-plancks-radiation-law":19011,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fblackbody-thermodynamics-and-radiation-pressure":19015,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fphonons-and-the-debye-model":19019,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-derived":19023,"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthermodynamics-of-the-bose-gas-and-superfluidity":19027,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fthe-ideal-fermi-gas-at-zero-temperature":19031,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fsommerfeld-expansion-and-electrons-in-metals":19036,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":19040,"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fneutron-stars-and-nuclear-matter":19044,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-cluster-expansion-and-virial-coefficients":19048,"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-van-der-waals-gas-and-liquid-gas-coexistence":19053,"\u002Fstatistical-mechanics\u002Finteractions\u002Fquantum-gases-with-interactions-and-exchange":19057,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fphases-coexistence-and-classification":19061,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-ising-model-and-exact-solutions":19066,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fmean-field-theory-and-the-weiss-model":19070,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fcritical-exponents-and-landau-theory":19074,"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-renormalization-group-idea":19078,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fthermodynamic-fluctuations-and-response":19082,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fbrownian-motion-and-the-langevin-equation":19087,"\u002Fstatistical-mechanics\u002Ffluctuations\u002Flinear-response-and-the-fluctuation-dissipation-theorem":19091,"\u002Fstatistical-mechanics":19095,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fbonding-mechanisms":19098,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fmolecular-orbitals-and-h2-plus":19103,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fhydrogen-molecule-and-exchange":19107,"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fvan-der-waals-forces":19111,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Frotational-vibrational-spectra":19115,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Fanharmonicity-and-rovibrational-structure":19120,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Framan-and-electronic-bands":19124,"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Flasers-and-masers":19128,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fstructure-of-solids":19132,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fbravais-lattices-and-crystal-systems":19137,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Freciprocal-lattice-and-brillouin-zones":19141,"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fdiffraction-and-structure-factors":19145,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonon-dispersion":19149,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonons-quantization-and-dos":19154,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fdebye-einstein-heat-capacity":19158,"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fanharmonicity-and-thermal-transport":19162,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ffree-electron-gas-and-conduction":19166,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fsommerfeld-model-and-heat-capacity":19171,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ftransport-and-the-hall-effect":19175,"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fscreening-and-plasmons":19179,"\u002Fcondensed-matter\u002Fband-theory\u002Fblochs-theorem-and-energy-bands":19183,"\u002Fcondensed-matter\u002Fband-theory\u002Fnearly-free-electron-model":19188,"\u002Fcondensed-matter\u002Fband-theory\u002Ftight-binding-method":19192,"\u002Fcondensed-matter\u002Fband-theory\u002Ffermi-surfaces-and-semiclassical-dynamics":19196,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fsemiconductor-bands-and-junctions":19200,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fintrinsic-and-extrinsic-semiconductors":19205,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fcarrier-transport-and-recombination":19209,"\u002Fcondensed-matter\u002Fsemiconductors\u002Fthe-pn-junction":19213,"\u002Fcondensed-matter\u002Fsemiconductors\u002Ftransistors-and-optoelectronics":19217,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fdielectrics-and-polarization":19221,"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fferroelectrics-and-piezoelectrics":19226,"\u002Fcondensed-matter\u002Fmagnetism\u002Fdiamagnetism-and-paramagnetism":19230,"\u002Fcondensed-matter\u002Fmagnetism\u002Fexchange-and-ferromagnetism":19235,"\u002Fcondensed-matter\u002Fmagnetism\u002Fantiferromagnetism-and-domains":19239,"\u002Fcondensed-matter\u002Fmagnetism\u002Fspin-waves-and-magnons":19243,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fsuperconductivity-phenomenology":19247,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Flondon-theory-and-the-meissner-effect":19252,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fginzburg-landau-theory":19256,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fbcs-theory":19260,"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fjosephson-and-high-tc":19264,"\u002Fcondensed-matter\u002Fnanostructures\u002Fquantum-wells-wires-and-dots":19268,"\u002Fcondensed-matter\u002Fnanostructures\u002Finteger-quantum-hall-effect":19273,"\u002Fcondensed-matter\u002Fnanostructures\u002Ffractional-quantum-hall-and-topology":19277,"\u002Fcondensed-matter\u002Fnanostructures\u002Fgraphene-and-dirac-materials":19281,"\u002Fcondensed-matter":19285,"\u002Flogic\u002Ffoundations\u002Flogic-as-a-mathematical-model":19288,"\u002Flogic\u002Fsentential-logic\u002Fformal-languages-and-well-formed-formulas":19292,"\u002Flogic\u002Fsentential-logic\u002Ftruth-assignments-and-tautologies":19297,"\u002Flogic\u002Fsentential-logic\u002Funique-readability-and-parsing":19301,"\u002Flogic\u002Fsentential-logic\u002Finduction-and-recursion":19305,"\u002Flogic\u002Fsentential-logic\u002Fexpressive-completeness-and-normal-forms":19309,"\u002Flogic\u002Fsentential-logic\u002Fboolean-circuits":19313,"\u002Flogic\u002Fsentential-logic\u002Fcompactness-and-effectiveness":19317,"\u002Flogic\u002Ffirst-order-languages\u002Ffirst-order-languages":19321,"\u002Flogic\u002Ffirst-order-languages\u002Fstructures-truth-and-satisfaction":19326,"\u002Flogic\u002Ffirst-order-languages\u002Fdefinability-and-elementary-equivalence":19330,"\u002Flogic\u002Ffirst-order-languages\u002Fterms-substitution-and-parsing":19334,"\u002Flogic\u002Fdeductive-calculus\u002Fa-deductive-calculus":19338,"\u002Flogic\u002Fdeductive-calculus\u002Fdeduction-theorem-and-derived-rules":19343,"\u002Flogic\u002Fdeductive-calculus\u002Fsoundness":19347,"\u002Flogic\u002Fdeductive-calculus\u002Fcompleteness-and-consistency":19351,"\u002Flogic\u002Fmodels-and-theories\u002Fcompactness-and-lowenheim-skolem":19355,"\u002Flogic\u002Fmodels-and-theories\u002Ftheories-elementary-classes-and-categoricity":19360,"\u002Flogic\u002Fmodels-and-theories\u002Finterpretations-between-theories":19364,"\u002Flogic\u002Fmodels-and-theories\u002Fnonstandard-analysis":19368,"\u002Flogic\u002Farithmetic-and-definability\u002Fdefinability-in-arithmetic":19372,"\u002Flogic\u002Farithmetic-and-definability\u002Fnatural-numbers-with-successor":19377,"\u002Flogic\u002Farithmetic-and-definability\u002Fpresburger-and-reducts":19381,"\u002Flogic\u002Farithmetic-and-definability\u002Fa-subtheory-and-representability":19385,"\u002Flogic\u002Fincompleteness\u002Farithmetization-of-syntax":19389,"\u002Flogic\u002Fincompleteness\u002Fincompleteness-and-undecidability":19394,"\u002Flogic\u002Fincompleteness\u002Fsecond-incompleteness-theorem":19398,"\u002Flogic\u002Fcomputability-and-representability\u002Frecursive-functions":19402,"\u002Flogic\u002Fcomputability-and-representability\u002Frepresenting-exponentiation":19407,"\u002Flogic\u002Fsecond-order-logic\u002Fsecond-order-languages":19411,"\u002Flogic\u002Fsecond-order-logic\u002Fskolem-functions-and-many-sorted-logic":19416,"\u002Flogic\u002Fsecond-order-logic\u002Fgeneral-structures":19420,"\u002Flogic":19424,"\u002Freinforcement-learning\u002Ffoundations\u002Fwhat-is-reinforcement-learning":19427,"\u002Freinforcement-learning\u002Ffoundations\u002Fa-brief-history-of-rl":19431,"\u002Freinforcement-learning\u002Ffoundations\u002Fmulti-armed-bandits":19435,"\u002Freinforcement-learning\u002Ffoundations\u002Fbandit-exploration-algorithms":19439,"\u002Freinforcement-learning\u002Ffoundations\u002Fmarkov-decision-processes":19443,"\u002Freinforcement-learning\u002Ffoundations\u002Fvalue-functions-and-optimality":19447,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdynamic-programming":19451,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdp-async-and-gpi":19455,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-methods":19459,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-off-policy":19463,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftemporal-difference-learning":19467,"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftd-control-sarsa-and-q-learning":19471,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-bootstrapping":19475,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-off-policy-methods":19479,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-and-learning":19483,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-focusing-and-decision-time":19487,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdecision-time-planning":19491,"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-tree-search":19495,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-prediction":19499,"\u002Freinforcement-learning\u002Fapproximation\u002Ffeature-construction-and-nonlinear":19504,"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-control":19508,"\u002Freinforcement-learning\u002Fapproximation\u002Faverage-reward-control":19512,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-and-the-deadly-triad":19516,"\u002Freinforcement-learning\u002Fapproximation\u002Fbellman-error-and-gradient-td":19520,"\u002Freinforcement-learning\u002Fapproximation\u002Feligibility-traces":19524,"\u002Freinforcement-learning\u002Fapproximation\u002Ftrue-online-and-sarsa-lambda":19528,"\u002Freinforcement-learning\u002Fapproximation\u002Fpolicy-gradient-methods":19532,"\u002Freinforcement-learning\u002Fapproximation\u002Factor-critic-and-continuous-actions":19536,"\u002Freinforcement-learning\u002Fapproximation\u002Fleast-squares-and-memory-based-methods":19540,"\u002Freinforcement-learning\u002Fapproximation\u002Fmemory-and-kernel-methods":19544,"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-eligibility-traces":19548,"\u002Freinforcement-learning\u002Fapproximation\u002Fstable-off-policy-traces":19552,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdeep-q-networks":19556,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdqn-improvements":19560,"\u002Freinforcement-learning\u002Fdeep-rl\u002Factor-critic-and-ppo":19564,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fppo-and-continuous-control":19568,"\u002Freinforcement-learning\u002Fdeep-rl\u002Fcase-studies":19572,"\u002Freinforcement-learning\u002Fdeep-rl\u002Frl-beyond-games":19576,"\u002Freinforcement-learning\u002Fdeep-rl\u002Ffrontiers":19580,"\u002Freinforcement-learning\u002Fdeep-rl\u002Freward-design-and-open-problems":19584,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow":19588,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow-part-2":19593,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control":19597,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control-part-2":19601,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl":19605,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl-part-2":19609,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration":19613,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration-part-2":19617,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl":19621,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl-part-2":19625,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl":19629,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl-part-2":19633,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl":19637,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl-part-2":19641,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl":19645,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl-part-2":19649,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Frlhf-and-language-models":19653,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps":19657,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps-part-2":19661,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl":19665,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl-part-2":19669,"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmeta-rl-and-generalization":19673,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fpsychology-of-reinforcement":19677,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Finstrumental-conditioning-and-control":19682,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-and-td-error":19686,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-in-the-brain":19690,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fanimal-learning-and-cognition":19694,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fcognitive-maps-and-planning":19698,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fneuroscience-of-reinforcement":19702,"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fseveral-learning-systems":19706,"\u002Freinforcement-learning":19710,"\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai":19712,"\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai":19716,"\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents":19720,"\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures":19724,"\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search":19728,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared":19733,"\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search":19737,"\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions":19741,"\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search":19745,"\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search":19749,"\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search":19753,"\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information":19757,"\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction":19761,"\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure":19765,"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty":19769,"\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search":19773,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic":19777,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference":19782,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic":19786,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use":19790,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution":19794,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution":19798,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning":19802,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan":19806,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world":19810,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty":19814,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation":19818,"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults":19822,"\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes":19826,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes":19831,"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks":19835,"\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks":19839,"\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time":19843,"\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association":19847,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions":19851,"\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes":19855,"\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory":19858,"\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design":19862,"\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples":19866,"\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families":19871,"\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning":19875,"\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization":19879,"\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning":19883,"\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search":19886,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning":19890,"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods":19894,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception":19898,"\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world":19903,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics":19907,"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control":19911,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai":19915,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech":19919,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future":19923,"\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future":19927,"\u002Fartificial-intelligence":19931,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart":19934,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions":19939,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy":19943,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula":19947,"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles":19951,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview":19955,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron":19960,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering":19964,"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin":19968,"\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model":19972,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates":19977,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle":19981,"\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations":19985,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes":19989,"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium":19994,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory":19998,"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance":20003,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino":20007,"\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay":20012,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation":20016,"\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass":20020,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation":20024,"\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers":20029,"\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer":20033,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections":20037,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances":20042,"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model":20046,"\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics":20050,"\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics":20055,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement":20059,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis":20064,"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis":20068,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power":20072,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions":20077,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors":20081,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology":20085,"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine":20089,"\u002Fnuclear-physics":20093,"\u002Fnatural-language-processing\u002Ffoundations\u002Fwhat-is-nlp":20096,"\u002Fnatural-language-processing\u002Ffoundations\u002Fregex-and-text-normalization":20100,"\u002Fnatural-language-processing\u002Ffoundations\u002Fminimum-edit-distance":20104,"\u002Fnatural-language-processing\u002Ffoundations\u002Fn-gram-language-models":20108,"\u002Fnatural-language-processing\u002Ffoundations\u002Fsmoothing-and-backoff":20112,"\u002Fnatural-language-processing\u002Fclassification\u002Fnaive-bayes-and-sentiment":20116,"\u002Fnatural-language-processing\u002Fclassification\u002Fevaluating-classifiers":20121,"\u002Fnatural-language-processing\u002Fclassification\u002Flogistic-regression":20125,"\u002Fnatural-language-processing\u002Fclassification\u002Fsentiment-and-affect-lexicons":20129,"\u002Fnatural-language-processing\u002Fsemantics\u002Fvector-semantics-and-embeddings":20133,"\u002Fnatural-language-processing\u002Fsemantics\u002Fstatic-word-embeddings":20138,"\u002Fnatural-language-processing\u002Fsemantics\u002Fneural-language-models":20142,"\u002Fnatural-language-processing\u002Fsequences\u002Fsequence-labeling":20146,"\u002Fnatural-language-processing\u002Fsequences\u002Fcrfs-and-neural-taggers":20150,"\u002Fnatural-language-processing\u002Fsequences\u002Frnns-and-lstms":20154,"\u002Fnatural-language-processing\u002Ftransformers\u002Ftransformers-and-attention":20158,"\u002Fnatural-language-processing\u002Ftransformers\u002Fthe-transformer-architecture":20162,"\u002Fnatural-language-processing\u002Ftransformers\u002Flarge-language-models":20165,"\u002Fnatural-language-processing\u002Ftransformers\u002Fllm-pretraining-and-scaling":20168,"\u002Fnatural-language-processing\u002Ftransformers\u002Ffine-tuning-and-prompting":20172,"\u002Fnatural-language-processing\u002Ftransformers\u002Fprompting-and-alignment":20176,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-parsing":20180,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcky-scoring-and-evaluation":20185,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdependency-parsing":20189,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fgraph-based-and-neural-dependency-parsing":20193,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fword-senses-and-wsd":20197,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fwsd-in-practice-and-induction":20201,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-roles-and-information-extraction":20205,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Frelations-events-and-templates":20209,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoreference-and-discourse":20213,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoherence-and-discourse-structure":20217,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Flogical-semantics":20221,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcompositional-semantics-and-description-logics":20225,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-parsing":20229,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fneural-semantic-parsing":20233,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Finformation-extraction":20237,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftimes-events-and-templates":20241,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdiscourse-coherence":20245,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fentity-based-and-global-coherence":20249,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-grammars":20253,"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftreebanks-and-lexicalized-grammars":20257,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation":20261,"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation-decoding-and-evaluation":20265,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering":20269,"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering-knowledge-and-llms":20273,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-and-chatbots":20277,"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-systems-and-assistants":20281,"\u002Fnatural-language-processing\u002Fapplications\u002Ftext-summarization":20285,"\u002Fnatural-language-processing\u002Fapplications\u002Fabstractive-summarization-and-evaluation":20289,"\u002Fnatural-language-processing\u002Fspeech\u002Fphonetics":20293,"\u002Fnatural-language-processing\u002Fspeech\u002Facoustic-phonetics":20298,"\u002Fnatural-language-processing\u002Fspeech\u002Fautomatic-speech-recognition":20302,"\u002Fnatural-language-processing\u002Fspeech\u002Fasr-evaluation-and-applications":20306,"\u002Fnatural-language-processing":20310,"\u002Fparticle-physics\u002Ffoundations\u002Fhistorical-overview-particle-zoo":20313,"\u002Fparticle-physics\u002Ffoundations\u002Fparticle-physics-basic-concepts":20317,"\u002Fparticle-physics\u002Ffoundations\u002Ffundamental-interactions-force-carriers":20321,"\u002Fparticle-physics\u002Funits-kinematics\u002Fnatural-units-and-scales":20325,"\u002Fparticle-physics\u002Funits-kinematics\u002Ffour-vectors-invariant-mass":20330,"\u002Fparticle-physics\u002Funits-kinematics\u002Fdecay-scattering-kinematics-mandelstam":20334,"\u002Fparticle-physics\u002Funits-kinematics\u002Fcross-sections-golden-rule":20338,"\u002Fparticle-physics\u002Fsymmetries\u002Fconservation-laws-symmetries":20342,"\u002Fparticle-physics\u002Fsymmetries\u002Fdiscrete-symmetries-cpt":20347,"\u002Fparticle-physics\u002Fsymmetries\u002Fparity-violation-weak":20351,"\u002Fparticle-physics\u002Fsymmetries\u002Fsu2-su3-flavor-symmetry":20355,"\u002Fparticle-physics\u002Fquark-model\u002Feightfold-way-su3":20359,"\u002Fparticle-physics\u002Fquark-model\u002Fmeson-spectroscopy":20364,"\u002Fparticle-physics\u002Fquark-model\u002Fbaryon-spectroscopy":20368,"\u002Fparticle-physics\u002Fquark-model\u002Fcolor-confinement-exotics":20372,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fklein-gordon-equation":20376,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fdirac-equation-spinors":20381,"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fantiparticles-hole-theory":20385,"\u002Fparticle-physics\u002Fqed\u002Ffeynman-rules-qed":20389,"\u002Fparticle-physics\u002Fqed\u002Fqed-tree-processes":20394,"\u002Fparticle-physics\u002Fqed\u002Frenormalization-running-coupling":20398,"\u002Fparticle-physics\u002Fqed\u002Felectron-g-2":20402,"\u002Fparticle-physics\u002Fweak-interaction\u002Fva-structure-weak":20406,"\u002Fparticle-physics\u002Fweak-interaction\u002Fw-z-bosons-decays":20411,"\u002Fparticle-physics\u002Fweak-interaction\u002Fckm-matrix":20415,"\u002Fparticle-physics\u002Fweak-interaction\u002Fcp-violation-kaons-b-mesons":20419,"\u002Fparticle-physics\u002Fqcd\u002Fcolor-su3-gluons":20423,"\u002Fparticle-physics\u002Fqcd\u002Fasymptotic-freedom-confinement":20428,"\u002Fparticle-physics\u002Fqcd\u002Fdeep-inelastic-scattering-partons":20432,"\u002Fparticle-physics\u002Fqcd\u002Fjets-hadronization":20436,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Felectroweak-su2-u1":20440,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fspontaneous-symmetry-breaking":20445,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-mechanism":20449,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-boson-discovery":20453,"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fstandard-model":20457,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-oscillations":20461,"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-mass-pmns":20466,"\u002Fparticle-physics\u002Fneutrinos\u002Fdirac-majorana-experiments":20470,"\u002Fparticle-physics\u002Fexperiment\u002Faccelerators-luminosity":20474,"\u002Fparticle-physics\u002Fexperiment\u002Fdetectors-subsystems":20479,"\u002Fparticle-physics\u002Fexperiment\u002Fhow-discoveries-are-made":20483,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fbeyond-standard-model":20487,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fgrand-unified-theories":20491,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fsupersymmetry":20495,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fhierarchy-problem-naturalness":20499,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fdark-matter-candidates":20503,"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fmatter-antimatter-open-questions":20507,"\u002Fparticle-physics":20511,"\u002Fastrophysics-cosmology\u002Forientation\u002Fthe-sun-and-stars":20514,"\u002Fastrophysics-cosmology\u002Forientation\u002Fstellar-death-final-states":20519,"\u002Fastrophysics-cosmology\u002Forientation\u002Fgalaxies-and-cosmology":20523,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fmagnitudes-fluxes-and-the-distance-modulus":20527,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fstellar-spectra-and-spectral-classification":20532,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Ftelescopes-and-detectors-across-the-spectrum":20536,"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fthe-cosmic-distance-ladder":20540,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fblackbody-radiation-and-specific-intensity":20544,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fradiative-transfer-and-the-transfer-equation":20549,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fspectral-line-formation-and-broadening":20553,"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fopacity-and-the-rosseland-mean":20557,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fhydrostatic-equilibrium-and-the-virial-theorem":20561,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equations-of-stellar-structure":20566,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equation-of-state-and-polytropes":20570,"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-standard-solar-model":20574,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fthermonuclear-reaction-rates-and-the-gamow-peak":20578,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhydrogen-burning-pp-chains-and-cno":20583,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhelium-burning-and-the-triple-alpha-process":20587,"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fadvanced-burning-and-neutron-capture-nucleosynthesis":20591,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fphases-of-the-interstellar-medium":20595,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fmolecular-clouds-and-gravitational-collapse":20600,"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fprotostars-and-the-pre-main-sequence":20604,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-main-sequence-and-its-structure":20608,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fpost-main-sequence-low-mass-evolution":20613,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-evolution-of-massive-stars":20617,"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fstellar-pulsation-and-the-instability-strip":20621,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fwhite-dwarfs-and-the-chandrasekhar-limit":20625,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fcore-collapse-supernovae":20629,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fthermonuclear-supernovae-type-ia":20633,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fneutron-stars-and-pulsars":20637,"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fblack-holes-schwarzschild-and-kerr":20641,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fbinary-systems-and-mass-transfer":20645,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Faccreting-compact-objects":20650,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fgravitational-waves-from-inspiraling-binaries":20654,"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fmultimessenger-astronomy-and-gamma-ray-bursts":20658,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fthe-milky-way":20662,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-morphology-and-classification":20667,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-rotation-curves-and-dark-matter":20671,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Factive-galactic-nuclei-and-supermassive-black-holes":20675,"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-clusters-and-large-scale-structure":20679,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-expanding-universe-and-hubbles-law":20683,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-frw-metric-and-cosmological-redshift":20688,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-friedmann-equations-and-cosmic-dynamics":20692,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fcosmological-models-and-distances":20695,"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fdark-energy-and-the-accelerating-universe":20699,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fthe-thermal-history-of-the-universe":20703,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fbig-bang-nucleosynthesis":20708,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Frecombination-and-the-cosmic-microwave-background":20712,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcmb-anisotropies-and-cosmological-parameters":20716,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcosmic-inflation":20720,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fstructure-formation-and-the-growth-of-perturbations":20724,"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fdark-matter-dark-energy-and-open-questions":20728,"\u002Fastrophysics-cosmology":20732,"\u002Fcolophon":20735,"\u002F":20738},{"path":16060,"title":16061,"module":16062,"summary":16063},"\u002Falgorithms\u002Ffoundations\u002Fwhat-is-an-algorithm","What Is an Algorithm?","Foundations","An algorithm is a finite, mechanical recipe that transforms inputs into outputs. We define what counts as an algorithm, how we write one down, and the three things we always ask of it: is it correct, is it fast, and can we prove it.\n",{"path":16065,"title":16066,"module":16062,"summary":16067},"\u002Falgorithms\u002Ffoundations\u002Fproof-techniques","Proof Techniques","An algorithm without a proof is a conjecture. This lesson collects the handful\nof arguments that certify the algorithms in this course — direct proof,\ncontrapositive, contradiction, ordinary and strong induction, construction, and\ndisproof by counterexample — each with a small worked\nexample and a picture. Loop invariants are a form of induction,\nrecursive correctness falls to strong induction, and the classic broken proofs\n(all horses are the same color) show where inductions go wrong.\n",{"path":16069,"title":16070,"module":16062,"summary":16071},"\u002Falgorithms\u002Ffoundations\u002Fasymptotic-analysis","Asymptotic Analysis","We measure an algorithm's running time as a function of its input size, then strip away machine-specific constants and lower-order terms to compare algorithms cleanly. This lesson defines the RAM model and the $O$, $\\Omega$, $\\Theta$, $o$, and $\\omega$ notations, proves the polynomial theorem, and shows how to rank growth rates with the limit test, L'Hôpital, base substitution, and the logarithm identities the arguments lean on.\n",{"path":16073,"title":16074,"module":16062,"summary":16075},"\u002Falgorithms\u002Ffoundations\u002Fgrowth-rates-and-loop-analysis","Growth Rates and Loop Analysis","With the asymptotic notations in hand, we rank the functions that actually arise in running times — from constant to factorial — proving the orderings between rungs, then read the running time of a loop nest straight off the page. Sequential blocks add, nested loops multiply, index scaling gives logarithms; a worked trace and a tour of cache-aware and galactic algorithms close the lesson.\n",{"path":16077,"title":16078,"module":16062,"summary":16079},"\u002Falgorithms\u002Ffoundations\u002Frecurrences","Recurrences and the Master Theorem","Recursive and divide-and-conquer algorithms describe their own running time with a recurrence: $T(n)$ in terms of $T$ on smaller inputs. We solve recurrences three ways — drawing the recursion tree, guessing-and-verifying by induction, and applying the Master Theorem — using merge sort as the running example, then handle unequal splits with Akra–Bazzi.\n",{"path":16081,"title":16082,"module":16062,"summary":16083},"\u002Falgorithms\u002Ffoundations\u002Famortized-analysis","Amortized Analysis","Some operations are occasionally expensive but cheap on average across any\nsequence. Amortized analysis bounds the average cost per operation over a\nworst-case sequence — not an expectation — so a rare costly step is paid for by\nthe many cheap ones around it. This lesson develops the aggregate, accounting,\nand potential methods on dynamic-array doubling, the binary counter, and a\nstack with multipop.\n",{"path":16085,"title":16086,"module":16087,"summary":16088},"\u002Falgorithms\u002Fdivide-and-conquer\u002Fmergesort","Divide and Conquer & Mergesort","Divide & Conquer","Divide and conquer breaks a problem into smaller copies of itself, solves\nthem recursively, and stitches the answers together. We meet the paradigm\nthrough mergesort — its merge step, its loop-invariant proof, and the\nrecursion tree that pins its cost at $\\Theta(n\\log n)$ — then count inversions\nwith the same machinery and distill the whole pattern into the master theorem.\n",{"path":16090,"title":16091,"module":16087,"summary":16092},"\u002Falgorithms\u002Fdivide-and-conquer\u002Fquicksort","Quicksort","Quicksort sorts in place by partitioning around a pivot and recursing on\neach side. We give Lomuto and Hoare partitioning with a correctness\ninvariant, see why a bad pivot costs $\\Theta(n^2)$ while a balanced one gives\n$\\Theta(n\\log n)$, and prove that randomizing the pivot makes the expected\ncost $\\Theta(n\\log n)$ on every input.\n",{"path":16094,"title":16095,"module":16087,"summary":16096},"\u002Falgorithms\u002Fdivide-and-conquer\u002Fselection","Linear-Time Selection","Finding the $k$-th smallest element looks like it should require sorting, but\nit does not. Quickselect adapts quicksort's partition to recurse on just one\nside, achieving expected $O(n)$. The median-of-medians algorithm guarantees a\ngood pivot with the groups-of-five trick, pushing the worst case down to a\nprovable $O(n)$.\n",{"path":16098,"title":16099,"module":16087,"summary":16100},"\u002Falgorithms\u002Fdivide-and-conquer\u002Ffast-multiplication","Fast Multiplication","Grade-school multiplication is $\\Theta(n^2)$, yet divide and conquer beats it.\nKaratsuba multiplies $n$-bit integers with three half-size products instead of\nfour, giving $\\Theta(n^{\\log_2 3})$, and Strassen multiplies matrices with\nseven block products instead of eight, giving $\\Theta(n^{\\log_2 7})$. Both\nspend cheap additions to save an expensive multiplication, and the master\ntheorem quantifies the savings.\n",{"path":16102,"title":16103,"module":16104,"summary":16105},"\u002Falgorithms\u002Fsorting\u002Fheaps-and-heapsort","Heaps and Heapsort","Sorting & Order Statistics","A binary heap is a tree we store flat in an array, with index arithmetic\nstanding in for pointers. We build the max-heap property bottom-up in $O(n)$\ntime, sort in place in $\\Theta(n\\log n)$ by repeatedly extracting the maximum,\nand reuse the same structure to implement a priority queue.\n",{"path":16107,"title":16108,"module":16104,"summary":16109},"\u002Falgorithms\u002Fsorting\u002Fsorting-lower-bounds","Lower Bounds for Comparison Sorting","Every sort we have seen runs in $\\Omega(n\\log n)$, and that is no accident.\nModeling a sort as a decision tree of comparisons, we show any such tree must\nhave $n!$ leaves, forcing height $\\ge \\log_2(n!) = \\Omega(n\\log n)$ — a bound\nno comparison sort beats in the worst case, on average, or with randomness.\n",{"path":16111,"title":16112,"module":16104,"summary":16113},"\u002Falgorithms\u002Fsorting\u002Flinear-time-sorting","Sorting in Linear Time","The $\\Omega(n\\log n)$ barrier only binds algorithms that compare. By instead\nusing keys as array indices we slip past it: counting sort runs in\n$\\Theta(n+k)$ and is stable, radix sort layers it digit by digit, and bucket\nsort averages $\\Theta(n)$ on uniform data. We see exactly when each applies.\n",{"path":16115,"title":16116,"module":16104,"summary":16117},"\u002Falgorithms\u002Fsorting\u002Fexternal-sorting","External Sorting","When the data dwarfs main memory, the cost that matters is no longer\ncomparisons but block transfers to and from disk. External merge sort sorts\nmemory-sized runs, then folds them together with a heap-driven $k$-way merge in\n$\\Theta(\\log_k(N\u002FM))$ passes. Larger fan-out cuts passes; replacement selection\nbuilds longer runs to cut them further.\n",{"path":16119,"title":16120,"module":16121,"summary":16122},"\u002Falgorithms\u002Fdata-structures\u002Felementary-structures","Elementary Data Structures","Data Structures","Every container is built one of two ways: **contiguous** in an array, or\n**linked** through pointers. We trade cache-friendly random access against\n$O(1)$ splicing, derive the **amortized $O(1)$** append of a doubling dynamic\narray, and assemble the two ordered access disciplines — the LIFO **stack** and\nthe FIFO **queue** (with its generalization, the **deque**) — on top of both.\n",{"path":16124,"title":16125,"module":16121,"summary":16126},"\u002Falgorithms\u002Fdata-structures\u002Fhash-tables","Hash Tables","A hash table implements the dictionary — insert, search, delete — in expected\n$O(1)$ time by scattering keys across an array with a hash function. We build\nup from direct addressing, handle collisions by chaining and by open\naddressing, analyze the load factor $\\alpha$, and see how universal hashing\nachieves its expected-time guarantee against every input.\n",{"path":16128,"title":16129,"module":16121,"summary":16130},"\u002Falgorithms\u002Fdata-structures\u002Fbinary-search-trees","Binary Search Trees","A binary search tree keeps keys ordered so that every operation follows a\nsingle root-to-leaf path. We state the BST property, trace search, insert,\nsuccessor, and all three delete cases on concrete trees, prove the inorder\nwalk sorts, and note the drawback — every operation costs $O(h)$, and a\ncarelessly built tree degrades to height $h = \\Theta(n)$, motivating balance.\n",{"path":16132,"title":16133,"module":16121,"summary":16134},"\u002Falgorithms\u002Fdata-structures\u002Favl-trees","AVL Trees","An AVL tree is the first balanced BST: at every node the two subtrees' heights\ndiffer by at most $1$. A Fibonacci-style minimal-node argument forces height\n$h \\le 1.44\\log_2 n = O(\\log n)$, so search, insert, and delete are all\n$O(\\log n)$. Insertion rebalances with at most one of four rotation cases\n(LL, RR, LR, RL); deletion may rotate all the way to the root.\n",{"path":16136,"title":16137,"module":16121,"summary":16138},"\u002Falgorithms\u002Fdata-structures\u002Fbalanced-trees","Balanced Search Trees","An ordinary BST can degrade to height $\\Theta(n)$; balanced search trees\nguarantee $h = O(\\log n)$ by maintaining invariants and repairing them after\nevery update. We meet rotations, the local restructuring primitive, then\nred-black trees, whose color invariants force logarithmic height, and finally\nB-trees, which trade tall-and-thin for short-and-wide to win on disk.\n",{"path":16140,"title":16141,"module":16121,"summary":16142},"\u002Falgorithms\u002Fdata-structures\u002Funion-find","Disjoint Sets (Union-Find)","The disjoint-set data structure tracks a partition of elements into groups,\nanswering \"are these two in the same group?\" and merging groups on demand. A\nforest of parent pointers, sped up by union by rank and path compression,\ndrives every operation to near-constant $O(\\alpha(n))$ amortized time — the\nstructure behind connectivity queries and Kruskal's minimum spanning tree.\n",{"path":16144,"title":16145,"module":16121,"summary":16146},"\u002Falgorithms\u002Fdata-structures\u002Ffenwick-and-segment-trees","Fenwick & Segment Trees","A prefix-sum array answers a range sum in $O(1)$ but pays $O(n)$ per update;\na plain array updates in $O(1)$ but pays $O(n)$ per range sum. Fenwick and\nsegment trees give us _both_ in $O(\\log n)$. The Fenwick (binary indexed) tree\nis a tiny array keyed by the low bit; the segment tree is a general balanced\ntree over canonical ranges that handles any associative aggregate and, with\nlazy propagation, range updates too.\n",{"path":16148,"title":16149,"module":16121,"summary":16150},"\u002Falgorithms\u002Fdata-structures\u002Fspatial-data-structures","Spatial Data Structures","A balanced BST orders keys on a line, but points in the plane have no single\nnatural order. Quadtrees subdivide space recursively into quadrants; k-d trees\nsplit on alternating coordinates at the median. Both make range and\nnearest-neighbour queries fast by carving the plane into boxes a query can\nprune away. Range trees nest a y-tree in an x-tree for fast orthogonal range\nreporting; interval trees index intervals to answer stabbing queries.\n",{"path":16152,"title":16153,"module":16121,"summary":16154},"\u002Falgorithms\u002Fdata-structures\u002Fskip-lists-and-probabilistic-structures","Skip Lists & Probabilistic Structures","Balanced trees achieve $O(\\log n)$ with rotations and invariants; randomization\ngives the same bound far more simply. A skip list is a layered linked list whose\nexpress lanes are chosen by coin flips, giving expected $O(\\log n)$ search and\ninsert with no rebalancing. A Bloom filter trades exactness for space: a bit\narray and a few hashes answer set membership with no false negatives and a\ntunable false-positive rate, but cannot delete.\n",{"path":16156,"title":16157,"module":16121,"summary":16158},"\u002Falgorithms\u002Fdata-structures\u002Fb-trees","B-Trees","When data lives on disk, the cost that dominates is block transfers, not\ncomparisons — and a binary tree of a billion keys is thirty reads deep. A\nB-tree of minimum degree $t$ is short and wide: $t-1$ to $2t-1$ keys per node,\nall leaves at one depth, height $O(\\log_t n)$. Insertion splits a full node on\nthe way down and pushes its median up; deletion borrows or merges to keep nodes\nfull enough. High fan-out is what minimizes disk I\u002FO.\n",{"path":16160,"title":16161,"module":16121,"summary":16162},"\u002Falgorithms\u002Fdata-structures\u002Fdata-stream-algorithms","Data-Stream Algorithms","Most of this course assumes data sits in fast memory, addressable at will.\nExternal sorting relaxed that to a re-readable disk. The streaming model goes\nfurther: items arrive one at a time, are seen once, and must be discarded, with\nonly sublinear, often polylogarithmic, memory. In exchange, the answers are\napproximate and probabilistic. We set up the model, then meet reservoir\nsampling for a uniform sample of an unknown-length stream and Morris counting\nfor an approximate tally in doubly-logarithmic space.\n",{"path":16164,"title":16165,"module":16121,"summary":16166},"\u002Falgorithms\u002Fdata-structures\u002Fstreaming-sketches","Streaming Sketches","Sampling and counting kept a random subset or a single approximate tally.\nSketches go further: fixed, tiny summaries that answer questions about a\nstream's frequencies. We meet the Count–Min sketch for point frequency\nestimation, Misra–Gries for heavy hitters, and HyperLogLog for distinct\ncounts, each trading a controlled error for space that never grows with the\nstream.\n",{"path":16168,"title":16169,"module":16170,"summary":16171},"\u002Falgorithms\u002Fsequences\u002Ftwo-pointers-and-windows","Two Pointers & Sliding Windows","Sequences & Strings","A family of array idioms that collapse an obvious $O(n^2)$ scan into a single\n$O(n)$ pass by maintaining an invariant as indices move. We meet two pointers\n(converging on a sorted array, and a fast\u002Fslow pair for in-place rewriting)\nand the sliding window (fixed and variable size, amortized $O(n)$). The\ncompanion lesson on prefix sums picks up where the window's positivity\nassumption fails.\n",{"path":16173,"title":16174,"module":16170,"summary":16175},"\u002Falgorithms\u002Fsequences\u002Fprefix-sums","Prefix Sums & Difference Arrays","Prefix sums precompute the running total once so that any range-sum query is a\nsingle subtraction, $P[r{+}1]-P[l]$, in $O(1)$. A hash map of prefix\nfrequencies then counts subarrays summing to $k$ in $O(n)$ — even with negative\nentries, where the sliding window fails. The difference-array dual turns $m$\nrange-adds into $O(m+n)$, and the whole idea lifts to 2-D rectangle sums by\ninclusion–exclusion.\n",{"path":16177,"title":16178,"module":16170,"summary":16179},"\u002Falgorithms\u002Fsequences\u002Fmonotonic-stacks","Monotonic Stacks & Queues","A **monotonic stack** keeps its contents sorted by popping every element that\nwould break the order before each push — turning a family of \"previous\u002Fnext\ngreater (or smaller) element\" questions into a single $O(n)$ scan. We trace\nthe next-greater-element routine push by push and prove its amortized bound,\nfuse two such scans to measure the **largest rectangle in a histogram** in\nlinear time, extend the idea to a **monotonic deque** that streams the\n**sliding-window maximum** in $O(n)$, and use asymmetric tie-breaking to\ncount **subarray minimums** without double-counting duplicates.\n",{"path":16181,"title":16182,"module":16170,"summary":16183},"\u002Falgorithms\u002Fsequences\u002Fbinary-search-on-the-answer","Binary Search on the Answer","Binary search locates the boundary of a **monotone predicate** $p(x)$ in\n$O(\\log(\\text{range}))$ probes; sorted arrays are only one instance. We first\nestablish the half-open `while (lo \u003C hi)` template for $\\textsc{lower\\_bound}$\nand $\\textsc{upper\\_bound}$, then generalize to \"binary search on the answer\":\nwhenever feasibility is monotone in a numeric parameter, we binary search the\nparameter itself, calling a feasibility check at each step.\n",{"path":16185,"title":16186,"module":16170,"summary":16187},"\u002Falgorithms\u002Fsequences\u002Fstring-matching","String Matching: Naive & Rabin–Karp","Given a text $T$ of length $n$ and a pattern $P$ of length $m$, find every\noccurrence of $P$ in $T$. The naive scan costs $O(nm)$ and re-reads text it has\nalready seen. Rabin–Karp fixes the first inefficiency with a **rolling hash**:\neach length-$m$ window is summarized by one number, updated in $O(1)$ per slide,\nverified on a hash match to kill collisions, for expected $O(n+m)$. A companion\nlesson removes the re-reading entirely with KMP and the Z-function.\n",{"path":16189,"title":16190,"module":16170,"summary":16191},"\u002Falgorithms\u002Fsequences\u002Fkmp-and-z-function","String Matching: KMP & the Z-Function","Two linear-time matchers that beat Rabin–Karp's expected bound with a\nworst-case guarantee and no randomness. KMP precomputes a **failure function**\n$\\pi$ so a mismatch slides the pattern by $q-\\pi[q-1]$ and the text pointer\nnever backs up, for $O(n+m)$. The **Z-function** computes the longest\nprefix-match at every position via the Z-box, giving the same bound from a\ndifferent angle; the two encodings of a string's self-overlap convert freely.\n",{"path":16193,"title":16194,"module":16170,"summary":16195},"\u002Falgorithms\u002Fsequences\u002Ftries","Tries & Prefix Trees","A **trie** stores a set of strings in a tree keyed by _characters_, so that\ninsert, search, delete, and prefix-test all run in $O(L)$ time — the length\nof the key, _independent of how many keys are stored_. Shared prefixes are\nstored once, which makes tries the natural structure for autocomplete,\nwildcard dictionaries, board word-search, and — over the alphabet $\\{0,1\\}$\n— the maximum-XOR-pair problem. Radix (Patricia) trees compress the chains.\n",{"path":16197,"title":16198,"module":16170,"summary":16199},"\u002Falgorithms\u002Fsequences\u002Fsuffix-arrays-and-aho-corasick","Suffix Arrays, LCP & Aho–Corasick","A **suffix array** sorts all $n$ suffixes of a string, indexing every substring\nat once; built in $O(n\\log n)$, it locates a pattern by binary search in\n$O(m\\log n)$. Its companion **LCP array** (Kasai's $O(n)$ algorithm) counts\ndistinct substrings and finds the longest repeated substring. **Aho–Corasick**\ngeneralises KMP to a whole dictionary: a trie of patterns plus failure links\nscans the text once in $O(\\text{text} + \\text{matches})$ to report every\noccurrence of every pattern. Manacher's algorithm finds all palindromic\nsubstrings in $O(n)$.\n",{"path":16201,"title":16202,"module":16203,"summary":16204},"\u002Falgorithms\u002Fgraphs\u002Frepresentations-and-traversal","Graph Representations and Traversal","Graphs","A graph captures _relationships_ — who connects to whom. We fix the\nvocabulary, weigh the two standard representations (adjacency list versus\nmatrix), then meet the single search skeleton behind everything that follows:\nWhatever-First-Search, and its breadth-first reading, which finds shortest\npaths by number of edges in $O(V + E)$.\n",{"path":16206,"title":16207,"module":16203,"summary":16208},"\u002Falgorithms\u002Fgraphs\u002Fdepth-first-search","Depth-First Search","Swap BFS's queue for a stack and the search plunges instead of fanning out.\nDepth-first search stamps every vertex with discovery and finish times that\nnest like parentheses, classifies each edge as tree, back, forward, or cross,\nand — through the back edge — decides in one pass whether a graph has a cycle.\nThese timestamps underpin topological sort, strong\nconnectivity, and the rest of this module.\n",{"path":16210,"title":16211,"module":16203,"summary":16212},"\u002Falgorithms\u002Fgraphs\u002Ftopological-sort-and-scc","Topological Sort and Strong Connectivity","Directed acyclic graphs model dependencies: tasks that must precede other\ntasks. A _topological order_ lays such a graph out in a line so every edge\npoints forward, and depth-first finish times yield one almost for free.\nWe then ask the harder question for graphs _with_ cycles: which vertices can\nreach each other? The answer is the strongly connected components, found by a\ntwo-pass DFS.\n",{"path":16214,"title":16215,"module":16203,"summary":16216},"\u002Falgorithms\u002Fgraphs\u002Fminimum-spanning-trees","Minimum Spanning Trees","Given a weighted network, how do we connect everything as cheaply as possible?\nThe answer is a minimum spanning tree, and one lemma — the cut property —\njustifies _every_ correct MST algorithm. We prove the cut and cycle\nproperties by exchange arguments, use them to settle uniqueness, and meet the\noldest MST algorithm, Borůvka's, whose parallel component-merging rounds fall\nstraight out of the cut rule.\n",{"path":16218,"title":16219,"module":16203,"summary":16220},"\u002Falgorithms\u002Fgraphs\u002Fkruskal-and-prim","Kruskal and Prim","The two minimum-spanning-tree algorithms you will actually implement.\nKruskal grows a forest edge by edge, cheapest first, using a union-find\nstructure to reject cycle-closing edges; Prim grows one tree outward from a\nroot with a priority queue, exactly Dijkstra rekeyed by attachment cost. Both\ntraced in full on a nine-town graph, with the edge cases, the bottleneck\nproperty, and where each one wins.\n",{"path":16222,"title":16223,"module":16203,"summary":16224},"\u002Falgorithms\u002Fgraphs\u002Fshortest-paths","Shortest Paths","Finding the cheapest route through a weighted network is one of the most-used\nalgorithms in computing, and a single operation — _relaxation_ — underlies\nevery method. We build the primitive, prove the triangle inequality and\noptimal substructure that make it work, then meet Dijkstra's algorithm: the\ngreedy solution for non-negative weights, traced vertex by vertex, with the\ncut argument that proves each extraction is final.\n",{"path":16226,"title":16227,"module":16203,"summary":16228},"\u002Falgorithms\u002Fgraphs\u002Fall-pairs-and-negative-weights","All-Pairs and Negative Weights","Dijkstra's greedy schedule breaks the moment an edge goes negative. We give it\nup for dynamic programming: Bellman-Ford derived as a DP over edge budgets,\nwith its negative-cycle detector, and Floyd-Warshall computing the distance\nbetween _every_ pair of vertices via a DP over which vertices a path may pass\nthrough. We close with Johnson's algorithm and the arbitrage problems that\nnegative cycles encode.\n",{"path":16230,"title":16231,"module":16203,"summary":16232},"\u002Falgorithms\u002Fgraphs\u002Fnetwork-flow","Network Flow","How much can flow through a network from source to sink? We build flow\nnetworks with capacity and conservation constraints, increase a flow by\npushing along augmenting paths in the residual graph, and see how reverse\nedges let the algorithm undo earlier routing. Ford-Fulkerson and its BFS refinement\nEdmonds-Karp find a maximum flow, traced end to end on a worked network.\n",{"path":16234,"title":16235,"module":16203,"summary":16236},"\u002Falgorithms\u002Fgraphs\u002Fmax-flow-min-cut","Max-Flow Min-Cut and Applications","Why is the flow found when no augmenting path remains actually optimal? The\nanswer is a duality theorem: the maximum flow equals the minimum cut. We prove\nit, read the minimum cut off the final residual graph, then derive bipartite\nmatching and a catalog of modeling reductions from the flow\nabstraction — before touching the modern algorithms that supersede\nEdmonds-Karp.\n",{"path":16238,"title":16239,"module":16203,"summary":16240},"\u002Falgorithms\u002Fgraphs\u002Fbridges-and-articulation-points","Bridges & Articulation Points","A **bridge** is an edge whose removal disconnects the graph; an **articulation\npoint** is a vertex whose removal does. Both are single points of failure in a\nnetwork. A single depth-first search computes discovery times and **low-links**,\nand two local criteria — $low[v] > disc[u]$ for bridges, $low[v] \\ge disc[u]$\nfor cut vertices — find them all in $O(V+E)$.\n",{"path":16242,"title":16243,"module":16203,"summary":16244},"\u002Falgorithms\u002Fgraphs\u002Flowest-common-ancestor","Lowest Common Ancestor & Binary Lifting","Given a rooted tree, the lowest common ancestor of $u$ and $v$ is the deepest\nnode that is an ancestor of both. A naive walk answers one query in $O(h)$;\n**binary lifting** precomputes the $2^k$-th ancestor of every node in\n$O(n\\log n)$, then answers $k$-th-ancestor and LCA queries in $O(\\log n)$ each.\nWe derive both jumps, apply them to tree distance, and compare against the\nEuler-tour + RMQ and Tarjan offline alternatives.\n",{"path":16246,"title":16247,"module":16203,"summary":16248},"\u002Falgorithms\u002Fgraphs\u002Ftwo-sat","2-SAT via Implication Graphs","A boolean formula whose every clause has exactly two literals can be solved in\n_linear_ time — even though its three-literal cousin is NP-complete. The idea\nis to read each clause as a pair of implications, build a directed graph on the\n$2n$ literals, and ask a question we already know how to answer: which literals\nshare a strongly connected component? The formula is satisfiable iff no variable\nlands in the same SCC as its own negation, and the SCCs' topological order\nyields a satisfying assignment for free.\n",{"path":16250,"title":16251,"module":16203,"summary":16252},"\u002Falgorithms\u002Fgraphs\u002Feulerian-tours","Eulerian Tours","An **Eulerian tour** uses every _edge_ of a graph exactly once. We give the\nexact parity and balance conditions under which one exists (even degree\nfor undirected graphs, in-degree equal to out-degree for directed) and Hierholzer's\n$O(E)$ algorithm that constructs one by splicing closed sub-tours. We contrast\nthis sharply with the **Hamiltonian** problem (visit every _vertex_ once),\nwhich is NP-complete: visiting edges is easy, visiting vertices is hard.\n",{"path":16254,"title":16255,"module":16203,"summary":16256},"\u002Falgorithms\u002Fgraphs\u002Fbipartite-matching","Bipartite Matching","Pairing applicants to jobs, students to slots, files to disks: all are\n**maximum bipartite matching**. We solve it combinatorially with **augmenting\npaths** (Kuhn's algorithm, $O(VE)$), speed it up to $O(E\\sqrt V)$ with\n**Hopcroft–Karp**, and uncover the structure behind it — **König's theorem**\n(max matching equals min vertex cover) and **Hall's marriage theorem** (a\nperfect matching exists iff every set has enough neighbors).\n",{"path":16258,"title":16259,"module":16260,"summary":16261},"\u002Falgorithms\u002Fgreedy\u002Fthe-greedy-method","The Greedy Method","Greedy Algorithms","A greedy algorithm builds a solution one locally-best choice at a time and\nnever looks back. We isolate the two properties that make this work — the\ngreedy-choice property and optimal substructure — prove the canonical\nactivity-selection algorithm correct with an exchange argument, watch greedy\nfail on the 0\u002F1 knapsack, and glimpse matroids as the theory\nthat says exactly when the greedy method is optimal.\n",{"path":16263,"title":16264,"module":16260,"summary":16265},"\u002Falgorithms\u002Fgreedy\u002Fscheduling-and-intervals","Scheduling & Interval Partitioning","Three classic scheduling problems all yield to greedy algorithms — and all\nthree turn on a single design decision: which key to sort by. Interval\nscheduling sorts by **finish** time to pack the most compatible jobs;\ninterval partitioning sorts by **start** time and proves the rooms needed\nequal the maximum overlap **depth**; minimizing maximum lateness sorts by\n**deadline** and is justified by an adjacent-swap exchange argument.\n",{"path":16267,"title":16268,"module":16260,"summary":16269},"\u002Falgorithms\u002Fgreedy\u002Fhuffman-codes","Huffman Codes","Huffman coding builds a\nprovably optimal prefix-free binary code by repeatedly merging the two least\nfrequent symbols. We develop prefix-free codes as binary trees, give the\nalgorithm with a priority queue, build a Huffman tree from example\nfrequencies, prove optimality with the same greedy-choice-plus-substructure\nargument, and pin the running time at $O(n\\log n)$.\n",{"path":16271,"title":16272,"module":16260,"summary":16273},"\u002Falgorithms\u002Fgreedy\u002Fmatroids","Matroids & Exchange Arguments","The capstone of the greedy module: _why_ and _when_ a greedy algorithm is\nprovably optimal. We recap the two correctness templates — **greedy-stays-ahead**\nand the **exchange argument** — then meet the **matroid** $M=(S,\\mathcal{I})$, an\nabstraction whose **exchange property** is the structure greedy needs.\nThe matroid–greedy theorem says sorting by weight and taking what stays\nindependent yields a maximum-weight basis _if and only if_ the structure is a\nmatroid. Kruskal's MST is the canonical instance; 0\u002F1 knapsack and TSP are the\ncanonical failures.\n",{"path":16275,"title":16276,"module":16260,"summary":16277},"\u002Falgorithms\u002Fgreedy\u002Fstable-matching","Stable Matching (Gale–Shapley)","Two sides each rank the other; we want a matching with no **blocking pair** — no\ntwo participants who both prefer each other to their assigned partners. The\n**Gale–Shapley deferred-acceptance** algorithm has proposers propose in\npreference order while receivers tentatively hold the best offer so far. We prove\nit terminates in $\\O(n^2)$ proposals, returns a **perfect** matching, and that\nthe matching is **stable**. A sharper asymmetry follows: deferred acceptance is\n**proposer-optimal** and **receiver-pessimal**, the structural fact behind the\nresidency match and school-choice systems.\n",{"path":16279,"title":16280,"module":16281,"summary":16282},"\u002Falgorithms\u002Fdynamic-programming\u002Fprinciples","Principles of Dynamic Programming","Dynamic Programming","Dynamic programming is recursion with memory: when a recursive solution\nre-solves the same subproblems again and again, we solve each one once and\nstore the answer. We identify the two structural conditions that make this\nwork — overlapping subproblems and optimal substructure — contrast top-down\nmemoization with bottom-up tabulation, and distil the whole method into a\nfive-step recipe.\n",{"path":16284,"title":16285,"module":16281,"summary":16286},"\u002Falgorithms\u002Fdynamic-programming\u002Fsequence-dp","Sequence Alignment & LCS","Two strings can be compared by how much of one appears inside the\nother. The longest common subsequence (LCS) and edit distance are the two\nclassic measures, and they are the _same_ dynamic program with different\ncosts. We derive the LCS recurrence by examining the last characters, fill a\nworked DP table, reconstruct the subsequence, and then show edit distance as\nthe identical $\\Theta(mn)$ pattern.\n",{"path":16288,"title":16289,"module":16281,"summary":16290},"\u002Falgorithms\u002Fdynamic-programming\u002Flongest-increasing-subsequence","Longest Increasing Subsequence","Given a sequence of numbers, how long is its longest strictly increasing\nsubsequence? A first dynamic program indexes subproblems by the element each\nsubsequence _ends at_, giving an $O(n^2)$ solution with parent-pointer\nreconstruction. A sharper idea, the patience-sorting _tails_ array searched by\nbinary search, drops the time to $O(n\\log n)$. We then fold in the\nvariants: non-decreasing, counting, Russian-doll envelopes, and bitonic.\n",{"path":16292,"title":16293,"module":16281,"summary":16294},"\u002Falgorithms\u002Fdynamic-programming\u002Fknapsack","Knapsack & Subset Problems","We start from $\\textsc{Subset-sum}$ — does some sublist hit a target $t$? — and its\ninclude\u002Fexclude recurrence over a boolean table $A(i, u)$, then bolt on values\nto get 0\u002F1 knapsack as the same machine with $\\lor$ promoted to $\\max$. We fill\nboth tables, recover the chosen items, and confront the surprise that the\n$\\Theta(nt)$ running time is only _pseudo-polynomial_ — exponential in the bit\nlength $b$, and unimprovable unless $\\mathrm{P}=\\mathrm{NP}$ since subset-sum is\n$\\textsc{NP-complete}$. The fractional variant reveals the sharp line between greedy\nand dynamic programming.\n",{"path":16296,"title":16297,"module":16281,"summary":16298},"\u002Falgorithms\u002Fdynamic-programming\u002Fcoin-change-and-unbounded","Coin Change & Unbounded Knapsack","The previous lesson let each item be taken at most once. Drop that cap — items\nmay be reused _any number of times_ — and the 0\u002F1 knapsack collapses from a\ntwo-dimensional table to a one-dimensional one, because there is no longer a\nprefix of \"already-used\" items to track. We meet **unbounded knapsack**, then\nits most famous instance, **coin change**: the minimum-coins recurrence\n$C[a] = 1 + \\min_c C[a-c]$, and the counting variant where the _order of the\nloops_ decides whether you count unordered combinations or ordered sequences —\nthe classic bug. Greed fails in general but works for canonical coin systems.\n",{"path":16300,"title":16301,"module":16281,"summary":16302},"\u002Falgorithms\u002Fdynamic-programming\u002Finterval-dp","Interval DP","Many problems ask for the best way to combine a contiguous range of items, and\nthe answer is a dynamic program over subintervals $[i,j]$ that chooses a split\npoint $k$. We derive the pattern from matrix-chain multiplication —\nparenthesising a product to minimize scalar multiplications in $O(n^3)$ — distil\nit into a reusable template filled by increasing interval length, and then meet\nits sharpest variant: the \"last operation\" trick behind Burst Balloons and\ncutting a stick, where fixing the _last_ move (not the first) makes the two\nsides independent.\n",{"path":16304,"title":16305,"module":16281,"summary":16306},"\u002Falgorithms\u002Fdynamic-programming\u002Ftree-dp","Dynamic Programming on Trees","When the subproblems of a dynamic program are _rooted subtrees_, a single\npost-order DFS solves the whole thing in $O(n)$: each node combines the\nalready-computed answers of its children. We meet the archetype — maximum-weight\nindependent set on a tree — then the \"path through a node\" pattern behind tree\ndiameter and maximum path sum, and finally **rerooting**, which computes a\nper-node answer for _every_ node as root in $O(n)$ with two passes.\n",{"path":16308,"title":16309,"module":16281,"summary":16310},"\u002Falgorithms\u002Fdynamic-programming\u002Fbitmask-dp","Bitmask DP","When a subproblem depends not on an index or a prefix but on _which subset_ of\na small ground set has been used, we can encode that subset as the bits of an\ninteger and index a DP table by it. With $n \\le \\sim 20$ the $2^n$ subsets fit\nin a table, turning $\\Theta(n!)$ brute force into $O(2^n \\cdot \\text{poly}(n))$.\nWe meet the bit tricks, the Held–Karp TSP archetype, assignment by mask,\nsubset-sum partitioning, and submask enumeration with its $3^n$ bound.\n",{"path":16312,"title":16313,"module":16281,"summary":16314},"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-optimizations","DP Optimizations","A correct DP recurrence is only half the battle; its naive evaluation is often\na factor of $n$ slower than necessary. This capstone surveys five techniques,\nmonotonic-queue, the convex hull trick, divide-and-conquer optimization,\nKnuth's optimization, and SOS DP, that each exploit _structure in the\ntransition_ (a sliding window, linear costs, monotone optimal splits, the\nquadrangle inequality, or subset lattices) to shave an $O(n)$, $O(\\log n)$, or\nworse factor off the running time.\n",{"path":16316,"title":16317,"module":16281,"summary":16318},"\u002Falgorithms\u002Fdynamic-programming\u002Fdp-on-graphs","Dynamic Programming on Graphs","Many graph algorithms are dynamic programs: the subproblem is the\n_best value reachable under a restricted resource_ — intermediate vertices\nallowed, edges allowed, or a topological prefix — and edge _relaxation_ is the\nDP transition. We frame Floyd–Warshall as the archetype ($O(V^3)$ all-pairs\nshortest paths), Bellman–Ford as a DP over path length (the at-most-$K$-stops\nvariant), DAG-DP in topological order ($O(V+E)$), and Warshall's transitive\nclosure as the boolean analog.\n",{"path":16320,"title":16321,"module":16281,"summary":16322},"\u002Falgorithms\u002Fdynamic-programming\u002Fdigit-and-probability-dp","Digit & Probability DP","Two DP patterns with unusual state. _Digit DP_ counts the\nintegers in a range $[L, R]$ that satisfy a digit constraint by walking the\ndecimal places of the bound, carrying a _tight_ flag that marks when the prefix\nstill equals the bound's. _Probability\u002FExpectation DP_ replaces \"best value\" with\n\"expected value,\" using linearity of expectation to make each state an\naverage over its weighted transitions — the natural tool for expected step\ncounts and absorbing Markov chains.\n",{"path":16324,"title":16325,"module":16326,"summary":16327},"\u002Falgorithms\u002Fbacktracking\u002Fbacktracking-fundamentals","Backtracking: Subsets, Permutations & Combinations","Backtracking & Search","Backtracking builds a solution one choice at a time and abandons a partial\nsolution the moment it cannot be completed, exploring a state-space tree by\ndepth-first search. We meet the universal choose\u002Fexplore\u002Fun-choose template,\nderive the canonical enumerations — subsets ($2^n$), permutations ($n!$), and\ncombinations ($\\binom{n}{k}$) — handle duplicate elements by skipping equal\nsiblings, and see how pruning turns an exponential search into a tractable one.\n",{"path":16329,"title":16330,"module":16326,"summary":16331},"\u002Falgorithms\u002Fbacktracking\u002Fconstraint-search","Constraint Search: N-Queens & Sudoku","Many hard puzzles are **constraint satisfaction problems**: assign each\nvariable a value from its domain so that every constraint holds. Backtracking\nsolves them by assigning variables one at a time and rejecting a partial\nassignment the instant a constraint breaks. We make the rejection cheap — $O(1)$\nconflict checks for N-Queens via column and diagonal sets — and prune harder\nwith **forward checking**, **MRV** ordering, and **constraint propagation**,\nwhich is what lets an exponential search actually finish.\n",{"path":16333,"title":16334,"module":16326,"summary":16335},"\u002Falgorithms\u002Fbacktracking\u002Fbranch-and-bound","Branch & Bound and Meet in the Middle","Plain backtracking prunes a search tree by _feasibility_; for _optimization_\nproblems we can prune far more aggressively by _value_. **Branch and bound**\nkeeps the best complete solution found so far and discards any partial solution\nwhose optimistic bound cannot beat it. **Meet in the middle** splits the\ninstance in two, enumerates each half, and recombines by binary search — turning\n$2^n$ into $O(2^{n\u002F2}\\,n)$ and pushing exact search out to $n \\approx 40$.\n",{"path":16337,"title":16338,"module":16326,"summary":16339},"\u002Falgorithms\u002Fbacktracking\u002Fgraph-backtracking","Graph Backtracking: m-Coloring & Hamiltonian Paths","Two famous graph problems have no known efficient algorithm, yet yield cleanly\nto backtracking with the right pruning. **Graph $m$-coloring** assigns one of\n$m$ colors to each vertex so no edge is monochromatic; we color vertices in turn\nand reject a color the instant a neighbor already has it. **Hamiltonian\npath\u002Fcycle** asks for a walk visiting every vertex exactly once; we extend a path\ngreedily and backtrack on dead ends. Both are NP-complete, so the worst case is\nexponential — but feasibility pruning and good vertex ordering make real\ninstances tractable, and the contrast with the easy Eulerian condition shows why.\n",{"path":16341,"title":16342,"module":16343,"summary":16344},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fnumber-theory-basics","Number Theory: GCD & Modular Arithmetic","Mathematical Algorithms","This lesson opens the mathematical-algorithms module with the bedrock of\ncomputational number theory. We prove Euclid's recurrence\n$\\gcd(a,b)=\\gcd(b,\\,a\\bmod b)$ and its $O(\\log\\min(a,b))$ running time, extend\nit to recover Bézout coefficients $x,y$ with $ax+by=\\gcd(a,b)$, and build\nmodular arithmetic on residue classes — including when a modular inverse\n$a^{-1}\\bmod m$ exists and how to compute it.\n",{"path":16346,"title":16347,"module":16343,"summary":16348},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmodular-exponentiation-and-primality","Modular Exponentiation & Primality","Computing $a^n \\bmod m$ naively costs $n$ multiplications; **repeated squaring**\ndoes it in $O(\\log n)$ by reading the bits of the exponent. We use this routine\nto state **Fermat's little theorem** (and the modular inverse it gives), then to\ntest primality — trial division, the probabilistic **Fermat** and **Miller–Rabin**\ntests, and the deterministic witness set that settles primality for every 64-bit\nnumber.\n",{"path":16350,"title":16351,"module":16343,"summary":16352},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fsieve-and-factorization","Sieves & Factorization","The previous lesson tested one number for primality; here we ask for _all_\nprimes up to $n$ at once. The **sieve of Eratosthenes** cross-cuts composites\nin $O(n\\log\\log n)$, and a **linear sieve** does it in $O(n)$ while recording\neach number's **smallest prime factor**, which then factors any $x \\le n$ in\n$O(\\log x)$. From a factorization $x = \\prod p_i^{e_i}$ the multiplicative\nfunctions $\\tau$, $\\sigma$, and Euler's totient $\\varphi$ fall out immediately.\n",{"path":16354,"title":16355,"module":16343,"summary":16356},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fcombinatorics","Combinatorics & Counting","Counting is the arithmetic of finite sets. We build up from permutations\n$n!$ and combinations $\\binom{n}{k}$, prove Pascal's rule by a bijection,\nand count multisets with stars and bars. The practical core is computing\n$\\binom{n}{k}\\bmod p$ in $O(1)$ from precomputed factorials and inverse\nfactorials. We close with inclusion–exclusion and the Chinese Remainder\nTheorem, both of which lean on the modular inverse from the previous lesson.\n",{"path":16358,"title":16359,"module":16343,"summary":16360},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fmatrix-exponentiation","Matrix Exponentiation","A linear recurrence advances by a fixed linear rule, so one step is a\n**matrix–vector** product and $n$ steps are a **matrix power**. Packaging\nFibonacci, and any $k$-term recurrence, into a transition matrix lets us jump\nto the $n$-th term in $O(k^3 \\log n)$ by **exponentiation by squaring** — the\nsame doubling trick from modular exponentiation, now over matrices.\n",{"path":16362,"title":16363,"module":16343,"summary":16364},"\u002Falgorithms\u002Fmathematical-algorithms\u002Ffast-fourier-transform","Fast Fourier Transform","Multiplying two degree-$n$ polynomials by the schoolbook method costs\n$\\Theta(n^2)$. Evaluating them at the **$n$-th roots of unity** turns\nmultiplication into pointwise products, and the **Cooley–Tukey FFT** computes\nall those evaluations in $\\Theta(n\\log n)$ by splitting even and odd\ncoefficients. The inverse FFT interpolates back, giving $\\Theta(n\\log n)$\npolynomial and big-integer multiplication.\n",{"path":16366,"title":16367,"module":16343,"summary":16368},"\u002Falgorithms\u002Fmathematical-algorithms\u002Fgradient-descent","Numerical Optimization and Gradient Descent","Most of this course chases **discrete** optima over finite structures; here the\nsearch space is **continuous** and the objective $f$ is differentiable. The\n**gradient** points uphill, so stepping against it —\n$x_{t+1} = x_t - \\eta\\,\\nabla f(x_t)$ — walks downhill. **Convexity** makes every\nlocal minimum global; for convex $L$-smooth $f$ gradient descent converges at\n$O(1\u002Ft)$, and **geometrically** under strong convexity. **Newton's method** uses\nthe Hessian for local quadratic convergence, and **bisection** is the robust\nbracketing fallback for roots.\n",{"path":16370,"title":16371,"module":16372,"summary":16373},"\u002Falgorithms\u002Fcomputational-geometry\u002Fgeometric-primitives","Geometric Primitives & Orientation","Computational Geometry","Computational geometry is built on a single reliable primitive — the\n**orientation test**, a sign of a cross product that tells whether three points\nturn left, right, or lie collinear. From points-as-vectors and the dot and\ncross products we derive orientation, segment intersection, the shoelace area\nformula, and point-in-polygon tests, keeping all arithmetic **exact and\ninteger** so that no floating-point rounding can corrupt a sign.\n",{"path":16375,"title":16376,"module":16372,"summary":16377},"\u002Falgorithms\u002Fcomputational-geometry\u002Fconvex-hull","Convex Hull","The convex hull is the smallest convex polygon enclosing a point set — the\nrubber band snapped around the nails. We build it with Andrew's monotone chain,\nsorting by $(x,y)$ and sweeping a lower and upper hull while popping any\nnon-left turn via the orientation primitive, in $O(n\\log n)$. A reduction from\nsorting shows that bound is optimal, and the hull yields diameter, smallest\nenclosing rectangle, and more through rotating calipers.\n",{"path":16379,"title":16380,"module":16372,"summary":16381},"\u002Falgorithms\u002Fcomputational-geometry\u002Fsweep-line","Sweep-Line Algorithms","The plane-sweep paradigm turns a static $2$-D geometry problem into a dynamic\n$1$-D ordered-set problem: a vertical line sweeps left to right, stopping at an\n$x$-sorted **event queue** while a balanced-BST **status structure** tracks the\nobjects it currently crosses, ordered by $y$. We derive Bentley–Ottmann segment\nintersection in $O((n+k)\\log n)$, recover closest-pair in $O(n\\log n)$, and\nreduce skyline, rectangle-area, and overlap problems to $\\pm1$ event sweeps.\n",{"path":16383,"title":16384,"module":16372,"summary":16385},"\u002Falgorithms\u002Fcomputational-geometry\u002Fpolygons-and-proximity","Polygons & Proximity","Four classics that live on top of the orientation primitive and the convex\nhull. **Closest pair** falls to divide-and-conquer in $\\Theta(n\\log n)$, where a\npacking argument caps the cross-boundary combine at seven neighbours per point.\n**Point-in-polygon** is the ray-casting parity test or the winding-number count\nthat also handles self-intersecting boundaries, both with their edge caveats. The **shoelace formula**\ngives signed area as a sum of cross products, and **rotating calipers** walk the\nhull to read off diameter and width in $O(n)$.\n",{"path":16387,"title":16388,"module":16389,"summary":16390},"\u002Falgorithms\u002Fintractability\u002Fp-np-reductions","P, NP, and Reductions","Intractability","Most problems we have met so far have fast algorithms. A vast and important\nfamily seemingly does not. This lesson builds the vocabulary for that\ndivide: decision problems, the class $\\mathsf{P}$ of problems we can solve\nquickly, the class $\\mathsf{NP}$ of problems whose solutions we can _check_\nquickly, and polynomial-time reductions, the tool that lets us compare the\ndifficulty of two problems without solving either.\n",{"path":16392,"title":16393,"module":16389,"summary":16394},"\u002Falgorithms\u002Fintractability\u002Fnp-completeness","NP-Completeness","Some problems in $\\mathsf{NP}$ are universally hardest: every other problem\nin $\\mathsf{NP}$ reduces to them. This lesson defines $\\mathsf{NP}$-hard and\n$\\mathsf{NP}$-complete, states the Cook–Levin theorem that anchors the\ntheory on **SAT**, walks the web of reductions that grows from it, and gives\nthe four-step recipe for proving a brand-new problem $\\mathsf{NP}$-complete.\n",{"path":16396,"title":16397,"module":16389,"summary":16398},"\u002Falgorithms\u002Fintractability\u002Fcoping-with-hardness","Coping with NP-Hardness","An $\\mathsf{NP}$-hardness proof rules out an exact polynomial-time algorithm,\nnot the need for answers. This lesson surveys four practical responses to\nhardness: approximation algorithms with a provable ratio (worked through a\n2-approximation for vertex cover), heuristics and local search, exact\nexponential methods like branch and bound, and exploiting special structure\nin the instances you actually face.\n",{"path":16400,"title":16401,"module":16389,"summary":16402},"\u002Falgorithms\u002Fintractability\u002Fapproximation-algorithms","Approximation Algorithms","When a problem is $\\mathsf{NP}$-hard we can still ask for a solution\nprovably close to optimal. This lesson makes the approximation ratio\n$\\rho$ precise, separates absolute from relative guarantees, and proves the\nratios of four classic algorithms: greedy set cover ($H_n \\approx \\ln n$),\nthe MST-doubling $2$-approximation for metric TSP, load balancing, and the\nknapsack FPTAS. It closes with the hierarchy PTAS \u002F FPTAS and the limits of\ninapproximability.\n",{"path":16404,"title":16405,"module":6,"summary":6},"\u002Falgorithms","Algorithms",{"path":16407,"title":16408,"module":16409,"summary":16410},"\u002Fcalculus\u002Flimits-and-continuity\u002Ffunctions-and-models","Functions and Mathematical Models","Limits and Continuity","A function assigns exactly one output to each input and can be presented four ways: verbally, numerically, graphically, or by a formula. The elementary families — linear, polynomial, power, rational, trigonometric, exponential — model most elementary phenomena, and transformation, combination, and composition build every other function from them.\n",{"path":16412,"title":16413,"module":16409,"summary":16414},"\u002Fcalculus\u002Flimits-and-continuity\u002Fthe-limit-of-a-function","The Limit of a Function","The tangent and velocity problems both ask for a value a ratio approaches but never reaches — the limit. Its intuitive two-sided form splits into one-sided limits that must agree; a limit fails to exist when they disagree or when the function grows without bound, the latter producing a vertical asymptote.\n",{"path":16416,"title":16417,"module":16409,"summary":16418},"\u002Fcalculus\u002Flimits-and-continuity\u002Flimit-laws-and-the-precise-definition","Limit Laws and the ε–δ Definition","The Limit Laws reduce a limit to arithmetic on simpler limits, and direct substitution settles polynomials and rational functions outright. The 0\u002F0 forms that resist substitution yield to algebra or the Squeeze Theorem, and the ε–δ definition makes \"arbitrarily close\" precise as a pair of quantified inequalities.\n",{"path":16420,"title":16421,"module":16409,"summary":16422},"\u002Fcalculus\u002Flimits-and-continuity\u002Fcontinuity","Continuity","A function is continuous at a point when its limit there equals its value, so the graph has no break. Continuity fails in three geometric ways; it is closed under arithmetic and composition, so the elementary families and their combinations are continuous; and on a closed interval it forces the Intermediate Value Theorem, which locates roots.\n",{"path":16424,"title":16425,"module":16426,"summary":16427},"\u002Fcalculus\u002Fderivatives\u002Fthe-derivative-and-rates-of-change","The Derivative and Rates of Change","Derivatives","A single limit with three readings: the slope of the tangent line, the instantaneous velocity of a moving object, and the rate of change of one quantity with respect to another. Built from the difference quotient, extended from a value at one point to a function of x, and undefined exactly where a corner, jump, or vertical tangent appears.\n",{"path":16429,"title":16430,"module":16426,"summary":16431},"\u002Fcalculus\u002Fderivatives\u002Fdifferentiation-rules-and-the-chain-rule","Differentiation Rules and the Chain Rule","Computing every derivative from the limit definition is tedious. A short list of rules — power, constant multiple, sum, product, quotient — differentiates any polynomial or rational function by inspection. The trigonometric derivatives follow from one limit, and the chain rule extends everything to composite functions by multiplying rates along the composition.\n",{"path":16433,"title":16434,"module":16426,"summary":16435},"\u002Fcalculus\u002Fderivatives\u002Fimplicit-differentiation-and-related-rates","Implicit Differentiation and Related Rates","Not every curve is the graph of y = f(x). Implicit differentiation finds a slope from an equation in x and y directly, treating y as an unknown function and differentiating both sides. The same chain-rule idea drives related rates, where one measured rate of change forces another through a geometric constraint, and interprets the derivative as a rate across the sciences.\n",{"path":16437,"title":16438,"module":16426,"summary":16439},"\u002Fcalculus\u002Fderivatives\u002Flinear-approximations-and-differentials","Linear Approximations and Differentials","A differentiable curve looks like its tangent line under enough magnification, so the tangent is a usable stand-in for the function near the point of contact. The linear approximation and its linearization, written in the language of differentials dy and dx, estimate both function values and the measurement error propagated into a computed quantity.\n",{"path":16441,"title":16442,"module":16443,"summary":16444},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fextrema-and-the-mean-value-theorem","Extrema and the Mean Value Theorem","Applications of Derivatives","Absolute and local extrema, the Extreme Value Theorem that guarantees them, and Fermat's Theorem pinning candidates to critical numbers. The Closed Interval Method turns the search for extrema into a finite checklist. Rolle's Theorem and the Mean Value Theorem then connect a function's values to its derivative, giving the tool that most of differential calculus rests on.\n",{"path":16446,"title":16447,"module":16443,"summary":16448},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fhow-derivatives-shape-a-graph","How Derivatives Shape a Graph","The sign of the first derivative fixes where a function rises and falls, and a sign change identifies each local extremum through the First Derivative Test. The second derivative sets concavity and inflection points and gives a faster Second Derivative Test. Limits at infinity describe end behavior and the horizontal asymptotes a curve settles toward.\n",{"path":16450,"title":16451,"module":16443,"summary":16452},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fcurve-sketching-and-optimization","Curve Sketching and Optimization","A checklist that synthesizes domain, symmetry, asymptotes, monotonicity, extrema, and concavity into a hand sketch of any function, plus the slant asymptote for rational functions whose degree exceeds the denominator's. The same extremum machinery, applied to a word problem, becomes the optimization template: model one quantity, reduce it to a function of a single variable, and find its absolute extremum.\n",{"path":16454,"title":16455,"module":16443,"summary":16456},"\u002Fcalculus\u002Fapplications-of-derivatives\u002Fnewtons-method-and-antiderivatives","Newton's Method and Antiderivatives","Newton's method solves $f(x) = 0$ by repeatedly replacing the curve with its tangent line and jumping to the tangent's root, converging fast when it works and diverging when the derivative is small. Antiderivatives reverse differentiation: every antiderivative of a function differs from another by a constant, so the general antiderivative is a family of parallel curves, pinned to one by an initial condition.\n",{"path":16458,"title":16459,"module":16460,"summary":16461},"\u002Fcalculus\u002Fintegrals\u002Farea-and-the-definite-integral","Area and the Definite Integral","Integrals","The area under a curve is defined as a limit of sums of rectangle areas. The same limit — a Riemann sum taken as the mesh shrinks to zero — defines the definite integral, a single number measuring signed area, total distance, and every accumulated quantity built the same way. Its properties, comparison bounds, and reading as net area follow directly from the limit.\n",{"path":16463,"title":16464,"module":16460,"summary":16465},"\u002Fcalculus\u002Fintegrals\u002Fthe-fundamental-theorem-of-calculus","The Fundamental Theorem of Calculus","Differentiation and integration are inverse operations. Part 1 says the derivative of an area-accumulation function is the integrand; Part 2 says a definite integral equals the change in any antiderivative across the interval. Together they replace limits of Riemann sums with antiderivative lookups, define the indefinite integral, and give the Net Change Theorem for rates.\n",{"path":16467,"title":16468,"module":16460,"summary":16469},"\u002Fcalculus\u002Fintegrals\u002Fthe-substitution-rule","The Substitution Rule","Substitution runs the Chain Rule backward: spotting an inner function whose derivative also appears in the integrand lets the variable change to $u$ and collapse a composite integral to a simple one. The rule applies to indefinite and definite integrals, with two ways to handle the limits, and it yields the symmetry shortcuts that double even integrands and vanish odd ones.\n",{"path":16471,"title":16472,"module":16473,"summary":16474},"\u002Fcalculus\u002Fapplications-of-integration\u002Fareas-and-volumes","Areas Between Curves and Volumes","Applications of Integration","A definite integral computes any quantity that a limit of Riemann sums approximates. Applied to geometry it gives the area between two curves and the volume of a solid: by cross-sections, by disks and washers when the region is revolved, and by cylindrical shells when inverting the boundary is awkward.\n",{"path":16476,"title":16477,"module":16473,"summary":16478},"\u002Fcalculus\u002Fapplications-of-integration\u002Fwork-average-value-and-arc-length","Work, Average Value, Arc Length, and Surface Area","The work done by a force that varies with position, the average value of a function and the Mean Value Theorem it satisfies, the length of a curve, and the area of a surface swept out by revolving that curve. Each is a limit of Riemann sums, hence a definite integral.\n",{"path":16480,"title":16481,"module":16473,"summary":16482},"\u002Fcalculus\u002Fapplications-of-integration\u002Fphysics-economics-and-probability","Applications to Physics, Economics, and Probability","Definite integrals in physics, economics, and statistics: the force a fluid exerts on a submerged plate, the balance point of a plane region, the money consumers save at a market price, and the probability that a continuous random variable lands in an interval, together with its mean.\n",{"path":16484,"title":16485,"module":16486,"summary":16487},"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Finverse-functions-logarithms-and-exponentials","Inverse Functions, Logarithms, and Exponentials","Exponential, Logarithmic, and Inverse Functions","A one-to-one function has an inverse that reverses it, with a graph mirrored across y = x and a derivative given by the reciprocal-slope rule. The exponential e^x is its own derivative and the natural logarithm has derivative 1\u002Fx; logarithmic differentiation turns products, quotients, and variable powers into sums.\n",{"path":16489,"title":16490,"module":16486,"summary":16491},"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Fgrowth-decay-inverse-trig-and-hyperbolic-functions","Growth, Decay, Inverse Trigonometric, and Hyperbolic Functions","Any quantity whose rate of change is proportional to its size grows or decays exponentially, the single equation y' = ky behind populations, radioactive decay, cooling, and continuously compounded interest. The inverse trigonometric functions have algebraic derivatives, and the hyperbolic functions, built from e^x and e^{-x}, describe the hanging cable.\n",{"path":16493,"title":16494,"module":16486,"summary":16495},"\u002Fcalculus\u002Fexponential-logarithmic-and-inverse-functions\u002Flhospitals-rule","Indeterminate Forms and l'Hospital's Rule","When a limit produces 0\u002F0 or infinity over infinity, the value is undetermined by the forms alone. l'Hospital's Rule resolves both by replacing the ratio of functions with the ratio of their derivatives. Products, differences, and powers reduce to a quotient the rule can handle, and repeated use ranks the growth of logarithms, powers, and exponentials.\n",{"path":16497,"title":16498,"module":16499,"summary":16500},"\u002Fcalculus\u002Ftechniques-of-integration\u002Fintegration-by-parts","Integration by Parts","Techniques of Integration","The product rule for derivatives reverses into integration by parts, trading the integral of $u\\,\\d v$ for the integral of $v\\,\\d u$ whenever the second is easier. The LIATE ordering fixes which factor to differentiate. Standard cases: a polynomial against a transcendental factor, repeated parts, cyclic integrals that solve for themselves, and reduction formulas that peel an exponent down by recursion.\n",{"path":16502,"title":16503,"module":16499,"summary":16504},"\u002Fcalculus\u002Ftechniques-of-integration\u002Ftrigonometric-integrals-and-substitution","Trigonometric Integrals and Substitution","Two related techniques. Trigonometric integrals evaluate powers and products of sine, cosine, tangent, and secant by splitting off one factor and converting the rest with a Pythagorean identity, or by dropping even powers with half-angle formulas. Trigonometric substitution runs the idea in reverse: replace x by a sine, tangent, or secant to clear a radical, integrate, then read the answer back off a reference triangle.\n",{"path":16506,"title":16507,"module":16499,"summary":16508},"\u002Fcalculus\u002Ftechniques-of-integration\u002Fpartial-fractions-and-integration-strategy","Partial Fractions and Integration Strategy","Any rational function integrates in closed form: factor the denominator, split the fraction into simple pieces by partial fractions, and integrate each piece as a logarithm or an arctangent. Four denominator cases exhaust the possibilities. A four-step strategy then sorts an arbitrary integrand by its shape to the technique that fits it, and a short catalog records elementary functions whose antiderivatives are not elementary.\n",{"path":16510,"title":16511,"module":16499,"summary":16512},"\u002Fcalculus\u002Ftechniques-of-integration\u002Fapproximate-and-improper-integrals","Approximate and Improper Integrals","Two definite integrals the Fundamental Theorem cannot reach. With no antiderivative available, the Midpoint, Trapezoidal, and Simpson rules approximate the integral from sample values, each carrying a provable error bound. With an infinite interval or an integrand that blows up, the improper integral is defined as a limit that either converges or diverges; the Comparison Test settles which without evaluating it.\n",{"path":16514,"title":16515,"module":16516,"summary":16517},"\u002Fcalculus\u002Fparametric-and-polar\u002Fparametric-curves-and-their-calculus","Parametric Curves and Their Calculus","Parametric Equations and Polar Coordinates","A parametric curve gives x and y separately as functions of a third variable, recording not only a path but the direction and timing with which it is traced. Eliminating the parameter recovers a Cartesian equation; the slope, area, arc-length, and surface-area formulas run directly on the parameter, with the cycloid and astroid as worked examples.\n",{"path":16519,"title":16520,"module":16516,"summary":16521},"\u002Fcalculus\u002Fparametric-and-polar\u002Fpolar-coordinates","Polar Coordinates","Polar coordinates locate a point by a distance from the pole and an angle from the polar axis, giving circles, spirals, and flower-shaped curves short equations. Conversion between the two systems is right-triangle trigonometry, and treating a polar curve as a parametric curve in the angle yields the tangent, area, and arc-length formulas.\n",{"path":16523,"title":16524,"module":16516,"summary":16525},"\u002Fcalculus\u002Fparametric-and-polar\u002Fconic-sections","Conic Sections","Parabolas, ellipses, and hyperbolas are the plane curves cut from a double cone. Each has a focus-based geometric definition and a standard Cartesian equation. A single number, the eccentricity, ties the three together, and placing a focus at the pole gives all of them one polar equation that describes planetary orbits.\n",{"path":16527,"title":16528,"module":16529,"summary":16530},"\u002Fcalculus\u002Fsequences-and-series\u002Fsequences","Sequences","Infinite Sequences and Series","A sequence is a function on the positive integers, and its limit is defined almost exactly like a limit at infinity. The Limit Laws and Squeeze Theorem carry over from functions, monotonic and bounded sequences give a convergence criterion, and the Monotonic Sequence Theorem guarantees a limit exists without naming it.\n",{"path":16532,"title":16533,"module":16529,"summary":16534},"\u002Fcalculus\u002Fsequences-and-series\u002Fseries-and-the-integral-test","Series and the Integral Test","Adding infinitely many terms is made precise as the limit of partial sums. The two series with closed-form partial sums are geometric and telescoping; the harmonic series diverges even as its terms shrink to zero. The Integral Test compares a positive series to an improper integral, settling the p-series and supplying a remainder bound for estimating sums.\n",{"path":16536,"title":16537,"module":16529,"summary":16538},"\u002Fcalculus\u002Fsequences-and-series\u002Fthe-convergence-tests","The Convergence Tests","The comparison, alternating-series, ratio, and root tests decide convergence without a closed-form partial sum. Absolute convergence is stronger than conditional convergence and is preserved under rearrangement; an alternating series errs by less than its first omitted term. A test is chosen from the shape of the general term.\n",{"path":16540,"title":16541,"module":16529,"summary":16542},"\u002Fcalculus\u002Fsequences-and-series\u002Fpower-series","Power Series","A power series is a polynomial of infinite degree whose convergence set is an interval centered at $a$, with a radius the Ratio Test finds and endpoints that must be tested by hand. Inside that interval the series represents a function that can be differentiated and integrated term by term, generating new representations from the geometric series.\n",{"path":16544,"title":16545,"module":16529,"summary":16546},"\u002Fcalculus\u002Fsequences-and-series\u002Ftaylor-and-maclaurin-series","Taylor and Maclaurin Series","If a function equals a power series, its coefficients are forced: the nth is the nth derivative at the center over n factorial. We derive that formula, use Taylor's Inequality to prove the standard series for the exponential, sine, and cosine, record the binomial series and a reference table, and bound the error when a Taylor polynomial replaces a function.\n",{"path":16548,"title":16549,"module":16550,"summary":16551},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvectors-and-the-dot-product","Three-Dimensional Coordinates, Vectors, and the Dot Product","Vectors and the Geometry of Space","Space needs three coordinates, so we set up the rectangular system, the distance formula, and the equation of a sphere. Vectors then package magnitude and direction into a single algebraic object with its own arithmetic. The dot product turns two vectors into a number that measures the angle between them, gives a clean test for orthogonality, and produces the projection of one vector onto another.\n",{"path":16553,"title":16554,"module":16550,"summary":16555},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fthe-cross-product-lines-and-planes","The Cross Product, Lines, and Planes","The cross product multiplies two vectors into a third perpendicular to both, with length equal to the area of the parallelogram they span. That one construction supplies the direction of a line, the normal of a plane, and, through the scalar triple product, the volume of a parallelepiped. Lines carry a point and a direction vector; planes carry a point and a normal, which fixes the angle between planes and the distance from a point to a plane.\n",{"path":16557,"title":16558,"module":16550,"summary":16559},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fcylinders-and-quadric-surfaces","Cylinders and Quadric Surfaces","A surface whose equation omits one variable is a cylinder: the graph of a plane curve swept along the missing axis. A second-degree equation in three variables is a quadric, and translation and rotation reduce every one to a short standard list. Traces — the curves cut by planes parallel to the coordinate planes — sort the six quadrics into ellipsoid, the two paraboloids, the cone, and the two hyperboloids.\n",{"path":16561,"title":16562,"module":16550,"summary":16563},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Fvector-functions-and-space-curves","Vector Functions and Space Curves","A vector function assigns a vector to each value of a parameter, and as the parameter runs its tip traces a space curve. Taking limits, derivatives, and integrals component by component carries all of single-variable calculus into three dimensions. The derivative of a vector function is the tangent vector to its curve, and normalizing it gives the unit tangent that points the way along the path.\n",{"path":16565,"title":16566,"module":16550,"summary":16567},"\u002Fcalculus\u002Fvectors-and-space-curves\u002Farc-length-curvature-and-motion","Arc Length, Curvature, and Motion in Space","Integrating the speed of a vector function gives the length of its curve and a natural parameter, arc length, that depends only on the curve's shape. Curvature measures how fast the unit tangent turns, and together with the normal and binormal it builds the moving TNB frame. Reading the same vector function as a trajectory, its first two derivatives are velocity and acceleration, and acceleration splits cleanly into tangential and normal parts.\n",{"path":16569,"title":16570,"module":16571,"summary":16572},"\u002Fcalculus\u002Fpartial-derivatives\u002Ffunctions-of-several-variables","Functions of Several Variables, Limits, and Continuity","Partial Derivatives","A function of several variables assigns one number to each point of a region in the plane or in space. Domain, graph, level curve, and level surface describe it; limits and continuity extend to two variables, where a limit must agree along every path of approach, not just from the left and the right.\n",{"path":16574,"title":16571,"module":16571,"summary":16575},"\u002Fcalculus\u002Fpartial-derivatives\u002Fpartial-derivatives","A partial derivative holds every variable but one fixed and differentiates in the ordinary sense. Geometrically it is the slope of a trace curve cut from the surface by a coordinate plane. The freeze-and-differentiate rule computes the two first partials; the four second partials follow, and the two mixed ones agree under Clairaut's Theorem when they are continuous.\n",{"path":16577,"title":16578,"module":16571,"summary":16579},"\u002Fcalculus\u002Fpartial-derivatives\u002Ftangent-planes-and-the-chain-rule","Tangent Planes, Linear Approximation, and the Chain Rule","Near a point, a smooth surface looks like its tangent plane, and the plane's equation is built from the two partial derivatives. That linearization defines the total differential and the meaning of differentiability in two variables. The chain rule then propagates derivatives through composed functions, tracked by a tree diagram, and yields clean formulas for implicit differentiation.\n",{"path":16581,"title":16582,"module":16571,"summary":16583},"\u002Fcalculus\u002Fpartial-derivatives\u002Fdirectional-derivatives-and-the-gradient","Directional Derivatives and the Gradient","The partial derivatives measure slope along the two axes; the directional derivative measures slope along any chosen direction, and equals the gradient dotted with a unit vector. The gradient points in the direction of steepest increase, its length is the greatest rate, and it stands perpendicular to level curves and surfaces, which fixes the tangent plane to a level surface.\n",{"path":16585,"title":16586,"module":16571,"summary":16587},"\u002Fcalculus\u002Fpartial-derivatives\u002Foptimization-and-lagrange-multipliers","Optimization and Lagrange Multipliers","Extrema of a two-variable function sit at critical points where the gradient vanishes; the Second Derivatives Test sorts them into peaks, valleys, and saddles by the sign of a discriminant. Absolute extrema on a closed region also need the boundary. When the domain is itself a constraint curve, Lagrange multipliers set the two gradients parallel and solve the constrained problem.\n",{"path":16589,"title":16590,"module":16591,"summary":16592},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fdouble-integrals","Double Integrals","Multiple Integrals and Vector Calculus","The double integral extends the definite integral to functions of two variables: a limit of Riemann sums that measures signed volume under a surface. Fubini's Theorem turns it into two ordinary integrations done one after the other, general regions of type I and type II fix the inner limits, polar coordinates absorb circular symmetry through the factor r, and the same machine computes mass, center of mass, and moments of a lamina.\n",{"path":16594,"title":16595,"module":16591,"summary":16596},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Ftriple-integrals-and-coordinate-systems","Triple Integrals and Coordinate Systems","The triple integral integrates a function of three variables over a solid, as a limit of Riemann sums evaluated by three nested single integrations. Cylindrical coordinates add the factor r to handle axial symmetry, spherical coordinates add rho-squared sine-phi for radial symmetry, and the general change of variables shows both volume elements are Jacobian determinants of the coordinate map. Surface area for a graph completes the measurement toolkit.\n",{"path":16598,"title":16599,"module":16591,"summary":16600},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fvector-fields-and-line-integrals","Vector Fields and Line Integrals","A vector field assigns a vector to every point of space; the line integral of a field along a curve accumulates its tangential component, measuring work. Conservative fields are gradients of a potential, and for them the Fundamental Theorem for Line Integrals makes the integral depend only on the endpoints. Path independence, closed-loop integrals of zero, and the component test for a potential are three faces of the same property.\n",{"path":16602,"title":16603,"module":16591,"summary":16604},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fgreens-theorem-curl-and-divergence","Green's Theorem, Curl, and Divergence","Green's Theorem equates the line integral of a field around a positively oriented closed curve with a double integral over the enclosed region, turning a boundary computation into an area computation and vice versa. Curl measures local circulation and divergence measures local outflow; the two vector forms of Green's Theorem express the boundary integral as the integrated curl or divergence, the planar case of Stokes' and the Divergence Theorem.\n",{"path":16606,"title":16607,"module":16591,"summary":16608},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fsurface-integrals","Parametric Surfaces and Surface Integrals","A parametric surface is the image of a two-variable vector function; its area element is the magnitude of the cross product of the two tangent vectors. The surface integral of a scalar function sums it over that area, and the flux integral of a vector field sums the field's normal component, measuring flow through the surface. Orientation by a choice of unit normal makes flux well-defined, the integral Stokes' and the Divergence Theorem operate on.\n",{"path":16610,"title":16611,"module":16591,"summary":16612},"\u002Fcalculus\u002Fmultiple-integrals-and-vector-calculus\u002Fstokes-and-the-divergence-theorem","Stokes' Theorem and the Divergence Theorem","Stokes' Theorem lifts Green's Theorem into space: the line integral of a field around the boundary of a surface equals the flux of its curl through the surface. The Divergence Theorem relates the outward flux across a closed surface to the triple integral of divergence over the solid it encloses. Together with the Fundamental Theorem of Calculus and its line-integral and Green counterparts, they are one theorem: the integral of a derivative over a region equals the integral of the field over its oriented boundary.\n",{"path":16614,"title":16615,"module":6,"summary":6},"\u002Fcalculus","Calculus",{"path":16617,"title":16618,"module":16062,"summary":16619},"\u002Fmechanics\u002Ffoundations\u002Fmeasurement-and-dimensions","Measurement and Dimensions","Every physical quantity is a number attached to a unit, and that pairing is what lets you check an equation before computing anything, since terms that add together must carry the same dimensions. We build the SI base units and the notion of dimension, then use dimensional analysis to test a proposed relation and form scaling groups — a method that fixes a formula's shape but never its numerical constants. The lesson also sets how precisely a result may be stated, through significant figures, propagated uncertainty, and order-of-magnitude checks that catch errors a raw calculator answer hides.\n",{"path":16621,"title":16622,"module":16062,"summary":16623},"\u002Fmechanics\u002Ffoundations\u002Fvector-algebra","Vector Algebra","Force, velocity, and displacement all carry a direction, so mechanics needs an arithmetic that respects it; adding magnitudes alone gives the wrong answer the moment two arrows point different ways. We set up vectors and their components in a chosen basis, then build the two products that carry most of the physics — the dot product, which extracts the part of one vector along another and yields work and power, and the cross product, which measures oriented area and yields torque and angular momentum. Rotating the axes changes the components while leaving the vector itself untouched, and the same component method resolves a force along whatever directions a constraint picks out.\n",{"path":16625,"title":16626,"module":16627,"summary":16628},"\u002Fmechanics\u002Fkinematics\u002Fone-dimensional-motion","One-Dimensional Motion","Kinematics","Motion along a line already forces the two questions the whole of kinematics repeats: how fast is the object moving now, and where will it be next? Velocity and acceleration answer the first as derivatives of position; integrating them back — the signed area under a graph — answers the second. We derive the constant-acceleration equations, mark exactly where the \"constant\" assumption is load-bearing, and see why sign, not magnitude, is what carries direction.\n",{"path":16630,"title":16631,"module":16627,"summary":16632},"\u002Fmechanics\u002Fkinematics\u002Fmotion-graphs","Motion Graphs","Draw a motion as a graph and its two most useful facts turn geometric: the slope of the position curve is the velocity, and the area under the velocity curve is the displacement. We read motion in both directions — differentiating a graph for the next rate, integrating it back to recover position — and handle the curved, piecewise, and noisy graphs that real measurements produce. Along the way we see why a velocity estimated from two positions belongs to the midpoint of their interval, not its end.\n",{"path":16634,"title":16635,"module":16627,"summary":16636},"\u002Fmechanics\u002Fkinematics\u002Fprojectile-motion","Projectile Motion","Throw an object and it seems to trace one curved path, but the motion is really two independent one-dimensional motions running at once: constant velocity across the ground and free fall in the vertical. Splitting it that way turns every projectile question — how long it stays up, how far it lands, how high it climbs, whether it clears an obstacle — into a pair of equations you already know. We derive the parabolic trajectory, work both the forward and the inverse problems, and show why the familiar $45^\\circ$ range-maximizing angle holds only when launch and landing heights match.\n",{"path":16638,"title":16639,"module":16627,"summary":16640},"\u002Fmechanics\u002Fkinematics\u002Frelative-motion","Relative Motion","A velocity is only ever measured relative to some observer, so a boat's speed through the water, over the ground, and as seen from another boat are three different vectors. Choosing the right frame — and subtracting one motion from another — collapses river crossings, crosswind headings, pursuit, and closest-approach problems into a single vector equation. We build the relative-velocity and relative-position relations for uniformly moving frames, show why acceleration is the one quantity all such observers agree on, and note where rotating frames break the simple subtraction.\n",{"path":16642,"title":16643,"module":16627,"summary":16644},"\u002Fmechanics\u002Fkinematics\u002Fcircular-motion","Circular Motion","An object going around a circle at a steady speed is still accelerating, because its velocity is forever changing direction — the fact that governs everything from a car on a curve to a satellite in orbit. We tie the angular description (angle, angular velocity, angular acceleration) to the linear one through $v=r\\omega$, split the acceleration into an inward part that turns the velocity and a tangential part that changes its speed, and extend the inward $v^2\u002Fr$ result to any curved path through its local radius of curvature. Constant angular acceleration then mirrors straight-line motion equation for equation.\n",{"path":16646,"title":16647,"module":16648,"summary":16649},"\u002Fmechanics\u002Fdynamics\u002Fnewtons-laws","Newton's Laws","Dynamics","What makes a body change its motion, and in which frames does the answer take its simplest form? Newton's three laws settle both: inertial frames are the ones where a force-free body coasts, force is whatever changes momentum, and every interaction pushes back on its source. We write the second law as $\\sum\\vec F=\\d\\vec p\u002F\\d t$, reduce it to $m\\vec a$ at constant mass, and separate what a scale actually reads — the support force — from the weight $m\\vec g$ it is so often mistaken for.\n",{"path":16651,"title":16652,"module":16648,"summary":16653},"\u002Fmechanics\u002Fdynamics\u002Ffree-body-diagrams","Free-Body Diagrams","Once several forces act on a body at once, the reliable way to predict its motion is to isolate that one body and draw every external push and pull on it — nothing more, nothing less. The free-body diagram is that discipline. We fix a system boundary, resolve $\\sum\\vec F=m\\vec a$ into components along axes chosen to fit the geometry, and solve for the unknowns a problem hands us — normal forces, tensions, friction, and the acceleration a constraint permits — seeing why internal forces drop out only when the boundary encloses both bodies that share them.\n",{"path":16655,"title":16656,"module":16648,"summary":16657},"\u002Fmechanics\u002Fdynamics\u002Ffriction-and-curved-motion","Friction and Curved Motion","Real surfaces grip before they slip, fluids push back harder the faster you move through them, and anything rounding a bend must be pulled toward the inside of the curve by something. This lesson supplies the force laws for those three cases. We bound static friction by $|f_s|\\leq\\mu_sN$ and switch to kinetic friction $\\mu_kN$ once sliding starts, model drag as a speed-dependent resistance that levels off at a terminal speed, and show that circular motion demands an inward net force $mv^2\u002Fr$ furnished by real interactions — friction, a banked normal force, tension — never by an invented outward one.\n",{"path":16659,"title":16660,"module":16648,"summary":16661},"\u002Fmechanics\u002Fdynamics\u002Fnumerical-dynamics","Numerical Dynamics","Most force laws — quadratic drag, coupled oscillators, anything nonlinear — admit no closed-form trajectory, so we advance the motion one small time step at a time and let arithmetic do what algebra cannot. This lesson turns $\\d\\vec y\u002F\\d t=f(t,\\vec y)$ into a marching rule. We derive the Euler, Euler--Cromer, midpoint, and Verlet updates, weigh their accuracy and stability, watch a drifting energy expose a bad scheme, and use step-halving and conserved quantities to separate the error of the method from the error of the model.\n",{"path":16663,"title":16664,"module":16648,"summary":16665},"\u002Fmechanics\u002Fdynamics\u002Fcenter-of-mass-systems","Center-of-Mass Systems","A firework bursts into a dozen fragments, yet one point keeps gliding along the original parabola as though nothing had happened. That point is the centre of mass, and following it collapses a many-body tangle into a single equation of motion. We define $\\vec R=\\frac1M\\sum_i m_i\\vec r_i$ and its continuous form, show that internal forces cancel so that only external ones move it, $M\\vec A_{\\rm cm}=\\sum\\vec F_{\\rm ext}$, and put the result to work on recoil, collisions viewed from the centre-of-mass frame, and rocket propulsion, where mass leaving the boundary carries momentum with it.\n",{"path":16667,"title":16668,"module":16669,"summary":16670},"\u002Fmechanics\u002Fenergy\u002Fwork-and-kinetic-energy","Work and Kinetic Energy","Energy","A constant push along a straight path is trivial to score, but real forces vary and bend along curved trajectories, and only the component along the motion transfers any energy. Work captures exactly that transfer as the line integral $W=\\int\\vec F\\cdot\\d\\vec r$, and the work-kinetic-energy theorem turns it into a statement about speed: the net work on a particle equals the change in its $\\tfrac12 mv^2$. We build work up from the dot product to the signed area under a force curve, derive the theorem from Newton's second law, and read power as its instantaneous rate $P=\\vec F\\cdot\\vec v$.\n",{"path":16672,"title":16673,"module":16669,"summary":16674},"\u002Fmechanics\u002Fenergy\u002Fpotential-energy","Potential Energy","When a force does the same work no matter which path a particle takes, that work can be stored as a function of position alone, and solving for the motion becomes bookkeeping instead of integration. We single out the forces that qualify — the conservative ones, for which $\\oint\\vec F\\cdot\\d\\vec r=0$ — define their potential energy through $\\vec F=-\\nabla U$, and use conservation of mechanical energy to read speeds, turning points, and equilibria straight off a potential curve. Friction breaks the shortcut, so we also track where mechanical energy leaks away as heat.\n",{"path":16676,"title":16677,"module":16669,"summary":16678},"\u002Fmechanics\u002Fenergy\u002Fmultiparticle-work","Multiparticle Work","A single particle has one velocity and one kinetic energy; a system of many can spin, deform, explode, and warm up while its centre of mass glides along as if nothing happened. Splitting the motion into a centre-of-mass part and an internal part separates the energy that momentum already fixes from the energy left free for relative motion, $K=\\tfrac12MV_{\\rm cm}^2+K'$. We derive the centre-of-mass work theorem, see why an explosion or a released spring can raise total kinetic energy with no external work at all, and use the reduced-mass and centre-of-mass frames to make collisions and internal transfers clean.\n",{"path":16680,"title":16681,"module":16669,"summary":16682},"\u002Fmechanics\u002Fenergy\u002Fmass-energy-and-binding","Mass-Energy and Binding","Relativity puts rest itself on the energy ledger: a mass $m$ carries energy $mc^2$ even when it sits still, so weighing a system's separated pieces and weighing the assembled whole give different answers, and the gap is binding energy. We convert freely between mass units and MeV, compute the energy that holds a nucleus together, and read the binding-energy-per-nucleon curve that explains why fusing light nuclei and splitting heavy ones both release energy. Reaction $Q$ values, thresholds, and recoil then follow from the same mass-difference accounting, once the frame and mass convention are fixed.\n",{"path":16684,"title":16685,"module":16669,"summary":16686},"\u002Fmechanics\u002Fenergy\u002Fphotons-and-quantization","Photons and Quantization","Light delivers its energy in indivisible lumps: a photon of frequency $f$ carries exactly $hf$, and this one fact explains why a dim blue lamp ejects electrons that an intense red one cannot. We fix a photon's energy and momentum from its wavelength, follow the quanta through emission, absorption, and the photoelectric threshold $K_{\\rm max}=hf-\\phi$, and watch energy and momentum conservation together produce the Compton wavelength shift when a photon scatters from an electron. The recurring discipline is unit and frame care, where a stray factor of $10^9$ or a forgotten rest energy quietly ruins an answer.\n",{"path":16688,"title":16689,"module":16690,"summary":16691},"\u002Fmechanics\u002Fmomentum\u002Fmomentum-and-collisions","Momentum and Collisions","Momentum","When two objects collide, the forces between them are too brief and too tangled to integrate directly, yet the result is fixed by one conserved quantity. Linear momentum $\\vec p=m\\vec v$ turns Newton's second law into the impulse-momentum theorem $\\vec J=\\Delta\\vec p$, and for an isolated system into a conservation law that holds through any internal collision, however dissipative. We use it to separate elastic from inelastic collisions, follow the centre of mass, and read impulse as the signed area under a force-time curve — always tracking which external impulses the chosen system and interval let us drop.\n",{"path":16693,"title":16694,"module":16690,"summary":16695},"\u002Fmechanics\u002Fmomentum\u002Fcenter-of-mass-collisions","Center-of-Mass Collisions","A two-body collision that looks asymmetric in the laboratory becomes almost trivial in the frame that rides along with the centre of mass, where the total momentum is zero and the two momenta stay equal and opposite. We build that frame, reduce the pair to a single relative coordinate carrying the reduced mass $\\mu$, and show that an elastic collision there only rotates one momentum vector while its length holds fixed. Transforming back to the laboratory then handles elastic and inelastic collisions, scattering angles, and reaction thresholds with the same construction — and shows why relative speed, not laboratory kinetic energy, measures what a collision can convert.\n",{"path":16697,"title":16698,"module":16690,"summary":16699},"\u002Fmechanics\u002Fmomentum\u002Frocket-propulsion","Rocket Propulsion","A rocket speeds up by throwing mass backward, so its own mass drops as it flies and $\\vec F=m\\vec a$ no longer applies to a fixed body. Tracking the momentum the exhaust carries across the vehicle boundary gives thrust $T=Ru_e$ and, for a force-free burn, the rocket equation $\\Delta v=u_e\\ln(m_i\u002Fm_f)$ — a logarithm that makes large velocity changes expensive in propellant and forces staging. We then add the forces a real ascent cannot ignore, gravity, drag, and steering, and show how thrust and mass-flow records are cross-checked to infer the exhaust speed.\n",{"path":16701,"title":16702,"module":16703,"summary":16704},"\u002Fmechanics\u002Frotation\u002Frotational-inertia","Rotational Inertia","Rotation","Push a wheel and a merry-go-round with the same force and they speed up at wildly different rates: the same mass resists rotation differently depending on where it sits relative to the axis. That single fact is the moment of inertia, $I=\\int r_\\perp^2\\,\\d m$, and this lesson builds it from the ground up. We tie angular motion to linear through $s=r\\theta$, $v=r\\omega$, and $a_t=r\\alpha$, derive $I$ for rods, disks, and spheres, and use the parallel- and perpendicular-axis theorems to move between axes — always naming the axis, because the same body has as many moments of inertia as it has lines to spin about.\n",{"path":16706,"title":16707,"module":16703,"summary":16708},"\u002Fmechanics\u002Frotation\u002Frotational-dynamics","Rotational Dynamics","A force applied to a wheel does nothing unless it acts off the axis: what turns a rigid body is torque, force times lever arm. This lesson makes that precise and turns it into the rotational Newton's second law, $\\sum\\tau=I\\alpha$ about a fixed axis, the exact analogue of $\\sum F=ma$. From there we get rotational work $W=\\int\\tau\\,\\d\\theta$ and power $P=\\tau\\omega$, size a motor to a load, and solve pulleys and Atwood machines where the pulley's own inertia can no longer be ignored — always insisting that every torque be measured about the same axis.\n",{"path":16710,"title":16711,"module":16703,"summary":16712},"\u002Fmechanics\u002Frotation\u002Frolling-motion","Rolling Motion","A rolling wheel is doing two things at once — translating and spinning — but the no-slip condition $v_{cm}=R\\omega$ locks them together, and that single constraint is what makes rolling tractable. We use it to split the kinetic energy into $\\tfrac12Mv_{cm}^2+\\tfrac12I\\omega^2$, find how fast a cylinder reaches the bottom of an incline, and show why the contact point is instantaneously at rest. The static friction that enforces rolling does no work; we track its direction from the tendency to slip, and mark exactly where the model breaks once the required friction exceeds $\\mu_sN$.\n",{"path":16714,"title":16715,"module":16703,"summary":16716},"\u002Fmechanics\u002Frotation\u002Fangular-momentum","Angular Momentum","A skater pulls in her arms and spins faster, with no torque acting: that is angular momentum conservation, and it lets us answer questions that would be hopeless force by force. We build $\\vec L=\\vec r\\times\\vec p$, show it obeys $\\vec\\tau_{ext}=\\d\\vec L\u002F\\d t$, and use its conservation under zero external torque to link before and after in collisions, reconfigurations, and coupled rotors without ever resolving the internal forces. The catch is bookkeeping: the origin, the system boundary, and the frame must be fixed first, and a change in total $\\vec L$ always points to an external impulse someone forgot.\n",{"path":16718,"title":16719,"module":16703,"summary":16720},"\u002Fmechanics\u002Frotation\u002Frolling-resistance","Rolling Resistance","Ideal rolling should coast forever, yet every real wheel slows down. The reason is that a deformable tire and road do not press through a single point: the contact patch spreads, the normal-force resultant shifts ahead of the axle, and that offset is a resisting moment even with no gross sliding. We package it as an equivalent force $F_{rr}=C_{rr}N$, tie the coefficient to load, surface, speed, and temperature, and use coast-down, towing, and traction tests to separate this contact loss from aerodynamic drag, bearing friction, and the adhesion limit where rolling gives way to skidding.\n",{"path":16722,"title":16723,"module":16703,"summary":16724},"\u002Fmechanics\u002Frotation\u002Fgyroscopic-precession","Gyroscopic Precession","A spinning top leans over but does not fall — it swings its axis in a slow horizontal circle instead. The paradox dissolves once torque is read as the rate of change of a vector: gravity's torque is perpendicular to the spin angular momentum, so it turns $\\vec L$ rather than toppling it. We derive the steady precession rate $\\Omega\\simeq Mgr\u002F(I_s\\omega_s)$ in the fast-top limit, state the assumptions it leans on — dominant spin, slow tilt, negligible bearing torque — and read nutation, support motion, and a decaying spin as the ways real gyroscopes depart from it.\n",{"path":16726,"title":16727,"module":16728,"summary":16729},"\u002Fmechanics\u002Fgravity-and-matter\u002Fkeplerian-orbits","Keplerian Orbits","Gravitation and Matter","Why do the planets trace ellipses rather than any other curve? Newton's inverse-square law collapses the two-body problem onto a single conic section, and the answer falls out of two conserved quantities: a central force can exert no torque, so angular momentum is fixed, and gravity is conservative, so energy is fixed. We read an orbit's size and shape straight off those invariants, recover all three of Kepler's laws, and derive escape speed, the vis-viva relation, and the timing of a pass. We also mark where the ideal ellipse breaks down — drag, oblateness, and a third body slowly move a real orbit.\n",{"path":16731,"title":16732,"module":16728,"summary":16733},"\u002Fmechanics\u002Fgravity-and-matter\u002Fgravitational-fields","Gravitational Fields","Instead of tracking the force between every pair of masses, we attach a field to the source and ask a test mass to read it off locally. That move pays off because gravity is conservative: the field is the gradient of a single scalar potential, and potentials from many sources simply add. We build the field-potential picture, use spherical symmetry and the shell theorem to get the point-mass exterior field and the zero interior field of a shell, and read tides straight out of the field's gradient. Along the way we mark exactly when the constant-$g$ and point-mass shortcuts hold and when a shape correction is needed.\n",{"path":16735,"title":16736,"module":16728,"summary":16737},"\u002Fmechanics\u002Fgravity-and-matter\u002Fstatic-equilibrium","Static Equilibrium","What does it take for a loaded structure to stay put? A body at rest needs its forces to cancel and its turning effects to cancel — $\\sum\\vec F=0$ and $\\sum\\vec\\tau=0$ about any point — and almost all of statics is the craft of turning a physical setup into those equations. We build free-body diagrams, replace supports, cables, friction, couples, and distributed loads with their idealized reactions, and locate the centre of gravity that decides whether a body tips. We also count equations against unknowns to separate a determinate problem from one that needs the material's deformation to resolve, and read every negative or inconsistent reaction as a sign that a contact or a boundary was chosen wrong.\n",{"path":16739,"title":16740,"module":16728,"summary":16741},"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-statics","Fluid Statics","A fluid at rest cannot support a shear, so the only stress it carries is a pressure that must grow with depth to hold up the fluid above it. That single balance, $\\d p\u002F\\d z=-\\rho g$, runs the whole subject: it sets manometer readings, the force on a dam, and — integrated over a submerged boundary — Archimedes' buoyant force $F_B=\\rho g V_{\\rm disp}$. We derive these, use them to decide when a body floats and whether it floats upright, and mark where acceleration, rotation, compressibility, or capillarity forces a richer pressure model.\n",{"path":16743,"title":16744,"module":16728,"summary":16745},"\u002Fmechanics\u002Fgravity-and-matter\u002Ffluid-flow","Fluid Flow","Two accounting rules carry most of steady flow: mass cannot pile up, so the same volume crosses every section each second, and mechanical energy is conserved along a streamline when the fluid is ideal. From those we get continuity, Bernoulli's relation between pressure, speed, and height, and the results that follow — Torricelli's efflux speed, the Venturi meter, the Pitot tube. We then let go of the ideal assumptions one at a time: viscosity adds wall shear and head loss, Reynolds number decides laminar versus turbulent, and Mach number marks where a gas stops behaving as incompressible.\n",{"path":16747,"title":16748,"module":16728,"summary":16749},"\u002Fmechanics\u002Fgravity-and-matter\u002Forbital-motion","Orbital Motion","A circular orbit is nothing but free fall with enough sideways speed to keep missing the ground, and setting gravity equal to the centripetal requirement fixes that speed and the period once and for all. From the same energy bookkeeping we read off escape speed, sort orbits into bound, parabolic, and hyperbolic by the sign of their specific energy, and see why a tangential burn is the efficient way to change an orbit. We build the Hohmann transfer and its launch window, work the numbers for a geostationary orbit and an escape burn, and mark where finite thrust, perturbations, and an uncertain initial state pull a real trajectory off the ideal.\n",{"path":16751,"title":16752,"module":16728,"summary":16753},"\u002Fmechanics\u002Fgravity-and-matter\u002Fstress-and-elasticity","Stress and Elasticity","Rigid bodies are a fiction; every real material stretches, shears, or squeezes under load, and the useful question is how much. We define stress as force per area and strain as fractional deformation, then find that for small deformations the two are simply proportional — Hooke's law — with Young's, shear, and bulk moduli as the constants for stretch, twist, and volume change. From these we compute extensions, torsional twist, and stored elastic energy, and read a tensile curve for the yield, ultimate, and fracture points where linear elasticity ends. We also mark the practical limits: stress concentrations, fatigue, and the multiaxial states a single uniaxial modulus cannot capture.\n",{"path":16755,"title":16756,"module":16757,"summary":16758},"\u002Fmechanics\u002Foscillations-waves\u002Fdamped-oscillators","Damped Oscillators","Oscillations and Waves","Every real oscillator eventually stops: friction, drag, and internal loss drain its energy, so free motion is a decay rather than a permanent swing. Adding a velocity-proportional resistance to the spring-mass equation produces one dimensionless number, $b\u002F(2\\sqrt{mk})$, that decides whether the mass rings down through many cycles, returns once without overshoot, or crawls back slowly. We solve the three regimes, tie the observed decay to the power balance $b\\dot x^2$, and turn a measured ring-down into the decay rate and quality factor of the apparatus — reading damping off the data instead of assuming it.\n",{"path":16760,"title":16761,"module":16757,"summary":16762},"\u002Fmechanics\u002Foscillations-waves\u002Ftravelling-waves","Travelling Waves","A wave carries a shape, not the material: each element of a rope or air column oscillates in place while the disturbance travels through it. Writing that shape as $f(x\\mp vt)$ turns \"the pattern moves\" into a statement about the cosine's argument, and a local force balance on one string segment fixes the speed at $v=\\sqrt{T\u002F\\mu}$ — restoring stiffness over inertia, with amplitude nowhere in it. We build the sinusoidal wave and its phase, derive the wave equation from Newton's second law, and follow the energy a travelling wave transports, then check speed and power against those predictions.\n",{"path":16764,"title":16765,"module":16757,"summary":16766},"\u002Fmechanics\u002Foscillations-waves\u002Fwave-superposition","Wave Superposition","When two waves cross the same point, what does a probe read? In a linear medium the answer is arithmetic: the displacements add, $y=y_1+y_2$, and the pulses pass through each other unchanged. That one rule produces interference — reinforcement where the signs agree, cancellation where they oppose — and it guards against a common mistake, since displacement can vanish at an instant while the energy sits in transverse motion instead. We work out the signed sum, the phase bookkeeping for equal-frequency components, and why a null in the record is not a null in the wave.\n",{"path":16768,"title":16769,"module":16757,"summary":16770},"\u002Fmechanics\u002Foscillations-waves\u002Fstanding-waves","Standing Waves","Clamp a string at both ends and only certain frequencies survive: the ends must be nodes, and that single geometric demand quantizes the wave into a discrete set of modes $f_n=nv\u002F(2L)$. The travelling wave becomes a fixed pattern of nodes and antinodes — standing, not moving — because equal waves running in opposite directions superpose. We build the standing wave from its counter-propagating pieces, read the harmonic sequence off the boundary conditions (half-wavelengths for a fixed-fixed string, odd quarter-wavelengths for a closed pipe), and test the ideal model against node scans and resonance peaks.\n",{"path":16772,"title":16773,"module":16757,"summary":16774},"\u002Fmechanics\u002Foscillations-waves\u002Fsound-waves","Sound Waves","Sound is a pressure wave so small that a loud tone displaces air molecules by less than the width of an atom, yet a microphone reads it easily — because pressure, not displacement, is what the ear and the instrument sense. The acoustic impedance $Z=\\rho c$ ties pressure, density, and particle velocity together, fixes the intensity a wave carries, and sets the reference for the decibel, a logarithm that tames a $10^{12}$ range in power. We derive the sound speed from the gas's stiffness, convert between pressure and intensity levels, and treat the measurement itself — calibration, geometry, background, averaging — as part of the physics.\n",{"path":16776,"title":16777,"module":16757,"summary":16778},"\u002Fmechanics\u002Foscillations-waves\u002Fdoppler-effect","Doppler Effect","A passing siren drops in pitch not because the source changes but because motion repacks the wavefronts: an approaching source crowds its crests, a receding one stretches them, and a moving listener samples them at a different rate. For mechanical waves every velocity is measured against the medium, and one signed ratio $f_r=f_s(v-u_r)\u002F(v-u_s)$ captures both effects at once. We separate source motion, which sets crest spacing, from receiver motion, which sets arrival rate, invert the shift to recover radial velocity, and mark where the model breaks — supersonic sources, moving air, and reflected paths that carry two shifts, not one.\n",{"path":16780,"title":16781,"module":16757,"summary":16782},"\u002Fmechanics\u002Foscillations-waves\u002Fwave-packets","Wave Packets","No real signal is a single frequency: a disturbance that starts and stops is built from a band of wave numbers, and the width of that band is what makes it local. We ask how such a packet moves — carrier crests at the phase velocity $v_\\mathrm p=\\omega\u002Fk$, the envelope at the group velocity $v_\\mathrm g=\\d\\omega\u002F\\d k$ — and why the two differ once a medium is dispersive. Curvature $\\d^2\\omega\u002F\\d k^2$ spreads and chirps the packet as it travels, and the Fourier reciprocity that ties bandwidth to duration explains why a finite record, aliasing, or a coarse probe can imitate that spreading unless the sampling limits are respected.\n",{"path":16784,"title":16785,"module":16757,"summary":16786},"\u002Fmechanics\u002Foscillations-waves\u002Fbeats-and-coupling","Beats and Coupling","Add two tones a few hertz apart and the sum swells and fades at their difference frequency — a beat — though neither source is changing. We work out that envelope, then ask the mechanical version of the same question: join two oscillators and a single resonance splits into normal modes, with energy sloshing between the coordinates at their frequency difference. The lesson identifies when a slow amplitude envelope signals genuine coupling rather than two independent sources, drift, or deliberate modulation, reading it from envelope timing, spectral sidebands, and the mode shapes.\n",{"path":16788,"title":16789,"module":16757,"summary":16790},"\u002Fmechanics\u002Foscillations-waves\u002Fsimple-harmonic-motion","Simple Harmonic Motion","Any system pushed back toward equilibrium by a force proportional to its displacement obeys one equation, $\\ddot x+\\omega_0^2x=0$, and so moves sinusoidally at $\\omega_0=\\sqrt{k\u002Fm}$ whatever the amplitude. We derive that motion, follow its energy $E=mv^2\u002F2+kx^2\u002F2$ trading between kinetic and potential form at constant total, and read the elliptical phase-space orbit Hooke's law implies. Period, amplitude, velocity, and acceleration then supply redundant checks: an amplitude-dependent period or a curved force residual is the signature that the linear model has failed, and mass-loading and offset tests separate a calibration error from a real frequency shift.\n",{"path":16792,"title":16793,"module":16757,"summary":16794},"\u002Fmechanics\u002Foscillations-waves\u002Fpendulum-motion","Pendulum Motion","A pendulum keeps time only because, for small swings, gravity supplies a restoring torque proportional to the angle — and $T=2\\pi\\sqrt{L\u002Fg}$ then follows without the mass appearing at all. We derive that result, mark exactly which assumptions carry it (small angle, negligible pivot loss, a rigid support), then relax them: finite amplitude lengthens the period through an elliptic integral, and an extended body replaces $L$ with the ratio of its moment of inertia to its center-of-mass distance. How the period drifts with amplitude or pivot position is what diagnoses the geometric, damping, and distributed-mass corrections.\n",{"path":16796,"title":16797,"module":16757,"summary":16798},"\u002Fmechanics\u002Foscillations-waves\u002Fdriven-oscillators","Driven Oscillators","Drive a damped oscillator at a frequency you control and it eventually forgets its own: $m\\ddot x+b\\dot x+kx=F_0\\cos\\omega t$ settles into a steady response whose amplitude and phase depend sharply on how close the drive sits to resonance. We solve for that response, show how damping alone fixes the resonance width, the peak power, and the settling time, and treat base excitation as the same problem with a different input. The steady-state formulas hold only for constant $m$, $b$, and $k$; level-dependent peaks or hysteresis between up- and down-sweeps are how nonlinearity or an extra mode announces itself.\n",{"path":16800,"title":16801,"module":16757,"summary":16802},"\u002Fmechanics\u002Foscillations-waves\u002Fwave-boundaries","Wave Boundaries","A pulse traveling along a string does something abrupt where the string's properties change: part reflects, part transmits, and which is which is set by the impedance mismatch alone. We impose continuity of displacement and transverse force at the join to get the reflection and transmission coefficients in terms of $Z=\\sqrt{T\\mu}$, fix their signs and the polarity flip, and balance the energy. The clean result assumes linear, nondispersive segments meeting at a localized join; pulse polarity, return timing, and energy ratios are the measurements that expose a real connector's mass, loss, or distributed transition.\n",{"path":16804,"title":16805,"module":16806,"summary":16807},"\u002Fmechanics\u002Fthermodynamics\u002Fkinetic-theory-of-ideal-gases","Kinetic Theory of Ideal Gases","Thermodynamics","A gas has no springs and no gears, yet it pushes on its container with a definite pressure and stores energy in a lawful way. Kinetic theory explains both from the motion of the molecules alone: pressure is the accumulated recoil of countless elastic impacts, and temperature is the average translational kinetic energy each molecule carries. We derive $pV=\\tfrac13Nm\\overline{v^2}$ from momentum transfer, read off $\\overline{K}_{\\rm tr}=\\tfrac32kT$, and use the Maxwell–Boltzmann distribution to separate the most probable, mean, and rms speeds — each the right average for a different question — while marking where the dilute, classical assumptions stop holding.\n",{"path":16809,"title":16810,"module":16806,"summary":16811},"\u002Fmechanics\u002Fthermodynamics\u002Ffirst-law-of-thermodynamics","First Law of Thermodynamics","Heat a gas and it may warm, expand, or both; compress it and the same energy can reappear as a temperature rise. The first law settles the bookkeeping: internal energy is a state property whose change equals the heat added plus the work done on the system, $\\Delta E_{\\rm int}=Q_{\\rm in}+W_{\\rm on}$. We fix a system boundary and one sign convention, compute boundary work as $\\int p\\,\\d V$ along a path, and use calorimetry to measure heat and heat capacities. The recurring point is that heat and work are path-dependent transfers while their sum is not, so an energy ledger closes only once every boundary crossing is named.\n",{"path":16813,"title":16814,"module":16806,"summary":16815},"\u002Fmechanics\u002Fthermodynamics\u002Fentropy-and-the-second-law","Entropy and the Second Law","The first law lets energy flow either way; it never says which way heat actually goes. The second law supplies the missing arrow. Entropy, defined through the reversible transfer $\\d S=\\delta Q_{\\rm rev}\u002FT$, can only increase in an isolated system, and that single inequality fixes the direction of heat flow and caps every engine, refrigerator, and heat pump at its Carnot value. We build entropy ledgers for reservoirs and working substances, separate the entropy carried by heat from the entropy generated by irreversibility, and read the sign of the total as a hard check on any proposed thermal machine.\n",{"path":16817,"title":16818,"module":16806,"summary":16819},"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-processes","Thermal Processes","Heat rarely sits still: it stretches solids, pushes real gases off their ideal isotherms, and leaks across walls by conduction, convection, and radiation. Each behavior becomes a number a designer can use. Thermal expansion sets the gaps in a bridge and the stress in a clamped rod; the van der Waals equation and a phase diagram fix when $pV=nRT$ or a latent-heat term applies; Fourier's law, Newton cooling, and Stefan–Boltzmann radiation give the rate of heat flow. We assemble these into thermal-resistance networks and transient time constants, then mark where contact resistance, phase change, or a hidden thermal bridge breaks the simple model.\n",{"path":16821,"title":16822,"module":16806,"summary":16823},"\u002Fmechanics\u002Fthermodynamics\u002Fphase-changes","Phase Changes","Add heat to ice and its temperature climbs — until it reaches $0\\ ^\\circ\\mathrm C$, where the thermometer stalls while the ice melts. That plateau is the whole subject: at a phase boundary the energy rearranges molecules, $Q=mL$, instead of raising temperature, which resumes only once one phase is gone. We stage a heating path into sensible-heat legs ($Q=mc\\Delta T$) and latent plateaus, use the Clausius–Clapeyron relation to track how a boiling point moves with pressure, and solve calorimetry by testing each coexistence endpoint — so a melt fraction that lands outside $[0,1]$ flags a wrong final-state guess rather than a real state.\n",{"path":16825,"title":16826,"module":16806,"summary":16827},"\u002Fmechanics\u002Fthermodynamics\u002Fthermal-machines","Thermal Machines","An engine, a refrigerator, and a heat pump are one machine read three ways: each shuttles heat between a hot and a cold reservoir while trading work at the boundary, and only the flow you call useful separates them. A heat engine turns part of $Q_h$ into work, $W=Q_h-Q_c$; a refrigerator spends work to pull $Q_c$ from the cold side; a heat pump counts the warm-side delivery instead. We measure each with its own ratio — efficiency or coefficient of performance — bound them all by the Carnot limit that reservoir temperatures alone set, and track how finite temperature differences, throttling, and friction generate entropy and pull real machines below that bound.\n",{"path":16829,"title":16830,"module":6,"summary":6},"\u002Fmechanics","Mechanics & Dynamics",{"path":16832,"title":16833,"module":16834,"summary":16835},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcharge-and-conductors","Charge and Conductors","Electric Fields","Rub two objects together and one pulls electrons from the other; nothing is created, only moved. We define what electric charge is — conserved, additive, and quantized in units of $e$ — and why a conductor's mobile carriers rearrange until its interior field vanishes and its surface sits at one potential. We follow charge through contact, induction, and grounding, treat the field-free cavity that turns a conductor into a shield, and mark where finite conductivity and leakage set the limits of the electrostatic picture.\n",{"path":16837,"title":16838,"module":16834,"summary":16839},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Fcoulombs-law","Coulomb's Law","Two charges at rest push or pull along the line joining them, and the whole of electrostatics is assembled by adding up such pairs. We measure that force — its inverse-square falloff, its linear dependence on each charge, the sign that says attract or repel — and write it as a vector so direction survives superposition. We work the magnitude and component forms on real numbers, check them against limiting cases and dimensions, and fix the point-charge approximation to source sizes small against every separation.\n",{"path":16841,"title":16842,"module":16834,"summary":16843},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-and-force","Electric Field and Force","Rather than ask how one charge reaches across empty space to another, we credit the source with a field that fills the space and let a second charge respond to whatever field sits at its own location. Electric field is force per unit positive test charge, $\\vec E=kq\\hat r\u002Fr^2$ for a point source, and source fields add before any receiving charge is placed. We compute those fields and the force $\\vec F=q\\vec E$ they exert, then follow a charge along its parabolic path through a uniform field and into nonuniform fields where the dynamics turn position-dependent.\n",{"path":16845,"title":16846,"module":16834,"summary":16847},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-field-maps","Electric Field Maps","A field is a vector at every point of space, and the quickest way to grasp one is to draw it. We build the two standard pictures — continuous field lines tangent to $\\vec E$, and scaled vector arrows — and read direction, magnitude, and the location of nulls straight off them. We fix what a line drawing can and cannot say: density encodes magnitude only under a stated seeding rule, and integral curves never cross at a regular point. From there we work the topology near sources, sinks, and conductor surfaces, and state the step-size and interpolation checks a numerical map must pass.\n",{"path":16849,"title":16850,"module":16834,"summary":16851},"\u002Felectricity-and-magnetism\u002Felectric-fields\u002Felectric-dipoles","Electric Dipoles","Most neutral matter carries no net charge yet still responds to an electric field, because its positive and negative charge sit slightly apart. That separation is a dipole, moment $\\vec p=q\\vec d$ pointing from the negative to the positive charge, and it is the leading term in how any neutral distribution looks from far away. We derive the torque $\\vec p\\times\\vec E$ and energy $-\\vec p\\cdot\\vec E$ a uniform field imposes, the net force a field gradient adds, and the axial and equatorial $1\u002Fr^3$ fields the pair produces, then measure how far out the point-dipole approximation still holds.\n",{"path":16853,"title":16854,"module":16855,"summary":16856},"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fcontinuous-charge-fields","Continuous Charge Fields","Continuous Charge Distributions","A charged rod, ring, or disk is not a point, yet its field is still nothing but Coulomb's law added up over the charge it carries. We replace the discrete sum by an integral, with $\\d q=\\lambda\\d\\ell$, $\\sigma\\d A$, or $\\rho\\d V$, so the real work becomes geometry: writing the vector from each source element to the field point, and letting symmetry cancel the components that must cancel before any integral is attempted. We carry the line, ring, and disk fields through in full, then check each result against its near field, its far field, and its dimensions.\n",{"path":16858,"title":16859,"module":16855,"summary":16860},"\u002Felectricity-and-magnetism\u002Fcontinuous-charge-distributions\u002Fgauss-law-and-conductors","Gauss's Law and Conductors","Adding up Coulomb's law over a whole distribution is laborious; Gauss's law trades that sum for a single statement, that the flux of $\\vec E$ out of any closed surface counts the charge inside, $\\oint\\vec E\\cdot\\d\\vec A=Q_{\\rm enc}\u002F\\varepsilon_0$. The law is always true, but it hands over the field only when the source is symmetric enough to pull $E$ outside the integral. We apply it to spheres, lines, and sheets, then turn it on conductors, where the zero interior field drives every excess charge to the surface and fixes the normal-field jump $\\sigma\u002F\\varepsilon_0$, the charge induced on a cavity wall, and electrostatic shielding.\n",{"path":16862,"title":16863,"module":16864,"summary":16865},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpoint-charge-potential","Point-Charge Potential","Electric Potential","The electrostatic force is conservative, so the work it does between two points\ndepends only on the endpoints. That lets us trade the vector field for a single\nscalar attached to each point, the electric potential, the potential energy a unit\ncharge would have there. We build potential from the work integral, fix the usual\nreference at infinity, and add point sources as scalars, $V=k\\sum_i q_i\u002Fr_i$,\navoiding the vector bookkeeping the field demands. Signed charges, the reference\nchoice, equipotential motion, and far-field expansions each give an independent\ncheck on a result.\n",{"path":16867,"title":16868,"module":16864,"summary":16869},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fpotential-gradients-and-equipotentials","Potential Gradients and Equipotentials","Given the potential everywhere, how do we recover the field? The field is the\nnegative gradient, $\\vec E=-\\nabla V$: it points down the steepest local drop in\npotential, and its magnitude is set by how fast $V$ changes, not by the shape of a\ncontour. We read off components with directional derivatives, reconstruct fields\nfrom measured potential grids using centered differences, and use closed-loop\nintegrals and grid refinement to test whether a reconstructed field is physically\nconsistent.\n",{"path":16871,"title":16872,"module":16864,"summary":16873},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Felectrostatic-energy-and-pressure","Electrostatic Energy and Pressure","Assembling a charge configuration takes work, and that work is stored, but where\nis it kept and how much is there? We total it two ways: as a sum over the charges,\n$U=\\tfrac12\\sum_i q_iV_i$, and as an integral over the field itself,\n$u_E=\\tfrac12\\varepsilon_0E^2$, energy the field carries in every region it fills.\nDifferentiating the stored energy at fixed charge or at fixed voltage recovers the\nmechanical force on a conductor, and at a charged surface the same field scale\nappears as an outward electrostatic pressure. We work the parallel-plate case in\nfull and mark where curvature and fringing make the pressure nonuniform.\n",{"path":16875,"title":16876,"module":16864,"summary":16877},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Flaplace-boundary-problems","Laplace Boundary Problems","Often the charges are not given, only the conductors and the voltages held on\nthem, and the potential in the empty space between has to be found. There $V$ obeys\nLaplace's equation $\\nabla^2V=0$, and the boundary data alone determine a unique solution.\nWe solve it two ways: separation of variables into boundary-matched modes, whose\nhigher spatial frequencies die away with depth into the domain, and finite-difference\nrelaxation for boundaries no analytic mode fits. Residual norms, boundary error, and\nflux balance tell us when the computed potential and its field can be trusted.\n",{"path":16879,"title":16880,"module":16864,"summary":16881},"\u002Felectricity-and-magnetism\u002Felectric-potential\u002Fcontinuous-charge-potentials","Continuous Charge Potentials","When charge is spread over a line, a surface, or a volume, the sum over point\nsources becomes an integral, $V(\\vec r)=k\\int \\d q\u002F|\\vec r-\\vec r'|$. Because\npotential is a scalar, this integral sidesteps the component algebra the field\nwould force, until the field is actually wanted through $\\vec E=-\\nabla V$. We set\nup the right density element for each geometry, choose a workable reference, handle\nthe integrable singularities that arise when the observation point sits on the\ncharge, and check every result against symmetry, dimensions, and the far-field\nmultipole limit.\n",{"path":16883,"title":16884,"module":16885,"summary":16886},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitance-fundamentals","Capacitance Fundamentals","Capacitance","How much charge must you separate onto two conductors to hold a given voltage between\nthem? That ratio, $C=Q\u002F\\Delta V$, is fixed by the conductor geometry and the medium,\nnot by how much charge is presently stored. We compute it from the field for the\nparallel-plate, isolated-sphere, concentric-sphere, and coaxial geometries, trace how\nsurface charge and boundary conditions set each result, and see where fringing,\nguarding, and stray coupling separate the ideal formula from what a bridge measures.\n",{"path":16888,"title":16889,"module":16885,"summary":16890},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-networks","Capacitor Networks","Wire several capacitors together and the source sees one equivalent capacitance — but\nwhich? The answer comes not from how the symbols are drawn but from which conductors\nshare a node: parallel branches hold a common voltage and add, $C_{\\rm eq}=\\sum_iC_i$,\nwhile series branches share a common charge and add reciprocally. We derive both rules\nfrom charge conservation on the floating internal node, then extend the node-charge\nmethod to unequal, precharged, and stray-coupled branches and carry a worked reduction\nthrough to the charge and voltage on every element.\n",{"path":16892,"title":16893,"module":16885,"summary":16894},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fcapacitor-energy-and-force","Capacitor Energy and Force","Charging a capacitor takes work, because every increment of charge is pushed through\nthe voltage the earlier charge already established. We total that work three\nequivalent ways, $U=Q^2\u002F(2C)=Q\\Delta V\u002F2=C(\\Delta V)^2\u002F2$, locate it in the field as\na density $u=\\tfrac12\\epsilon_0E^2$, then let the plates move. Differentiating the\nstored energy at fixed charge, or the coenergy at fixed voltage, gives the mechanical\nforce; the two boundaries differ only by the work the source supplies. We work the\nparallel-plate attraction and its electrostatic pressure in full, and follow the same\ngradient into pull-in, tilt, comb drives, and traceable force calibration.\n",{"path":16896,"title":16897,"module":16885,"summary":16898},"\u002Felectricity-and-magnetism\u002Fcapacitance\u002Fdielectric-polarization-and-breakdown","Dielectric Polarization and Breakdown","Slide a dielectric between the plates and the capacitance rises — but why, and how\nhard can you drive it before the insulator fails? Bound charge answers the first:\npolarization $\\vec P$ sets up surface and volume charge that partly cancels the\napplied field, so $\\vec D=\\varepsilon_0\\vec E+\\vec P$ separates what the circuit\ncontrols from what the material contributes. We follow the field across layered\ndielectrics and interfaces, tie permittivity and loss to their frequency dependence,\nand treat dielectric strength as a measured, geometry-dependent limit rather than one\nmaterial number.\n",{"path":16900,"title":16901,"module":16902,"summary":16903},"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fcurrent-and-resistance","Current and Resistance","Direct-Current Circuits","What does it mean, physically, for charge to flow, and what sets how hard a wire resists that flow? Current counts charge crossing a surface, $I=\\int\\vec J\\cdot\\d\\vec A$, and traces back to a slow drift of many carriers, $\\vec J=nq\\vec v_d$. We establish when the linear law $V=IR$ actually holds, how resistivity and geometry combine into bulk resistance, why real sources sag under load through their internal resistance, and how the three power forms $P=IV=I^2R=V^2\u002FR$ tie electrical work to heating and component ratings.\n",{"path":16905,"title":16906,"module":16902,"summary":16907},"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Fkirchhoff-network-analysis","Kirchhoff Network Analysis","Once a circuit has more than one loop, no amount of series-parallel folding will reduce it — you need the two conservation laws written as equations. Kirchhoff's junction law is charge conservation at a node; his loop law is energy conservation around a closed path. We turn a labelled network into a linear system in node voltages or mesh currents, fix the sign conventions so a negative answer just means a reversed arrow, and use power balance as an independent check that the algebra describes the circuit that was actually built.\n",{"path":16909,"title":16910,"module":16902,"summary":16911},"\u002Felectricity-and-magnetism\u002Fdirect-current-circuits\u002Frc-transients","RC Transients","How does a circuit get from one steady state to the next when a capacitor refuses to change its voltage all at once? Because a jump would demand infinite current, an RC circuit slides between states exponentially, with a single time constant $\\tau=RC$ that sets the whole schedule: charging fills as $1-e^{-t\u002F\\tau}$, discharge empties as $e^{-t\u002F\\tau}$. We solve the first-order loop equation, read the response off three numbers — the switch-instant voltage, the final dc voltage, and the Thevenin resistance the capacitor sees — and mark where source and probe resistance shift $\\tau$ or where a second storage element hides a mode a one-$\\tau$ fit misses.\n",{"path":16913,"title":16914,"module":16915,"summary":16916},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-trajectories","Magnetic Trajectories","Magnetic Field","A charged particle in a magnetic field never speeds up or slows down, yet its path curves relentlessly. We work out why: the magnetic force is always perpendicular to velocity, so it does no work and bends the transverse motion into a circle of radius $r=mv_\\perp\u002F(|q|B)$ while leaving the parallel motion untouched, producing a helix. We derive the cyclotron frequency, show why it is independent of speed until relativity intervenes, and turn the geometry around: a measured curvature reads back a particle's momentum, which is how tracking detectors weigh what they cannot see.\n",{"path":16918,"title":16919,"module":16915,"summary":16920},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fhall-effect","Hall Effect","Current tells you charge is moving, but not whether the movers are positive or negative, nor how many there are. A magnetic field settles both questions. Push current through a strip in a transverse field and the carriers pile up on one edge until a transverse electric field just balances the magnetic deflection; the sign of the resulting Hall voltage names the carrier's charge and its size counts the carriers per volume. We derive the balance $q\\vec E+q\\vec v_d\\times\\vec B=0$, read off $V_H=IB\u002F(nqt)$, and see why field-and-current reversal is what separates the real Hall signal from the offsets that mimic it.\n",{"path":16922,"title":16923,"module":16915,"summary":16924},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-force-on-conductors","Magnetic Force on Conductors","A magnet pushes on a current-carrying wire even though the wire is electrically neutral. The reason is that each moving carrier feels the Lorentz force, and those microscopic pushes add up to a force the wire's supports must hold. We sum them into $\\d\\vec F=I\\,\\d\\vec\\ell\\times\\vec B$, collapse it to $\\vec F=I\\vec L\\times\\vec B$ for a straight segment in a uniform field, and see exactly when that shortcut fails and the full path integral is needed. The same law runs backward as a measurement: a force-versus-current slope weighs a magnetic field against a known length.\n",{"path":16926,"title":16927,"module":16915,"summary":16928},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmagnetic-dipoles","Magnetic Dipoles","A compass needle turns to point north; a current loop in a field does the same thing, and for the same reason. Both are magnetic dipoles, and a uniform field cannot push a dipole anywhere, only twist it. We package a loop's response into one vector, the magnetic moment $\\vec\\mu=IA\\hat n$, from which torque $\\vec\\tau=\\vec\\mu\\times\\vec B$ and orientation energy $U=-\\vec\\mu\\cdot\\vec B$ both follow. Stable alignment sits at the energy minimum, a field gradient is what it takes to produce a net force $\\vec F=\\nabla(\\vec\\mu\\cdot\\vec B)$, and the same moment reappears whenever anything from an electron to a planet acts magnetic.\n",{"path":16930,"title":16931,"module":16915,"summary":16932},"\u002Felectricity-and-magnetism\u002Fmagnetic-field\u002Fmass-spectrometry","Mass Spectrometry","To weigh a single atom you cannot use a scale, so you use a magnetic field instead. A charged ion of unknown mass bends in a field by an amount that depends on its momentum and charge, so if every ion enters with the same velocity, its landing position reads off its mass-to-charge ratio directly. We build the instrument in two stages: crossed electric and magnetic fields that pass only ions with $v=E\u002FB$, and a magnetic sector that bends the survivors along $r=mv\u002F(|q|B)$. Then we ask what blurs a spectral line and how reference ions turn a position into a calibrated mass.\n",{"path":16934,"title":16935,"module":16936,"summary":16937},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmoving-charge-fields","Moving-Charge Fields","Magnetic Sources","Every magnetic field comes from charge in motion, and the simplest source is a single point charge drifting past. We work out the field it produces — normal to both the velocity and the line of sight, falling off as the inverse square — and read off why it vanishes straight ahead of the charge and peaks broadside. Summing many such charges is the bridge to steady currents, valid while speeds stay far below $c$ and the motion changes little during the time its field takes to propagate outward.\n",{"path":16939,"title":16940,"module":16936,"summary":16941},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fbiot-savart-law","Biot–Savart Law","A steady current is a continuous stream of current elements, and the Biot–Savart law hands each one a magnetic contribution — a right-hand cross product that falls off as the inverse square of distance. Summing the contributions along a conductor is a vector line integral, which we carry out for the straight wire to get the endpoint-angle formula. The infinite-wire field $B=\\mu_0 I\u002F2\\pi s$ falls out as the limit where both ends recede, and we mark how fast a finite wire departs from it and when a thin-filament model is safe.\n",{"path":16943,"title":16944,"module":16936,"summary":16945},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fcircular-current-loops","Circular Current Loops","A ring of current is the simplest source with a well-defined magnetic axis, and it is the building block of every coil and electromagnet. Symmetry kills the transverse Biot–Savart contributions along that axis and leaves a single clean integral; we evaluate it to get $B_z=\\mu_0 I R^2\u002F[2(R^2+z^2)^{3\u002F2}]$, read off the centre field $\\mu_0 I\u002F2R$, and watch it fall into the $1\u002Fz^3$ tail of a magnetic dipole far away. Stacking turns just adds their axial contributions, which is what makes a solenoid out of a pile of loops.\n",{"path":16947,"title":16948,"module":16936,"summary":16949},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Famperes-law","Ampère’s Law","When a current arrangement is symmetric enough, the Biot–Savart integral is overkill: Ampère's law, $\\oint_C\\vec B\\cdot\\d\\vec\\ell=\\mu_0 I_{\\rm enc}$, gets the field from a single line of reasoning about how much current a loop encloses. We see why the law holds for any steady current, then use cylindrical, planar, and toroidal symmetry to turn the circulation into simple algebra — the field inside and outside a wire, an infinite sheet, a solenoid, and a toroid. We also mark the catch: without symmetry the law still holds but no longer hands you the field pointwise.\n",{"path":16951,"title":16952,"module":16936,"summary":16953},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fgauss-law-for-magnetism","Gauss’s Law for Magnetism","Electric field lines start and end on charges; magnetic field lines do neither, because no one has ever found an isolated magnetic pole. That single experimental fact is Gauss's law for magnetism: the flux of $\\vec B$ through any closed surface is zero, $\\oint\\vec B\\cdot\\d\\vec A=0$, or in differential form $\\nabla\\cdot\\vec B=0$. We work through what it says — every field line that enters a closed surface must leave it, so field lines close on themselves — and, just as important, what it does not say, since flux through an open surface is generally nonzero.\n",{"path":16955,"title":16956,"module":16936,"summary":16957},"\u002Felectricity-and-magnetism\u002Fmagnetic-sources\u002Fmagnetic-materials","Magnetic Materials","Put matter in a magnetic field and its atoms respond, each acting as a tiny current loop; the aligned moments per unit volume are the magnetization $\\vec M$, whose bound currents add to the field. Separating what we control (the free current) from what the material supplies leads to $\\vec H$ and the relation $\\vec B=\\mu_0(\\vec H+\\vec M)$. We sort materials into diamagnets, paramagnets, and ferromagnets by how $\\vec M$ answers, follow a ferromagnet around its hysteresis loop, and see why the loop's area is the energy dissipated per cycle and why a sample's shape changes the field it actually feels.\n",{"path":16959,"title":16960,"module":16961,"summary":16962},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-flux","Magnetic Flux","Electromagnetic Induction","A magnetic field threading a loop collapses to one signed number, the flux, and every induced voltage in this module turns out to be a rate of change of that number — so defining the flux and its sign comes first. We define it as the surface integral of $\\vec B$ over an oriented surface, reduce it to $BA\\cos\\theta$ for a uniform field on a flat loop, and carry the flux linkage $N\\Phi_B$ of a coil. The chosen normal fixes the sign; reversing it flips the sign without touching the field. Nonuniform fields and curved surfaces force the integral, so we also build the numerical estimate and the checks that separate a reliable value from a nominal field-times-area product.\n",{"path":16964,"title":16965,"module":16961,"summary":16966},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Ffaradays-law","Faraday's Law","Move a magnet toward a coil, or ramp the current in a nearby circuit, and a voltage appears with no battery in sight. Faraday's law names the cause: the emf around a loop equals minus the rate of change of the magnetic flux through it, so any change of field, area, orientation, or position that alters the flux drives an emf. We separate the emf, which lives around the boundary whether or not current can flow, from the current that follows only when the path is closed; fix the single sign convention that ties flux to loop orientation; and read the emf off rotating coils and off flux sampled at discrete times.\n",{"path":16968,"title":16969,"module":16961,"summary":16970},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Flenzs-law","Lenz's Law","The minus sign in Faraday's law is not decoration: it decides which way the induced current flows, and it always chooses the direction that fights the change that produced it. Lenz's law reads that sign off energy conservation — a current that aided the change would be free energy — and turns it into a repeatable procedure. We fix a surface normal and a positive loop direction so the sign is calculable, then work through approaching magnets, expanding loops, coupled coils, and rotating generators, using mechanical work and Joule heating as an independent check on every direction we draw.\n",{"path":16972,"title":16973,"module":16961,"summary":16974},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmotional-emf","Motional EMF","Push a wire through a magnetic field and its free charges feel a sideways magnetic force that piles them up at the ends — a battery made of motion. Motional emf is that effect: the work per unit charge a moving conductor supplies is the line integral of $\\vec v\\times\\vec B$ along it, which for a rod moving perpendicular to both its length and the field collapses to $B\\ell v$. We chase where the energy comes from — the hand or motor fighting the magnetic drag, never the magnetic force itself — solve the sliding-rail circuit from both flux and carrier forces, and carry the idea into rotating rods, homopolar disks, generators, and the back emf of a motor.\n",{"path":16976,"title":16977,"module":16961,"summary":16978},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Feddy-currents","Eddy Currents","A wire carries current along one path; a solid block of metal offers a continuum of them, and any changing flux threading that block sets charge circulating in closed loops it chooses for itself. We ask what those eddy currents do — where they heat, where they drag, and how Lenz's law fixes their direction — and why the same circulation is a feature in an induction furnace and a loss to be suppressed in a transformer core. From a representative-loop estimate we get the scaling (heating grows with the square of frequency and flux rate) and the two design levers, lamination and resistivity, that break the paths a solid conductor would otherwise hand the current.\n",{"path":16980,"title":16981,"module":16961,"summary":16982},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fself-inductance","Self-Inductance","A coil resists changes to its own current. Drive current through it and the flux it produces threads its own turns; change that current and Faraday's law turns the coil against the source with a back emf $\\mathcal E_L=-L\\,\\d I\u002F\\d t$. We define self-inductance as the flux linkage per ampere fixed by winding and core geometry, derive the long-solenoid value $L=\\mu_0 N^2A\u002F\\ell$, and follow the consequence that dominates circuits: because a finite voltage can only sustain a finite $\\d I\u002F\\d t$, an inductor's current cannot jump — which is why opening a switch on a live coil throws a spark.\n",{"path":16984,"title":16985,"module":16961,"summary":16986},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Fmagnetic-energy","Magnetic Energy","Building current in a coil means working against its back emf, and that work does not vanish — it sits in the magnetic field as recoverable energy $U_B=\\tfrac12LI^2$, spread through space at density $u_B=B^2\u002F(2\\mu_0)$. We derive both forms, show they agree for a solenoid, and read a force out of the same energy: an armature is pulled toward higher inductance, and $B^2\u002F(2\\mu_0)$ doubles as a magnetic pressure. The lesson closes on the accounting a real switching event demands, where recoverable energy, copper heating, core loss, and clamp dissipation must balance a single ledger.\n",{"path":16988,"title":16989,"module":16961,"summary":16990},"\u002Felectricity-and-magnetism\u002Felectromagnetic-induction\u002Frl-circuits","RL Circuits","Put a resistor and an inductor in series and the current cannot switch on or off at will: it climbs to $V_0\u002FR$ and falls away exponentially on a single time scale $\\tau=L\u002FR$ set by how much flux the coil hoards against how fast the resistor bleeds it. We solve the turn-on and turn-off, then confront the practical sting — because the coil's current refuses to stop instantly, breaking its path throws up a large voltage, which is why real inductive circuits carry freewheel diodes and clamps that trade voltage stress against how quickly the current dies.\n",{"path":16992,"title":16993,"module":16994,"summary":16995},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-fundamentals","AC Fundamentals","Alternating Current","A wall socket delivers a voltage that averages to zero over each cycle, yet it still heats a filament and runs a motor. The resolution is that dissipation follows the mean of the square, not the mean, so we define the root-mean-square value that makes an alternating source the equal of a DC one for resistive heating. We show a sinusoid's RMS is its peak divided by $\\sqrt2$, work out the average power an ideal resistor draws when its current stays in phase with the applied voltage, and separate the peak, average, and RMS descriptions that a single number cannot combine.\n",{"path":16997,"title":16998,"module":16994,"summary":16999},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Freactance","Reactance","A resistor obeys Ohm's law instant by instant, but a capacitor responds to how fast its voltage changes and an inductor to how fast its current changes. Under a steady sinusoid that rate-dependence collapses to a fixed quarter-cycle phase shift and a frequency-dependent amplitude ratio, the reactance. We derive $X_C=1\u002F(\\omega C)$ and $X_L=\\omega L$, adopt phasors to turn the defining derivatives into multiplication by $j\\omega$ so a single complex impedance carries amplitude and phase together, and track the energy an ideal reactance stores and returns without dissipating it. Real windings and dielectrics add loss, leakage, and self-resonance that bound where the ideal formulas hold.\n",{"path":17001,"title":17002,"module":16994,"summary":17003},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Frlc-resonance","RLC Resonance","Put a resistor, inductor, and capacitor in one loop and their reactances work against each other: inductive reactance grows with frequency while capacitive reactance shrinks, and at one frequency they cancel exactly. There the branch looks purely resistive, the current peaks, and the inductor and capacitor voltages can swing far above the source. We locate that resonance at $\\omega_0=1\u002F\\sqrt{LC}$, measure how sharp the peak is with the quality factor $Q=\\omega_0L\u002FR$, tie its half-power bandwidth $R\u002FL$ to the ringdown of the unforced circuit, and read the same poles off as bandpass and peaked filters at the R, L, or C terminals.\n",{"path":17005,"title":17006,"module":16994,"summary":17007},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Fac-power","AC Power","Multiply an AC load's RMS voltage by its RMS current and you get an answer in volt-amperes that the wiring must carry, but not in general the watts the load consumes. The phase between voltage and current splits that product into a part that does net work and a part that merely sloshes energy back and forth. We derive the average power $P=V_{\\rm rms}I_{\\rm rms}\\cos\\phi$, package amplitude and phase into complex power $S=P+jQ$ so that real, reactive, and apparent power form one right triangle, and see why a harmonic-rich current forces the time-domain definition $P=\\langle vi\\rangle$ in place of a single phase angle.\n",{"path":17009,"title":17010,"module":16994,"summary":17011},"\u002Felectricity-and-magnetism\u002Falternating-current\u002Ftransformers","Transformers","Two coils sharing an iron core exchange no charge, yet a changing current in one drives a voltage in the other, and the ratio of their turns sets how voltage and current trade off between the windings. That lets a transformer step a voltage up or down, isolate two circuits, and make a load look larger or smaller to the source by the square of the turns ratio. We build the ideal ratio element from Faraday's law and the dot convention, derive the reflected-impedance rule, then add the winding resistance, leakage, magnetizing current, and core loss that turn the ideal ratios into real regulation, efficiency, and a bounded voltage-frequency range.\n",{"path":17013,"title":17014,"module":17015,"summary":17016},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdisplacement-current","Displacement Current","Maxwell’s Equations and Electromagnetic Waves","Ampère's law asks for the current through a surface bounded by a loop, but a charging capacitor breaks it: slide the surface off the wire and into the gap and the enclosed conduction current drops to zero, while the magnetic field around the loop plainly does not. Maxwell's repair is to count a changing electric flux as itself a source of magnetic circulation. We derive the displacement-current term $\\varepsilon_0\\,\\d\\Phi_E\u002F\\d t$, show that charge continuity demands it, compute the magnetic field it produces inside a charging capacitor, and see how it closes the Ampère–Maxwell law so that electric and magnetic fields can sustain one another as a wave.\n",{"path":17018,"title":17019,"module":17015,"summary":17020},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-waves","Electromagnetic Waves","Once a changing electric flux can drive a magnetic field, the two curl laws feed each other: a disturbance in one regenerates the other, and the pair walks off through empty space with no medium holding it up. We take the curl of Faraday's law, land on a wave equation whose speed is fixed entirely by $\\mu_0$ and $\\varepsilon_0$, and find that $c=1\u002F\\sqrt{\\mu_0\\varepsilon_0}$ falls out of purely electric and magnetic constants. The plane-wave solution then fixes the geometry — $\\vec E$, $\\vec B$, and the propagation direction mutually perpendicular, oscillating in phase, with amplitudes locked at $E=cB$ — a set of independent predictions any real measurement must meet at once.\n",{"path":17022,"title":17023,"module":17015,"summary":17024},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Felectromagnetic-momentum","Electromagnetic Momentum","A light beam carries no mass, yet it pushes: shine it on a surface and the surface feels a force. We trace that force back to the fields, which store energy with density $\\varepsilon_0E^2$ and carry it along the Poynting vector $\\vec S=\\vec E\\times\\vec B\u002F\\mu_0$. Because that energy also carries momentum $U\u002Fc$, an absorbed beam presses with $I\u002Fc$ and a mirror with $2I\u002Fc$. We derive the Poynting theorem as local energy conservation, tie intensity to field amplitude, and work the momentum balance carefully enough that oblique incidence, partial reflection, and finite beams all drop out of one accounting.\n",{"path":17026,"title":17027,"module":17015,"summary":17028},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fdipole-radiation","Dipole Radiation","Only accelerating charge radiates, and the simplest accelerator is a charge sloshing back and forth: an oscillating electric dipole. We work out the field it throws off, keeping the part that survives to large distance — the $1\u002Fr$ radiation field whose intensity goes as $\\sin^2\\theta\u002Fr^2$, zero along the dipole axis and strongest broadside. From it follow the $\\omega^4$ scaling of total radiated power, radiation resistance as the feed's view of that escaping power, and, through reciprocity, the fact that a good transmitter receives well in the same directions. The near-zone terms that fall off faster carry no net power, and we mark carefully where each description is allowed to be used.\n",{"path":17030,"title":17031,"module":17015,"summary":17032},"\u002Felectricity-and-magnetism\u002Fmaxwell-electromagnetic-waves\u002Fpolarization","Polarization","A plane wave still leaves one thing free: which way its electric field points as it oscillates. That freedom is polarization, set entirely by the relative amplitude and phase of the two transverse field components — in phase gives a line, equal amplitudes a quarter cycle apart give a circle, everything else an ellipse. We work out how a linear analyzer reads a state through Malus's law $I=I_0\\cos^2\\theta$, why that scan alone cannot tell circular light from unpolarized, and how a quarter-wave plate plus a few analyzer settings recover the full Stokes vector and the degree of polarization.\n",{"path":17034,"title":17035,"module":17036,"summary":17037},"\u002Felectricity-and-magnetism\u002Foptics\u002Freflection-and-refraction","Reflection and Refraction","Geometrical Optics","Light meeting a boundary between two transparent media splits into a reflected ray and a bent transmitted one, and predicting where those rays go is the whole starting point of geometrical optics. Fixing one convention — every angle measured from the surface normal — we get reflection's equal angles and derive Snell's law $n_1\\sin\\theta_1=n_2\\sin\\theta_2$ from wavefront timing. That single relation, applied once or twice, yields the critical angle and total internal reflection, prism deviation, the lateral shift through a window, apparent depth, and a fiber's acceptance cone; a wavelength-dependent index then adds dispersion. We mark throughout where the ray picture is trustworthy: feature sizes large against the wavelength and clean interface geometry.\n",{"path":17039,"title":17040,"module":17036,"summary":17041},"\u002Felectricity-and-magnetism\u002Foptics\u002Fthin-lenses","Thin Lenses","A lens gathers the light spreading from one point back onto another, and a single paraxial relation $1\u002Fs+1\u002Fs'=1\u002Ff$ predicts where that image lands and how large it is. We collapse two refractions into one bending plane, read image position and orientation off the three principal rays, and trace focal length back to glass and curvature through the lensmaker equation. Sign conventions carry the physics here — they separate real from virtual images and upright from inverted — so we drill them before chaining lenses in sequence and in contact. The lesson ends on how focal length is actually measured on a bench, and where finite thickness, aperture, and dispersion break the thin-lens picture.\n",{"path":17043,"title":17044,"module":17036,"summary":17045},"\u002Felectricity-and-magnetism\u002Foptics\u002Fspherical-mirrors","Spherical Mirrors","Curve a mirror and it stops merely reflecting an image and starts forming one: the same $1\u002Fs+1\u002Fs'=1\u002Ff$ that governs lenses reappears, now with $f=R\u002F2$ and reflected rays and object sharing one side of the glass. We derive the mirror equation from the reflection geometry of a single paraxial ray, then let signed distances do the sorting — real inverted images on the near branch, virtual upright ones behind the surface — and check the concave, convex, and plane-mirror limits against each other. The second half turns to how focal length is actually measured on a bench, by finite conjugates, distant targets, return imaging, and sagitta, and to the aperture and off-axis aberrations the single paraxial focus cannot capture.\n",{"path":17047,"title":17048,"module":6,"summary":6},"\u002Felectricity-and-magnetism","Electricity & Magnetism",{"path":17050,"title":17051,"module":17052,"summary":17053},"\u002Flinear-algebra\u002Flinear-systems\u002Fsystems-and-echelon-forms","Systems of Linear Equations and Row Reduction","Linear Equations in Linear Algebra","A linear system is a finite set of linear equations in shared variables. Elementary row operations rewrite it without changing its solution set, and reducing the augmented matrix to echelon form decides both existence and uniqueness. Pivot positions say whether the solution set is empty, a single point, or infinite.\n",{"path":17055,"title":17056,"module":17052,"summary":17057},"\u002Flinear-algebra\u002Flinear-systems\u002Fvector-and-matrix-equations","Vector Equations and the Matrix Equation Ax = b","The same linear system reads three equivalent ways: a system of equations, a vector equation asking whether b is a linear combination of fixed vectors, and a matrix equation Ax = b. Ax is the linear combination of A's columns weighted by x, so consistency for a given b means b lies in the span of the columns, and consistency for every b means the columns span all of R^m.\n",{"path":17059,"title":17060,"module":17052,"summary":17061},"\u002Flinear-algebra\u002Flinear-systems\u002Fsolution-sets-and-applications","Solution Sets and Applied Linear Systems","A homogeneous system Ax = 0 has a solution set that is a span through the origin; a consistent Ax = b has that same span translated by any one particular solution. Parametric vector form writes both explicitly. The structure shows up in applied systems with many solutions: equilibrium prices, balanced chemical reactions, network flows, weight-loss diets, and migration models.\n",{"path":17063,"title":17064,"module":17052,"summary":17065},"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-independence","Linear Independence","A set of vectors is linearly independent when the only linear combination equal to zero is the trivial one; otherwise a dependence relation writes one vector in terms of the others. For the columns of A the question becomes whether Ax = 0 has only the trivial solution — a pivot in every column. Counting pivots settles independence, and any set with more vectors than entries is automatically dependent.\n",{"path":17067,"title":17068,"module":17052,"summary":17069},"\u002Flinear-algebra\u002Flinear-systems\u002Flinear-transformations","Linear Transformations and Their Matrices","Reading A as an action rather than an array, x maps to Ax is a transformation from R^n to R^m. The ones that preserve addition and scalar multiplication are the linear transformations, and every one is x maps to Ax for a unique standard matrix whose columns are the images of the standard basis vectors. Onto and one-to-one translate into the span and independence of those columns.\n",{"path":17071,"title":17072,"module":17073,"summary":17074},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-operations","Matrix Operations","Matrix Algebra","Matrices add and scale entrywise, but their product is defined so that multiplication corresponds to composition of linear maps: the columns of AB are A applied to the columns of B. From that requirement follow the row-column rule, the algebra of products (associative and distributive but not commutative), powers, and the transpose.\n",{"path":17076,"title":17077,"module":17073,"summary":17078},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fmatrix-inverse-and-invertibility","The Inverse and the Invertible Matrix Theorem","The inverse of a square matrix is the matrix analogue of a reciprocal, defined by AA⁻¹ = I. A closed form settles the 2×2 case; the Gauss–Jordan algorithm row reduces [A | I] to [I | A⁻¹] in general; and elementary matrices record single row operations. The Invertible Matrix Theorem collects a dozen equivalent conditions for invertibility into one statement.\n",{"path":17080,"title":17081,"module":17073,"summary":17082},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fpartitioned-matrices-and-lu","Block Matrices and the LU Factorization","Partitioning a matrix into blocks lets sums, products, and inverses be computed block by block, as if the submatrices were scalars. Block structure also underlies the LU factorization A = LU, which splits solving Ax = b into two fast triangular solves and repays the cost whenever many systems share one coefficient matrix.\n",{"path":17084,"title":17085,"module":17073,"summary":17086},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fsubspaces-dimension-rank","Subspaces of Rⁿ, Dimension, and Rank","A subspace is a set closed under addition and scalar multiplication. Every matrix carries two: the column space of all attainable outputs Ax, and the null space of all solutions of Ax = 0. A basis measures each with a minimal spanning set, dimension counts it, and the Rank Theorem ties pivots and free variables together as rank + nullity = n.\n",{"path":17088,"title":17089,"module":17073,"summary":17090},"\u002Flinear-algebra\u002Fmatrix-algebra\u002Fapplications-leontief-and-graphics","Applications: Leontief Economics and Computer Graphics","The Leontief input–output model balances an economy through (I − C)x = d and expands the inverse as a geometric series in the consumption matrix. Computer graphics moves figures with matrix products, using homogeneous coordinates so that translation and perspective projection become matrix multiplications too.\n",{"path":17092,"title":17093,"module":17094,"summary":17095},"\u002Flinear-algebra\u002Fdeterminants\u002Fdeterminants-and-cofactors","Introduction to Determinants","Determinants","The determinant of a square matrix is defined recursively by cofactor expansion: an n-by-n determinant is a signed sum of (n-1)-by-(n-1) determinants built from the first row. The expansion can equally run along any row or down any column, and a triangular matrix has determinant equal to the product of its diagonal.\n",{"path":17097,"title":17098,"module":17094,"summary":17099},"\u002Flinear-algebra\u002Fdeterminants\u002Fproperties-of-determinants","Properties of Determinants","Row operations act on the determinant in three predictable ways, and this turns row reduction into a fast algorithm: the determinant is the product of the pivots times a sign for the interchanges. The same properties yield the invertibility test det A is nonzero, the transpose identity, and the multiplicative law det(AB) equals det A times det B.\n",{"path":17101,"title":17102,"module":17094,"summary":17103},"\u002Flinear-algebra\u002Fdeterminants\u002Fcramer-volume-and-area","Cramer's Rule, Volume, and Linear Transformations","Cramer's rule writes each unknown of an invertible system as a ratio of determinants, and the same idea gives a closed formula for the inverse through the adjugate. Geometrically the absolute determinant is the area of the parallelogram or the volume of the parallelepiped spanned by the columns, so a linear map scales every region's measure by that factor.\n",{"path":17105,"title":17106,"module":17107,"summary":17108},"\u002Flinear-algebra\u002Fvector-spaces\u002Fvector-spaces-and-subspaces","Vector Spaces and Subspaces","Vector Spaces","A vector space is any set closed under addition and scalar multiplication that obeys ten algebraic axioms. The same axioms that govern arrows in the plane govern polynomials, functions, matrices, and infinite signals, so one theory covers them all. A subspace is a subset that is a vector space in its own right, tested by three conditions, and the span of any set of vectors is the smallest subspace containing them.\n",{"path":17110,"title":17111,"module":17107,"summary":17112},"\u002Flinear-algebra\u002Fvector-spaces\u002Fnull-and-column-spaces","Null Spaces, Column Spaces, and Linear Transformations","Two subspaces sit inside every matrix. The null space collects all solutions of $Ax = 0$ and lives in the domain; the column space collects every attainable $Ax$ and lives in the codomain. One is defined implicitly by a condition, the other explicitly by a spanning set, and the same pair appears for an abstract linear transformation as its kernel and range.\n",{"path":17114,"title":17115,"module":17107,"summary":17116},"\u002Flinear-algebra\u002Fvector-spaces\u002Fbases-and-independent-sets","Linearly Independent Sets and Bases","A basis is a spanning set with no redundancy: linearly independent and still large enough to reach every vector. The spanning-set theorem shows any spanning set can be trimmed to a basis by discarding dependent vectors, and the pivot columns of a matrix give a basis for its column space. Independence and spanning are defined for abstract spaces exactly as in $\\mathbb{R}^n$.\n",{"path":17118,"title":17119,"module":17107,"summary":17120},"\u002Flinear-algebra\u002Fvector-spaces\u002Fcoordinate-systems","Coordinate Systems","Fixing a basis assigns every vector a unique list of coordinates, turning an abstract space into $\\mathbb{R}^n$. The coordinate mapping is a one-to-one linear transformation onto $\\mathbb{R}^n$ — an isomorphism — so any $n$-dimensional space is indistinguishable from $\\mathbb{R}^n$ as far as vector-space computations go. In $\\mathbb{R}^n$ the change-of-coordinates matrix $P_B$ and its inverse convert between basis coordinates and standard coordinates.\n",{"path":17122,"title":17123,"module":17107,"summary":17124},"\u002Flinear-algebra\u002Fvector-spaces\u002Fdimension-and-rank","The Dimension of a Vector Space and Rank","Every basis of a space has the same number of vectors, and that number is the dimension. Rank is the dimension of the column space, equal to the dimension of the row space and to the number of pivots. The Rank Theorem, rank plus nullity equals the number of columns, ties the four fundamental subspaces of a matrix together and adds six lines to the Invertible Matrix Theorem.\n",{"path":17126,"title":17127,"module":17107,"summary":17128},"\u002Flinear-algebra\u002Fvector-spaces\u002Fchange-of-basis","Change of Basis","Two bases give the same vector two different coordinate vectors, and a single invertible matrix converts between them. Its columns are the coordinate vectors of the old basis expressed in the new one, and its inverse reverses the conversion. In $\\mathbb{R}^n$ the change-of-coordinates matrix between two bases is found by one row reduction.\n",{"path":17130,"title":17131,"module":17107,"summary":17132},"\u002Flinear-algebra\u002Fvector-spaces\u002Fdifference-equations-and-markov","Applications: Difference Equations and Markov Chains","The solutions of an nth-order linear difference equation form an $n$-dimensional vector space, so finding $n$ independent solutions gives them all. A Markov chain evolves a probability distribution by repeated multiplication by a stochastic matrix, and a regular chain converges to a unique steady-state vector fixed by that matrix. Both applications turn a dynamic process into a subspace or a fixed-point question.\n",{"path":17134,"title":17135,"module":17136,"summary":17137},"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-eigenvalues","Eigenvectors and Eigenvalues","Eigenvalues and Eigenvectors","An eigenvector of a square matrix is a nonzero vector the matrix only stretches; its eigenvalue is the stretch factor. The eigenspace of an eigenvalue is the null space of A minus lambda times the identity, the eigenvalues of a triangular matrix are its diagonal entries, and eigenvectors for distinct eigenvalues are linearly independent.\n",{"path":17139,"title":17140,"module":17136,"summary":17141},"\u002Flinear-algebra\u002Feigenvalues\u002Fthe-characteristic-equation","The Characteristic Equation","The eigenvalues of a matrix are the roots of its characteristic polynomial det(A minus lambda I). This degree-n polynomial carries an algebraic multiplicity at each repeated root, a nonzero determinant is equivalent to zero not being an eigenvalue, and similar matrices share a characteristic polynomial and hence the same eigenvalues.\n",{"path":17143,"title":17144,"module":17136,"summary":17145},"\u002Flinear-algebra\u002Feigenvalues\u002Fdiagonalization","Diagonalization","A matrix is diagonalizable when it factors as A equals P D P inverse with D diagonal, which happens exactly when it has n linearly independent eigenvectors. The factorization computes matrix powers cheaply, distinct eigenvalues guarantee it, and a repeated eigenvalue permits it only when its eigenspace dimension equals its multiplicity.\n",{"path":17147,"title":17148,"module":17136,"summary":17149},"\u002Flinear-algebra\u002Feigenvalues\u002Feigenvectors-and-linear-transformations","Eigenvectors and Linear Transformations","Every linear transformation between finite-dimensional spaces has a matrix relative to chosen bases, built from the coordinate vectors of the images of the basis vectors. For a map from a space to itself, an eigenvector basis makes that matrix diagonal, and that change of basis is diagonalization; the matrices similar to A are the representations of the map in every basis.\n",{"path":17151,"title":17152,"module":17136,"summary":17153},"\u002Flinear-algebra\u002Feigenvalues\u002Fcomplex-eigenvalues","Complex Eigenvalues","A real matrix with no real eigenvalues still has complex ones, occurring in conjugate pairs. A real 2-by-2 matrix with eigenvalue a plus b i is similar to a rotation-scaling matrix, whose rotation angle is the argument of the eigenvalue and whose scale factor is its modulus; the modulus decides whether the trajectories close up, spiral in, or spiral out.\n",{"path":17155,"title":17156,"module":17136,"summary":17157},"\u002Flinear-algebra\u002Feigenvalues\u002Fdynamical-systems","Discrete and Continuous Dynamical Systems","Eigenvalues govern the long-term behavior of a system that evolves by x becomes A x or by x prime equals A x. An eigenvector basis decouples both kinds of system into independent scalar equations; the eigenvalues then classify the origin as attractor, repeller, saddle, or spiral, and the dominant eigenpair fixes the growth rate and limiting direction.\n",{"path":17159,"title":17160,"module":17136,"summary":17161},"\u002Flinear-algebra\u002Feigenvalues\u002Fpower-method","Iterative Estimates for Eigenvalues","When only a numerical eigenvalue is needed, iteration is preferred over the characteristic polynomial. The power method repeatedly multiplies by A to converge on the dominant eigenvalue and its eigenvector; the Rayleigh quotient sharpens the estimate for symmetric matrices; and the inverse power method targets any eigenvalue near a known guess.\n",{"path":17163,"title":17164,"module":17165,"summary":17166},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-length-orthogonality","Inner Product, Length, and Orthogonality","Orthogonality and Least Squares","The dot product turns the algebra of vectors in R^n into geometry: length, distance, and perpendicularity. The inner product yields the norm, the Pythagorean theorem, and the orthogonal complement, and the null space of a matrix is the orthogonal complement of its row space.\n",{"path":17168,"title":17169,"module":17165,"summary":17170},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Forthogonal-sets-and-projections","Orthogonal Sets and Orthogonal Projections","An orthogonal basis makes coordinates trivial: each weight is a single dot product, no linear system required. Orthogonal and orthonormal bases give a direct projection formula onto a line and onto a subspace, the orthogonal decomposition and best-approximation theorems, and the matrix form U U-transpose of a projection.\n",{"path":17172,"title":17173,"module":17165,"summary":17174},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fgram-schmidt-and-qr","The Gram-Schmidt Process and QR Factorization","Gram-Schmidt turns any basis into an orthogonal one by repeatedly subtracting off projections onto the span already built. Normalizing the result and recording the coefficients factors the matrix as A = QR, with Q orthonormal and R upper triangular, the factorization behind stable least-squares and eigenvalue algorithms.\n",{"path":17176,"title":17177,"module":17165,"summary":17178},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-problems","Least-Squares Problems","When Ax = b has no solution, the least-squares solution makes Ax as close to b as possible. The closest Ax is the projection of b onto the column space, and the vector that produces it solves the normal equations A-transpose A x = A-transpose b. Uniqueness, the residual error, and the stabler QR route follow.\n",{"path":17180,"title":17181,"module":17165,"summary":17182},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Fleast-squares-applications","Applications to Linear Models","Curve fitting is a least-squares problem in statistical notation. The least-squares line, polynomial fits, and multiple regression all reduce to X beta = y with a design matrix X built from the data, solved by the same normal equations.\n",{"path":17184,"title":17185,"module":17165,"summary":17186},"\u002Flinear-algebra\u002Forthogonality-least-squares\u002Finner-product-spaces","Inner Product Spaces","Promoting the four properties of the dot product to axioms defines an inner product on any vector space, including spaces of functions. Length, distance, orthogonality, Gram-Schmidt, and best approximation all carry over, along with the Cauchy-Schwarz and triangle inequalities and the integral inner product behind Fourier approximation.\n",{"path":17188,"title":17189,"module":17190,"summary":17191},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fdiagonalizing-symmetric-matrices","Diagonalization of Symmetric Matrices","Symmetric Matrices, Quadratic Forms, and the SVD","A symmetric matrix is one that equals its own transpose. Every such matrix can be diagonalized by an orthogonal change of basis, A = PDPᵀ, with real eigenvalues and perpendicular eigenvectors. This is the Spectral Theorem, and it rewrites A as a weighted sum of rank-one projections onto its eigenvectors.\n",{"path":17193,"title":17194,"module":17190,"summary":17195},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fquadratic-forms","Quadratic Forms","A quadratic form xᵀAx is the second-degree analogue of a linear map, attached to a symmetric matrix A. Orthogonal diagonalization changes variables to the eigenbasis, removing all cross-terms and rotating the form into standard position. The signs of the eigenvalues then classify it as definite or indefinite.\n",{"path":17197,"title":17198,"module":17190,"summary":17199},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fconstrained-optimization","Constrained Optimization","Maximizing a quadratic form xᵀAx over the unit sphere has an exact answer: the maximum is the largest eigenvalue of A, attained at its eigenvector, and the minimum is the smallest eigenvalue. Adding orthogonality constraints peels off the eigenvalues in order, characterizing the whole spectrum by optimization.\n",{"path":17201,"title":17202,"module":17190,"summary":17203},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsingular-value-decomposition","The Singular Value Decomposition","The singular value decomposition factors any m×n matrix as A = UΣVᵀ, with orthogonal U and V and a nonnegative diagonal Σ of singular values. The singular values are the square roots of the eigenvalues of AᵀA, and they describe the matrix geometrically as a rotation, an axiswise stretch, and another rotation, exposing rank, the four fundamental subspaces, and a best low-rank approximation.\n",{"path":17205,"title":17206,"module":17190,"summary":17207},"\u002Flinear-algebra\u002Fsymmetric-quadratic-svd\u002Fsvd-applications-pca-imaging","Applications: Image Processing and Statistics","Principal component analysis diagonalizes the covariance matrix of a data set, producing uncorrelated variables ordered by variance. The leading components capture most of the variation, which reduces dimension, compresses images through low-rank SVD approximation, and connects directly to the singular values of the data matrix.\n",{"path":17209,"title":17210,"module":17211,"summary":17212},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-thinking-and-matrix-computation","Numerical Thinking and Matrix Computation","Numerical Linear Algebra","Numerical analysis builds efficient discrete algorithms for continuous problems, and its cost is dominated as much by memory traffic as by arithmetic. Block matrix calculus, flop counts, and the BLAS efficiency ratio fix the cost model; triangular and unitary matrices are the two computational building blocks every factorization rests on.\n",{"path":17214,"title":17215,"module":17211,"summary":17216},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Flu-and-cholesky","LU and Cholesky Factorization in Practice","Gaussian elimination, read as a factorization A = LU, turns a linear system into two triangular solves. A single near-zero pivot wrecks it, so partial pivoting reorders rows to pick the largest available pivot and makes the method work for every invertible matrix. For symmetric positive-definite systems, Cholesky halves the cost and needs no pivoting.\n",{"path":17218,"title":17219,"module":17211,"summary":17220},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fconditioning-and-floating-point","Conditioning and Floating-Point Arithmetic","A problem's condition number measures how much its answer moves when its data is perturbed, independent of any algorithm. Subtraction is ill-conditioned under cancellation, and for a linear system the amplifier is the matrix condition number κ(A). Floating-point arithmetic supplies the perturbation: every real number is rounded to within a relative machine precision, so even perfect computation inherits an error of order κ times the unit roundoff.\n",{"path":17222,"title":17223,"module":17211,"summary":17224},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fstability-and-error-analysis","Numerical Stability and Backward Error Analysis","An algorithm is backward stable when its computed answer is the exact answer to a slightly perturbed problem. Combined with the condition number this gives the governing rule of thumb: forward error is at most condition times stability. Three cancellation case studies make the point, then the residual-based backward error applies it to Ax = b and shows why partial pivoting keeps Gaussian elimination stable.\n",{"path":17226,"title":17227,"module":17211,"summary":17228},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fqr-and-numerical-least-squares","QR, Householder, and Numerical Least Squares","The least-squares problem reduces to the normal equations, but forming AᵀA squares the condition number and can wreck accuracy. The stable route computes a QR factorization directly on A and solves Rx = Qᵀb. Householder reflectors build that QR one column at a time using length-preserving reflections, the unconditionally backward-stable building block behind every serious least-squares solver.\n",{"path":17230,"title":17231,"module":17211,"summary":17232},"\u002Flinear-algebra\u002Fnumerical-linear-algebra\u002Fnumerical-eigenvalues-and-svd","Numerical Eigenvalue Problems and the SVD","Eigenvalues cannot be found by a formula for large matrices, so they are found by iteration. Power and inverse iteration converge to one eigenvector at a rate set by the eigenvalue gap; the QR algorithm sweeps a matrix to Schur form and, with a good shift and a Hessenberg reduction, computes the whole spectrum in cubic time. Singular values follow from the same machinery applied without ever forming AᵀA.\n",{"path":17234,"title":17235,"module":17236,"summary":17237},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-combinations","Affine Combinations","Geometry of Vector Spaces","An affine combination is a linear combination whose weights sum to one. The affine hull of a set is the smallest flat containing it: a point, a line, a plane, or a translated subspace. Homogeneous coordinates turn every affine combination into an ordinary linear combination one dimension up.\n",{"path":17239,"title":17240,"module":17236,"summary":17241},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Faffine-independence-and-barycentric-coordinates","Affine Independence and Barycentric Coordinates","Affine independence is linear independence for the translated or lifted points, and it guarantees each point of an affine hull a unique weight vector. Those weights are barycentric coordinates: centers of mass, ratios of triangle areas, and the interpolation rule behind smooth shading in computer graphics.\n",{"path":17243,"title":17244,"module":17236,"summary":17245},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fconvex-combinations-and-convex-sets","Convex Combinations and Convex Sets","A convex combination is an affine combination with nonnegative weights, and the convex hull of a set is the smallest convex set containing it. Convex sets are closed under intersection, and Carathéodory's theorem bounds how many points a convex combination in $\\mathbb{R}^n$ ever needs: at most $n+1$.\n",{"path":17247,"title":17248,"module":17236,"summary":17249},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fhyperplanes-and-polytopes","Hyperplanes and Polytopes","A hyperplane is a level set of a linear functional, the set where an inner product equals a constant. Hyperplanes separate disjoint convex sets and support them at their boundaries. Polytopes are convex hulls of finite point sets; their vertices are the extreme points, and a linear functional attains its extremes there.\n",{"path":17251,"title":17252,"module":17236,"summary":17253},"\u002Flinear-algebra\u002Fgeometry-of-vector-spaces\u002Fcurves-and-surfaces","Curves and Surfaces","Bézier curves are affine combinations of control points with polynomial weights, so they lie in the convex hull of those points and bend toward them. The de Casteljau algorithm evaluates them by repeated interpolation, a matrix form factors them for computation, and matching endpoints and tangents joins segments into smooth curves and surfaces.\n",{"path":17255,"title":17256,"module":6,"summary":6},"\u002Flinear-algebra","Linear Algebra",{"path":17258,"title":17259,"module":6,"summary":6},"\u002Ftheory-of-computation","Theory of Computation",{"path":17261,"title":17262,"module":16062,"summary":17263},"\u002Fcomputer-architecture\u002Ffoundations\u002Fbits-bytes-and-words","Bits, Bytes, and Words","Everything a machine stores is a string of bits grouped into bytes. We set out binary and hexadecimal, the byte as the unit of addressing, the word as the machine's natural integer size, and byte ordering — why the same four bytes read as 0x01234567 on one machine and 0x67452301 on another.\n",{"path":17265,"title":17266,"module":16062,"summary":17267},"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-representation","Integer Representation","A fixed-width byte string is just a pattern; what makes it a number is the rule we read it by. We define unsigned encoding and two's complement — where the top bit carries a negative weight — derive the ranges UMax, TMin, and TMax, and show how the same bits reinterpret between signed and unsigned, how widening sign-extends, and what truncation throws away.\n",{"path":17269,"title":17270,"module":16062,"summary":17271},"\u002Fcomputer-architecture\u002Ffoundations\u002Finteger-arithmetic","Integer Arithmetic","Fixed-width integer arithmetic is arithmetic modulo a power of two: add past the top and the result wraps. We work out unsigned and two's-complement addition and the rules that detect their overflow, why negation is a complement-plus-one, how multiplication truncates to the low-order bits and how compilers turn constant multiplies into shifts and adds, why C declares signed overflow undefined, and the bias fix that keeps shift-based signed division rounding toward zero.\n",{"path":17273,"title":17274,"module":16062,"summary":17275},"\u002Fcomputer-architecture\u002Ffoundations\u002Ffloating-point","Floating Point","IEEE-754 trades the exactness of integers for enormous range by storing numbers as sign, exponent, and fraction — scientific notation in binary. We lay out the single and double formats, the bias that encodes the exponent, the three regimes (normalized, denormalized, special), a worked encode\u002Fdecode, the four rounding modes and round-to-even at the bit level, why addition is not associative, the pitfalls of float-int conversion, and why 0.1 has no exact binary representation.\n",{"path":17277,"title":17278,"module":16062,"summary":17279},"\u002Fcomputer-architecture\u002Ffoundations\u002Fboolean-algebra-and-bit-manipulation","Boolean Algebra and Bit Manipulation","Treat a word as a vector of independent bits and the bitwise operators become an algebra. We define AND, OR, NOT, and XOR as bit vectors, build the masking idioms that set, clear, toggle, and test individual bits, extract fields with zero- and sign-extension, count set bits three ways, derive the classic x & (x - 1) family of tricks, and distinguish bitwise operators from C's short-circuiting logical operators.\n",{"path":17281,"title":17282,"module":17283,"summary":17284},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fthe-machines-view","The Machine's View","Machine-Level Programming","The instruction set architecture is the contract a compiler writes against: the program counter, sixteen integer registers with their sub-register widths, and the condition codes. We follow one C function down through gcc to assembly, learn to read an instruction as operation plus operands, and fix the vocabulary the rest of the module uses.\n",{"path":17286,"title":17287,"module":17283,"summary":17288},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fdata-movement","Data Movement","Most instructions a program runs simply move data. We cover the mov family and its size suffixes, the three operand forms, the full memory addressing mode D(Rb,Ri,S) and its special cases, lea for address arithmetic, and how push and pop manipulate the stack pointer %rsp on a stack that grows toward lower addresses.\n",{"path":17290,"title":17291,"module":17283,"summary":17292},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farithmetic-and-logic","Arithmetic and Logic","The ALU instructions that compute on register and memory values: add, sub, and imul; the unary inc\u002Fdec\u002Fneg\u002Fnot; the shifts sal\u002Fshr\u002Fsar; the bitwise and\u002For\u002Fxor; and lea reused as a fast arithmetic trick. Each binary operation also sets the condition-code flags CF, ZF, SF, and OF, which cmp and test compute without keeping a result.\n",{"path":17294,"title":17295,"module":17283,"summary":17296},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fcontrol-flow","Control Flow","How a flat instruction stream realizes branches and loops. The conditional jumps read the condition-code flags; set instructions turn flags into a 0\u002F1 byte. We translate if\u002Felse into the standard compare-and-branch pattern, while\u002Ffor loops into the guarded-do form, and dense switches into jump tables that index a target directly.\n",{"path":17298,"title":17299,"module":17283,"summary":17300},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fprocedures","Procedures","How a function call works at the machine level: the run-time stack, call and ret passing control through a saved return address, the System V convention that routes the first six arguments through %rdi..%r9 and the result through %rax, the caller-saved versus callee-saved split, the stack frame, and a recursive factorial traced through its frames.\n",{"path":17302,"title":17303,"module":17283,"summary":17304},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Farrays-structs-and-alignment","Arrays, Structs, and Alignment","How aggregate data lays out in memory. Arrays as base-plus-scaled-index, the row-major ordering of multidimensional arrays, pointer arithmetic in units of the pointed-to type, struct fields at fixed byte offsets, the overlapping storage of unions, and the alignment rules that force padding into a struct.\n",{"path":17306,"title":17307,"module":17283,"summary":17308},"\u002Fcomputer-architecture\u002Fmachine-level-x86-64\u002Fmemory-layout-and-buffer-overflows","Memory Layout and Buffer Overflows","The process address space — text, data, heap, and stack — and the classic vulnerability it enables. A stack buffer that is written past its end can overwrite the saved return address and redirect ret, so we sketch the mechanism defensively and then the three standard protections: stack canaries, a non-executable stack, and address-space layout randomization.\n",{"path":17310,"title":17311,"module":17312,"summary":17313},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fwhat-an-isa-is","What an ISA Is","Instruction Set Architecture","The instruction set architecture is the contract that lets a compiler and a chip be written by people who never meet: the stable interface software targets and hardware implements. We separate architecture from microarchitecture, read RISC and CISC as opposite answers to where complexity should live, price out what each choice costs in decode hardware, code density, and pipeline friendliness, and see how x86-64 endures by translating its instructions into RISC-like operations on the fly.\n",{"path":17315,"title":17316,"module":17312,"summary":17317},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Finstruction-formats-and-operands","Instruction Formats and Operands","An instruction is an opcode plus a way to name its operands. We count operands — 3-address, 2-address, 1-address accumulator, and 0-address stack machines — by writing the same C = A + B four ways, weigh register operands against memory operands, then lay out the same add byte by byte in x86-64 (REX prefix, opcode, ModRM) and in Y86-64, and what fixed versus variable length costs at fetch time.\n",{"path":17319,"title":17320,"module":17312,"summary":17321},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Faddressing-modes","Addressing Modes","Once an operand field exists, it needs a rule for turning its bits into the data it names. That rule is the addressing mode. We walk the standard set — immediate, register, direct, register-indirect, displacement, scaled-indexed, and PC-relative — fixing the effective-address computation for each, run every mode against one concrete machine state, and price out what Y86-64 loses by keeping only base plus displacement.\n",{"path":17323,"title":17324,"module":17312,"summary":17325},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fthe-y86-64-instruction-set","The Y86-64 Instruction Set","Y86-64 is a teaching ISA — a stripped-down x86-64 simple enough to implement by hand yet real enough to compile to. We fix its programmer-visible state (fifteen registers, three condition codes, the PC, memory, and a status code), give the instruction set with exact byte encodings, spell out how the condition codes decide every jXX and cmovXX, and run the encoding both directions: assembly to bytes and raw bytes back to meaning.\n",{"path":17327,"title":17328,"module":17312,"summary":17329},"\u002Fcomputer-architecture\u002Finstruction-set-architecture\u002Fy86-64-programming","Y86-64 Programming","With the encodings fixed, we write real Y86-64 assembly: the .pos, .align, and .quad directives, the calling convention borrowed from x86-64, a stack set up by hand, and complete programs — an array sum and a branch-free max. We watch the assembler turn the listing into the exact byte image the processor will execute, and trace the stack across the call.\n",{"path":17331,"title":17332,"module":17333,"summary":17334},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Ftransistors-gates-and-boolean-functions","Transistors, Gates, and Boolean Functions","Digital Logic","A processor is built from millions of transistor switches. We start at the MOS transistor as a voltage-controlled switch, build the CMOS inverter and NAND transistor by transistor, meet the seven standard gates with their truth tables, show that NAND alone is functionally complete, price each gate in transistors and in time, and turn any truth table into a sum-of-products circuit.\n",{"path":17336,"title":17337,"module":17333,"summary":17338},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fcombinational-logic-and-hcl","Combinational Logic and HCL","A combinational circuit is a pure Boolean function of its current inputs — no memory, no clock. We draw the line between combinational and sequential logic, do the gate-delay accounting that finds a circuit's critical path and bounds the clock, meet don't-cares, then introduce CS:APP's Hardware Control Language: bit-level operators, word-level signals, equality nets, and the case expression that compiles to a multiplexer tree.\n",{"path":17340,"title":17341,"module":17333,"summary":17342},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmultiplexers-decoders-and-the-alu","Multiplexers, Decoders, and the ALU","The combinational building blocks that make a datapath. We build the 2:1 and 4:1 multiplexer and tie it back to HCL's case expression, the n-to-2^n decoder, a one-bit full adder (sum is XOR, carry is majority), the ripple-carry adder that chains them, and finally the ALU — a function unit that selects among add, sub, and, and xor under a control input and exposes condition flags.\n",{"path":17344,"title":17345,"module":17333,"summary":17346},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fmemory-elements-latches-flip-flops-and-clocking","Memory Elements: Latches, Flip-Flops, and Clocking","A combinational circuit holds no state; feeding a circuit's output back to its input creates memory. We build the SR latch from cross-coupled gates, the level-sensitive D latch, and the master\u002Fslave edge-triggered D flip-flop, then introduce the clock and the synchronous design discipline, the setup\u002Fhold timing window, clock skew, metastability, and the register as n flip-flops sharing one clock.\n",{"path":17348,"title":17349,"module":17333,"summary":17350},"\u002Fcomputer-architecture\u002Fdigital-logic\u002Fregister-files-and-random-access-memory","Register Files and Random-Access Memory","Storage organized for access by address. We build the register file (a small bank of registers with addressed read ports and clocked write ports, the exact structure Y86-64's decode and write-back stages use), then descend to the SRAM and DRAM cells of main memory, why one is fast and dear and the other dense and slow, and how a row decoder picks a word out of a memory array.\n",{"path":17352,"title":17353,"module":17354,"summary":17355},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-fetch-decode-execute-cycle","The Fetch-Decode-Execute Cycle","Processor Design","A processor is a machine that repeats one loop forever: read the next instruction from memory, figure out what it asks for, do it, and advance. We fix the stored-program idea, lay out the datapath at a high level — PC, instruction memory, register file, ALU, data memory — and the control unit that sequences them, break the work into the six stages the rest of the module builds in hardware, and work out exactly how fetch parses variable-length instructions and computes the next PC.\n",{"path":17357,"title":17358,"module":17354,"summary":17359},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fthe-seq-stages","The SEQ Stages","The six SEQ stages, made exact. For every Y86-64 instruction — halt, nop, the moves, OPq, the jumps, call and ret, pushq and popq — we write down what Fetch, Decode, Execute, Memory, Write-back, and PC update each compute, as per-instruction stage tables with every row justified. Once the tables are filled in, the processor is fully specified; the remaining lessons turn them into wires.\n",{"path":17361,"title":17362,"module":17354,"summary":17363},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fcontrol-logic-and-sequencing","Control Logic and Sequencing","The stage tables say what each instruction needs; the control logic computes it from icode. We write the HCL for the register-port selections (srcA, srcB, dstE, dstM), the ALU function and input selection, the memory read\u002Fwrite and address, the branch condition, and the next-PC mux — each a case expression on icode that compiles to a mux — and see how one blob of combinational logic serves every instruction at once. We close by contrasting hardwired control with the microprogrammed alternative.\n",{"path":17365,"title":17366,"module":17354,"summary":17367},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Fassembling-seq","Assembling SEQ","We wire the whole thing together. The functional units from digital logic and the control signals from the last lesson assemble into the complete SEQ datapath, laid out the way CS:APP draws it — six stages stacked bottom to top, Fetch at the floor and PC update at the ceiling, signals flowing up the margins. Then the timing analysis: why everything must settle in one cycle, the no-reading-back principle that makes single-cycle execution consistent, and the critical path that sets the clock. We close by walking an OPq and a ret through the assembled machine.\n",{"path":17369,"title":17370,"module":17354,"summary":17371},"\u002Fcomputer-architecture\u002Fprocessor-design\u002Ftracing-a-program","Tracing a Program","To close the module, we take a complete Y86-64 program — a loop that sums 1 through 3 — and run it through SEQ one cycle at a time, recording the PC, the fetched instruction, every stage computation, and the registers, condition codes, and memory after each cycle. Then we examine single cycles in detail: every named signal of an OPq in concrete hex, and a second program whose call and ret we trace through the stack. The traces confirm that the assembled datapath and control logic behave as a processor.\n",{"path":17373,"title":17374,"module":17375,"summary":17376},"\u002Fcomputer-architecture\u002Fpipelining\u002Fpipelining-principles","Pipelining Principles","Pipelining","A processor that runs one instruction to completion before starting the next wastes most of its hardware most of the time. Pipelining splits the work into stages separated by registers so several instructions are in flight at once. We separate throughput from latency, work the 300 ps example through one, two, and three stages, and derive the three ceilings on the gain: uneven stages, register overhead, and the dependencies between instructions.\n",{"path":17378,"title":17379,"module":17375,"summary":17380},"\u002Fcomputer-architecture\u002Fpipelining\u002Ffrom-seq-to-pipe","From SEQ to PIPE","We turn the sequential Y86-64 processor into a pipelined one by inserting pipeline registers between its stages so each cycle holds one instruction per stage. Doing it correctly forces a rearrangement: the next-PC computation must move into Fetch as a prediction, because the later stages that used to compute it are now busy with other instructions. We walk SEQ to SEQ+ to PIPE, spell out exactly what each pipeline register carries, and fix the naming discipline (D_stat versus d_stat) that keeps five in-flight instructions straight.\n",{"path":17382,"title":17383,"module":17375,"summary":17384},"\u002Fcomputer-architecture\u002Fpipelining\u002Fdata-hazards-stalling-and-forwarding","Data Hazards: Stalling and Forwarding","Overlapping instructions collide when a later one needs a value an earlier one has not finished computing: a read-after-write data hazard. We map exactly which instruction distances are dangerous, fix hazards the slow way by stalling (three bubbles), then the fast way by forwarding from five distinct sources into Decode, in a priority order that sequential semantics forces. Forwarding handles almost everything; the load-use hazard still needs exactly one stall.\n",{"path":17386,"title":17387,"module":17375,"summary":17388},"\u002Fcomputer-architecture\u002Fpipelining\u002Fcontrol-hazards-and-branch-prediction","Control Hazards and Branch Prediction","A pipeline must fetch an instruction every cycle, but after a conditional jump or a ret the next address is not yet known: a control hazard. We measure the branch penalty, weigh predict-taken against its alternatives with real loop arithmetic, watch PIPE detect a misprediction in Execute and squash the two wrong-path instructions, and meet the ret hazard, which has nothing to predict and stalls three cycles. A 2-bit counter gives a taste of dynamic prediction.\n",{"path":17390,"title":17391,"module":17375,"summary":17392},"\u002Fcomputer-architecture\u002Fpipelining\u002Fthe-complete-pipe-processor","The Complete PIPE Processor","We assemble the full pipelined Y86-64: five stages, five pipeline registers, forwarding paths, and a small control unit that decides, each cycle, whether to stall or bubble each register. The subtle part is when hazards combine: one pairing hides a genuine bug. A fourth control case reads stat and keeps exceptions precise. Performance reduces to CPI = 1 + lp + mp + rp, worked out to 1.27 with realistic frequencies, and PIPE beats SEQ by several times despite every penalty.\n",{"path":17394,"title":17395,"module":17396,"summary":17397},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fstorage-technologies-and-the-latency-gap","Storage Technologies and the Latency Gap","The Memory Hierarchy","No single memory is both fast and large and cheap. We survey the technologies a machine can store bits in — SRAM, DRAM, flash, and rotating disk — open up a DRAM chip to find the row buffer, work a disk access down to the millisecond, and rank everything by speed, density, and cost per bit. Then we watch the processor outrun memory decade after decade. That widening gap is the whole reason a machine stacks fast small storage on top of slow large storage into a hierarchy.\n",{"path":17399,"title":17400,"module":17396,"summary":17401},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Flocality","Locality","A hierarchy only pays off because programs do not touch memory at random. They reuse recently-used data (temporal locality) and touch nearby data soon after (spatial locality). We make both precise and then quantitative: miss rates for stride-1 and stride-k traversals against a concrete block size, and the loop-order pair on a 2-D array where the same sum misses 16 times one way and 64 times the other — why row-major versus column-major order can change a program's speed by an order of magnitude.\n",{"path":17403,"title":17404,"module":17396,"summary":17405},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-memories-direct-mapped","Cache Memories and Direct Mapping","A cache is fast SRAM that holds copies of recently-used blocks of main memory. We fix its organization — S sets, E lines per set, B bytes per block — and the way it dissects an address into tag, set index, and block offset, worked bit by bit on a concrete 16-byte cache. Then we run the direct-mapped (E=1) access algorithm end to end on a seven-access trace: index to a set, compare the tag, hit or miss, evict. Cold and conflict misses fall out of the structure, and a two-array ping-pong shows conflict thrashing and its padding fix.\n",{"path":17407,"title":17408,"module":17396,"summary":17409},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fset-associative-and-write-policies","Set-Associative Caches and Write Policies","Give each set several lines and a block has a choice of homes — fewer conflict misses, at the cost of comparing E tags in parallel and choosing a victim to evict. We re-run the direct-mapped ping-pong trace on a 2-way cache and watch the conflicts vanish, weigh LRU against random replacement, then turn to writes: write-through versus write-back with a dirty bit on a hit, write-allocate versus no-write-allocate on a miss, and a worked traffic count showing when each pairing wins.\n",{"path":17411,"title":17412,"module":17396,"summary":17413},"\u002Fcomputer-architecture\u002Fmemory-hierarchy\u002Fcache-performance-and-cache-friendly-code","Cache Performance and Cache-Friendly Code","Turn the cache mechanism into a number. Hit time, miss rate, and miss penalty combine into the average memory access time; we compute AMAT for a two-level hierarchy with real numbers, weigh the design knobs against each other, and read the memory mountain. Then we write cache-friendly code — the matrix-multiply loop-order case study (ijk versus kij, misses counted per iteration) and loop blocking, where cache-sized tiles turn evicted reuse back into hits.\n",{"path":17415,"title":17416,"module":17417,"summary":17418},"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Faddress-spaces-and-translation","Address Spaces and Translation","Virtual Memory","Every process runs as if it owns a private, contiguous span of memory — its virtual address space — while the hardware maps those addresses onto a single shared physical memory. We fix virtual memory's three jobs (a cache for disk, a memory manager, a protection boundary), the page as the unit of mapping, and the MMU replacing the virtual page number while the offset passes through untouched — then run one translation end to end at the bit level and trace the control flow of a page hit against a page fault.\n",{"path":17420,"title":17421,"module":17417,"summary":17422},"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fpage-tables-and-page-faults","Page Tables and Page Faults","The page table is an array of page-table entries indexed by virtual page number; each entry's valid bit says whether the page is in DRAM, on disk, or unallocated, and its permission, reference, and dirty bits drive protection and replacement. We walk translation as a table lookup, the page fault and demand paging, the clock algorithm the OS uses to approximate LRU, memory mapping and copy-on-write (why fork is cheap), the taxonomy of bad references, and thrashing.\n",{"path":17424,"title":17425,"module":17417,"summary":17426},"\u002Fcomputer-architecture\u002Fvirtual-memory\u002Fthe-tlb-and-multi-level-page-tables","The TLB and Multi-Level Page Tables","A page-table read on every access would double memory traffic; a flat table for a 48-bit space would occupy 512 GB per process. The TLB fixes the first: a small set-associative cache of PTEs inside the MMU whose tag and index come from the VPN. Multi-level page tables fix the second, allocating only the sub-tables a process uses; x86-64 walks four levels with a 9+9+9+9+12 split. We trace one reference end to end through TLB, walk, and cache, and close with the overlap trick that lets the L1 cache start before translation ends.\n",{"path":17428,"title":17429,"module":17430,"summary":17431},"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Fexceptional-control-flow","Exceptional Control Flow","Exceptions & I\u002FO","Beyond the sequential, branch, and call flow a program controls itself, the hardware can divert the processor in response to events. We sort these into four classes — interrupts (asynchronous, from devices), traps (intentional syscalls), faults (recoverable, like a page fault), and aborts (unrecoverable) — then take the mechanism apart: exception numbers and the table dispatch, what the hardware pushes and why it differs from a procedure call, the divide-error \u002F page-fault \u002F general-protection trio on x86-64, the full syscall round trip with a worked write in assembly, and processes and signals as the abstractions ECF makes possible.\n",{"path":17433,"title":17434,"module":17430,"summary":17435},"\u002Fcomputer-architecture\u002Fexceptions-and-io\u002Finterrupts-and-the-kernel","Interrupts and the Kernel","An I\u002FO device signals completion by raising an interrupt, crossing the privilege boundary from user mode into the kernel. We fix that boundary, follow an interrupt from device through the interrupt controller to its vectored handler, and use the timer interrupt to drive preemptive scheduling and the context switch. Then the I\u002FO mechanics: polling versus interrupt-driven I\u002FO with a cycle count, device registers and memory-mapped I\u002FO versus port I\u002FO, DMA's full transfer walkthrough and its cache hazard, and a disk read traced end to end, from the read syscall to the completion interrupt.\n",{"path":17437,"title":17438,"module":17439,"summary":17440},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fprocesses-threads-and-parallelism","Processes, Threads, and Parallelism","Multithreading & Multicore","Around 2004 the single core stopped getting faster, and the industry's answer was to hand programmers more cores instead. This lesson builds the vocabulary that shift demands: process versus thread and exactly which hardware state each one owns, concurrency versus parallelism, the three kinds of parallelism a machine can exploit, why Dennard scaling ended and forced the multicore turn, and Amdahl's law — the arithmetic that bounds the speedup those cores can deliver.\n",{"path":17442,"title":17443,"module":17439,"summary":17444},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fhardware-multithreading","Hardware Multithreading","A pipeline spends much of its life waiting — on cache misses, on dependences, on branches. Hardware multithreading fills the dead cycles with instructions from another thread. We compare coarse-grained switching (change threads on a long stall), fine-grained interleaving (change every cycle), and simultaneous multithreading (mix threads inside a single cycle), work out exactly which hardware a second thread context duplicates and which it shares, and weigh when SMT pays off and when two threads just fight over one cache.\n",{"path":17446,"title":17447,"module":17439,"summary":17448},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fcache-coherence","Cache Coherence","Give each core its own cache and the same address can live in two places at once, with copies that disagree. We reproduce the stale-copy bug with a two-core trace, then fix it the way hardware does: snooping caches that watch a shared bus and keep every line in a protocol state. We build MSI in full, upgrade it to MESI, contrast invalidation with updating, add coherence misses as the fourth C, and end with false sharing: the performance bug where cores fight over a line while never touching the same byte.\n",{"path":17450,"title":17451,"module":17439,"summary":17452},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmemory-consistency-and-synchronization","Memory Consistency and Synchronization","Coherence keeps cores agreeing about one location; consistency is the contract about many. We define sequential consistency, then watch real hardware break it: the store buffer lets a load slip ahead of an older store, and the classic two-thread litmus test ends with both sides reading zero. We state x86-TSO precisely, restore order with mfence, build atomic read-modify-write from the lock prefix, xchg, and cmpxchg, and write a spinlock twice — once naively, once bus-friendly — closing with what lock-free progress actually guarantees.\n",{"path":17454,"title":17455,"module":17439,"summary":17456},"\u002Fcomputer-architecture\u002Fmultithreading-and-multicore\u002Fmulticore-organization","Multicore Organization","Where everything sits on the die. A modern die gives each core private L1 and L2 caches, spreads a shared last-level cache across slices, and wires it all together with a ring or mesh; multi-socket servers add NUMA, where memory is local to one socket and every remote access pays a latency penalty. We walk the floorplan, put numbers on local versus remote latency, meet thread affinity, and account for the two shared resources — coherence traffic and LLC capacity — that decide how far a parallel program scales.\n",{"path":17458,"title":17459,"module":17460,"summary":17461},"\u002Fcomputer-architecture\u002Fcapstone\u002Fthe-whole-machine","The Whole Machine","Capstone","We take one line of C down the whole tower the course built — compiler to assembly, assembly to machine-code bytes, the bytes into the fetch–decode–execute datapath — then trace one load and one add through the pipelined, cached, translated, interruptible machine, each step cross-linked to the lesson that built it. We close with the map of the course as a stack of layers and an accounting of what we simplified: out-of-order execution, superscalar issue, and speculation past the branch predictor.\n",{"path":17463,"title":17464,"module":17460,"summary":17465},"\u002Fcomputer-architecture\u002Fcapstone\u002Fassembling-a-complete-cpu","Assembling a Complete CPU","We bolt the parts the course built — PC, instruction memory and its fetch logic, register file, ALU, condition codes, data memory, and the control unit — into one complete CPU, name the lesson that built each, wire them in a deliberate order, and power the machine on from reset. Then we assemble a real test program (sum a four-element array through a call\u002Fret procedure), give its exact bytes and memory layout, and trace it cycle by cycle to the answer 0xabcdabcdabcd. We close with how to validate such a machine, and what it takes to put two of them on one die.\n",{"path":17467,"title":17468,"module":6,"summary":6},"\u002Fcomputer-architecture","Computer Architecture",{"path":17470,"title":17471,"module":16062,"summary":17472},"\u002Fdifferential-equations\u002Ffoundations\u002Fmodels-and-direction-fields","Models, Direction Fields, and Solution Curves","A differential equation relates an unknown function to its own rates of change. Three first-order models — a falling body, a cooling object, a population under predation — share the form dy\u002Fdt = ay - b; the slope field fixes their equilibria and long-run behavior before any formula is found. Solving the linear case gives the general solution, its integral curves, and the particular solution selected by an initial condition.\n",{"path":17474,"title":17475,"module":16062,"summary":17476},"\u002Fdifferential-equations\u002Ffoundations\u002Fclassification-and-terminology","Classifying Equations: Order, Linearity, ODE vs. PDE","Every solution method targets a specific class of equation, so the first question about any differential equation is which classes it belongs to. Four independent axes sort them: ordinary versus partial, order, linear versus nonlinear, and homogeneous versus nonhomogeneous. Systems, verification of a solution by substitution, and the split between initial and boundary value problems complete the vocabulary.\n",{"path":17478,"title":17479,"module":17480,"summary":17481},"\u002Fdifferential-equations\u002Ffirst-order\u002Flinear-first-order-integrating-factors","Linear Equations and Integrating Factors","First-Order Equations","A first-order linear equation has the unknown and its derivative to the first power only. Multiplying by an integrating factor collapses the left side into a single derivative, and one integration gives the general solution in closed form. The solution exists wherever the coefficients are continuous, and for a constant coefficient it splits into a decaying transient and a steady state set by the forcing.\n",{"path":17483,"title":17484,"module":17480,"summary":17485},"\u002Fdifferential-equations\u002Ffirst-order\u002Fseparable-and-exact","Separable and Exact Equations","Two nonlinear first-order classes solve by direct integration. A separable equation splits so that each variable can be integrated on its own side, giving an implicit relation. An exact equation is the total differential of a hidden potential function, recognized by a symmetry test on its coefficients; when the test fails, an integrating factor can sometimes restore exactness. A change of variable brings homogeneous equations into the separable class.\n",{"path":17487,"title":17488,"module":17480,"summary":17489},"\u002Fdifferential-equations\u002Ffirst-order\u002Fmodeling-first-order","Modeling with First-Order Equations","A rate law is a differential equation. Each first-order model starts from one governing principle: conservation of mass for a mixing tank, proportional change for interest and radioactive decay, Newton's law of cooling, a force balance for a body falling against drag, and Kirchhoff's law for a series circuit. Setting the derivative to zero recovers the steady state, and the transient records how the initial condition relaxes toward it.\n",{"path":17491,"title":17492,"module":17480,"summary":17493},"\u002Fdifferential-equations\u002Ffirst-order\u002Fautonomous-and-population-dynamics","Autonomous Equations, Phase Lines, and Population Dynamics","An autonomous equation y' = f(y) can be analyzed qualitatively without being solved. Its constant solutions are the zeros of f, and the sign of f between them fixes whether nearby solutions rise or fall, which the phase line records as a column of arrows. The logistic and threshold models, constant- and effort-proportional harvesting, and the properties nonlinear equations lose all follow from this reading.\n",{"path":17495,"title":17496,"module":17480,"summary":17497},"\u002Fdifferential-equations\u002Ffirst-order\u002Fexistence-uniqueness-euler","Existence, Uniqueness, and Euler's Method","Existence and uniqueness can be settled before any attempt to solve. The existence-uniqueness theorem gives sufficient conditions on f, and a standard example shows what fails when they do not hold. Picard's successive approximations build the solution as the limit of an iteration, and Euler's method turns the same tangent-line idea into a numerical procedure for the equations no formula reaches.\n",{"path":17499,"title":17500,"module":17480,"summary":17501},"\u002Fdifferential-equations\u002Ffirst-order\u002Ffirst-order-difference-equations","First-Order Difference Equations","A difference equation advances a sequence one index at a time by a rule y_{n+1} = f(y_n). The linear case y_{n+1} = rho*y_n + b solves in closed form and converges to its equilibrium exactly when the ratio has magnitude below one, which underlies compound-interest and loan calculations. The logistic difference equation shows the nonlinear counterpart: an exchange of stability, a cascade of period doublings, and the onset of chaos.\n",{"path":17503,"title":17504,"module":17505,"summary":17506},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhomogeneous-constant-coefficients","Homogeneous Equations, the Wronskian, and Real Roots","Second-Order Linear Equations","A second-order linear homogeneous equation with constant coefficients is solved by guessing an exponential and reducing to the quadratic characteristic equation. Two solutions span every solution exactly when their Wronskian is nonzero; that condition, superposition, and Abel's formula give the full structure of the general solution for the case of two distinct real roots.\n",{"path":17508,"title":17509,"module":17505,"summary":17510},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fcomplex-and-repeated-roots","Complex Roots, Repeated Roots, and Reduction of Order","When the characteristic equation has complex conjugate roots, Euler's formula converts the complex exponentials into a real fundamental set of decaying or growing oscillations. When it has a repeated root, one exponential is lost and reduction of order recovers the missing second solution as $t\\,e^{rt}$. The same substitution $y = v(t)y_1(t)$ finds a second solution from any known one.\n",{"path":17512,"title":17513,"module":17505,"summary":17514},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fnonhomogeneous-undetermined-coefficients","Nonhomogeneous Equations: Undetermined Coefficients","The general solution of a nonhomogeneous linear equation is a complementary solution plus any one particular solution. When the forcing term is a polynomial, exponential, sine, or cosine, a particular solution can be found by assuming a trial form of the same shape with unknown coefficients and solving for them. The one complication is resonance, handled by multiplying the trial by a power of $t$.\n",{"path":17516,"title":17517,"module":17505,"summary":17518},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fvariation-of-parameters","Variation of Parameters","Variation of parameters finds a particular solution of any nonhomogeneous linear equation from a fundamental set of the homogeneous one. Replacing the constants in the complementary solution by functions and imposing one convenient constraint reduces the problem to a two-by-two linear system whose solution is expressed through the Wronskian, giving an integral formula that works for forcing terms undetermined coefficients cannot touch.\n",{"path":17520,"title":17521,"module":17505,"summary":17522},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fmechanical-electrical-vibrations","Mechanical and Electrical Vibrations","A spring-mass-damper obeys a second-order linear equation, and so does a series RLC circuit, with the same mathematics governing both. Free undamped motion is a pure sinusoid; damping adds a decaying envelope with three regimes; periodic forcing produces a transient that dies out and a steady-state oscillation whose amplitude peaks sharply near the natural frequency, the phenomenon of resonance.\n",{"path":17524,"title":17525,"module":17505,"summary":17526},"\u002Fdifferential-equations\u002Fsecond-order-linear\u002Fhigher-order-linear","Higher-Order Linear Equations","The second-order theory extends directly to order $n$: the solution space is $n$-dimensional, spanned by any $n$ solutions with nonzero Wronskian. For constant coefficients the characteristic polynomial has degree $n$, and its roots (counted with multiplicity, real and complex) build the basis by the same rules as before. Coupled oscillators are the natural application that raises the order.\n",{"path":17528,"title":17529,"module":17530,"summary":17531},"\u002Fdifferential-equations\u002Fseries-solutions\u002Fpower-series-ordinary-points","Power Series Solutions Near Ordinary Points","Series Solutions and Special Functions","A linear equation with variable coefficients has no characteristic equation. A power series substituted into the equation matches coefficients to a recurrence relation, which near an ordinary point yields two independent analytic solutions. The radius of convergence is at least the distance from the expansion point to the nearest singular point in the complex plane.\n",{"path":17533,"title":17534,"module":17530,"summary":17535},"\u002Fdifferential-equations\u002Fseries-solutions\u002Fregular-singular-frobenius","Euler Equations, Regular Singular Points, and Frobenius","The Euler equation x^2 y'' + a x y' + b y = 0 is solved outright by y = x^r, and its three root cases fix the behavior at any regular singular point. The Frobenius method multiplies x^r by a power series; the indicial equation chooses the exponents, and equal or integer-separated roots force a logarithm in the second solution. Gauss's hypergeometric equation is the archetype containing most classical functions as special cases.\n",{"path":17537,"title":17538,"module":17530,"summary":17539},"\u002Fdifferential-equations\u002Fseries-solutions\u002Fbessel-and-special-functions","Bessel's Equation, Legendre Polynomials, and Special Functions","Bessel's equation puts the Frobenius machinery through all three of its cases and produces the functions J and Y that govern anything vibrating or diffusing with circular symmetry. The gamma function extends the factorial so that Bessel functions of every order make sense; Legendre's equation, run through the hypergeometric form, yields the polynomials that play the same role in spherical geometry. Orthogonality ties both families to the eigenfunction expansions of Sturm–Liouville theory.\n",{"path":17541,"title":17542,"module":17543,"summary":17544},"\u002Fdifferential-equations\u002Flaplace\u002Flaplace-definition-ivps","The Laplace Transform: Definition, Properties, and Solving IVPs","The Laplace Transform","The Laplace transform sends a function of time to a function of a complex frequency by integrating it against the kernel e^{-st}. Differentiation in t becomes multiplication by s, so a linear constant-coefficient initial value problem turns into an algebraic equation. Existence rests on piecewise continuity and exponential order; the derivative rule folds in the initial data; and inversion runs through a transform table and partial fractions.\n",{"path":17546,"title":17547,"module":17543,"summary":17548},"\u002Fdifferential-equations\u002Flaplace\u002Fstep-impulse-convolution","Step Functions, Discontinuous Forcing, Impulses, and Convolution","The Heaviside step function and the second shifting theorem transform switches and discontinuous forcing into exponential factors on the transform. The Dirac delta idealizes an instantaneous impulse and transforms to a pure exponential. The convolution theorem inverts a product of transforms, writes the forced response as the impulse response convolved with the input, and solves Abel's tautochrone by transform.\n",{"path":17550,"title":17551,"module":17552,"summary":17553},"\u002Fdifferential-equations\u002Fsystems\u002Fmatrices-eigenvalues-review","Matrices, Linear Systems, and the Eigenvalue Toolkit","Systems of First-Order Linear Equations","Any nth-order linear equation, and any coupled collection of them, rewrites as a single first-order system x' = P(t)x + g(t). The matrix and vector algebra behind that form, the eigenvalue problem det(A - λI) = 0 that drives every solution method, and the fundamental theory — superposition, the Wronskian, Abel's theorem — together establish that n independent solutions span all solutions.\n",{"path":17555,"title":17556,"module":17552,"summary":17557},"\u002Fdifferential-equations\u002Fsystems\u002Fconstant-coefficient-systems-phase-portraits","Homogeneous Constant-Coefficient Systems and Phase Portraits","For x' = Ax with A constant, the trial x = ξe^{rt} turns the differential equation into the eigenvalue problem Aξ = rξ. The eigenvalues fix the geometry of the phase plane: real opposite signs give a saddle, real same sign a node, complex a spiral, purely imaginary a center. Worked in the plane, these cases form the eigenvalue-type classification of equilibria.\n",{"path":17559,"title":17560,"module":17552,"summary":17561},"\u002Fdifferential-equations\u002Fsystems\u002Frepeated-eigenvalues-fundamental-matrices","Repeated Eigenvalues, Fundamental Matrices, and Nonhomogeneous Systems","When a repeated eigenvalue supplies too few eigenvectors, a generalized eigenvector supplies the missing solution as ξte^{ρt} + ηe^{ρt}, giving an improper node. A fundamental set packaged as a matrix Φ(t) yields the matrix exponential e^{At}, the propagator mapping initial states to later ones. Variation of parameters solves the nonhomogeneous system x' = Ax + g(t).\n",{"path":17563,"title":17564,"module":17565,"summary":17566},"\u002Fdifferential-equations\u002Fnumerical\u002Feuler-and-runge-kutta","Euler, Improved Euler, and Runge–Kutta","Numerical Methods","Most initial value problems have no closed-form solution, so the solution is approximated on a grid. Euler's method steps along the tangent line, the improved Euler method averages two slopes, and the classical Runge–Kutta method averages four. Each added stage raises the order of accuracy at the cost of more evaluations per step, measured by how the local and global truncation errors scale with the step size.\n",{"path":17568,"title":17569,"module":17565,"summary":17570},"\u002Fdifferential-equations\u002Fnumerical\u002Fmultistep-systems-stability","Multistep Methods, Systems, and Stability","One-step methods discard everything but the last point. Multistep methods fit a polynomial to several past values and integrate it forward: the explicit Adams–Bashforth formulas, the implicit and more accurate Adams–Moulton formulas, and predictor–corrector pairs that combine them. The same rules extend verbatim to systems in vector form. A separate concern is stability: round-off can dominate truncation, and stiff equations force a tiny step for stability even when accuracy would allow a large one.\n",{"path":17572,"title":17573,"module":17574,"summary":17575},"\u002Fdifferential-equations\u002Fnonlinear\u002Fphase-plane-autonomous-stability","The Phase Plane, Critical Points, and Stability","Nonlinear Systems and Stability","Most nonlinear systems cannot be solved in closed form, so they are studied geometrically. The phase plane turns an autonomous planar system into a family of trajectories; the five archetypes of critical point follow from the eigenvalues of the coefficient matrix; the trace-determinant plane reads off type and stability directly; and epsilon-delta definitions make stability, asymptotic stability, and instability precise.\n",{"path":17577,"title":17578,"module":17574,"summary":17579},"\u002Fdifferential-equations\u002Fnonlinear\u002Flocally-linear-and-liapunov","Locally Linear Systems and Liapunov's Method","Near a critical point a nonlinear system looks linear, and the linear part is the Jacobian. The linearization fixes the type and stability of the nonlinear critical point in every case except a center or a repeated eigenvalue. Liapunov's direct method settles those cases and bounds the basin of attraction by constructing an energy-like function, without solving the system.\n",{"path":17581,"title":17582,"module":17574,"summary":17583},"\u002Fdifferential-equations\u002Fnonlinear\u002Fcompeting-species-predator-prey-limit-cycles","Population Models, Limit Cycles, and Chaos","The phase-plane methods apply directly to interacting-population models. Competing species either coexist or drive one another to extinction, decided by a single inequality among the interaction constants; the Lotka-Volterra predator-prey system produces closed population cycles. Limit cycles and the Poincaré-Bendixson theorem, the van der Pol oscillator, and the Lorenz equations with their strange attractor carry the theory into chaos.\n",{"path":17585,"title":17586,"module":17587,"summary":17588},"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Ffourier-series","Fourier Series and Convergence","PDEs, Fourier Series, and Boundary Value Problems","A two-point boundary value problem has nontrivial solutions only at a discrete set of eigenvalues, the same trichotomy that governs a singular linear system. For y'' + lambda y = 0 with zero endpoints the eigenfunctions are sines and cosines, and their orthogonality gives the Euler-Fourier coefficient formulas. The convergence theorem fixes when the series returns the function, the Gibbs phenomenon measures the overshoot at a jump, and even\u002Fodd symmetry produces half-range sine and cosine series.\n",{"path":17590,"title":17591,"module":17587,"summary":17592},"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fheat-wave-laplace-equations","Separation of Variables: Heat, Wave, and Laplace Equations","Separation of variables replaces a partial differential equation by a pair of ordinary ones joined through a shared separation constant. Applied to the heat equation it produces the eigenvalue problem X'' + lambda X = 0, and the solution assembles as a Fourier series in the eigenfunctions. The same steps solve the wave equation, whose modes are standing waves, and Laplace's equation, the steady-state limit posed on a region rather than an interval.\n",{"path":17594,"title":17595,"module":17587,"summary":17596},"\u002Fdifferential-equations\u002Fpdes-fourier-bvp\u002Fsturm-liouville","Sturm-Liouville Theory","The eigenvalue problem behind separation of variables generalizes to the self-adjoint Sturm-Liouville form. Lagrange's identity makes the operator symmetric, and from that one fact follow real eigenvalues, orthogonal eigenfunctions, and eigenfunction expansions that behave like Fourier series. Singular problems admit Bessel and Legendre functions, and Sturm's separation and comparison theorems describe how the eigenfunctions oscillate.\n",{"path":17598,"title":17599,"module":17600,"summary":17601},"\u002Fdifferential-equations\u002Fhistory-variations\u002Fcalculus-of-variations","The Calculus of Variations","Historical Notes and the Calculus of Variations","Ordinary calculus finds the point where a function is stationary; the calculus of variations finds the whole curve where an integral is stationary. Euler's differential equation is the necessary condition for an extremal, and it becomes integrable in three cases, solving the shortest-path, minimal-surface, and brachistochrone problems. Lagrange multipliers extend the method to isoperimetric constraints, and Hamilton's principle recovers Newton's law from a single stationary integral.\n",{"path":17603,"title":17604,"module":17600,"summary":17605},"\u002Fdifferential-equations\u002Fhistory-variations\u002Fhistorical-notes","Great Problems and the People Who Solved Them","Differential equations grew out of specific problems, not a plan: the invention of calculus by Newton and Leibniz, the Bernoulli brachistochrone challenge, Euler's flood of methods, Lagrange's analytical mechanics, Gauss and Riemann's rigor, Laplace's celestial mechanics, and Poincaré's qualitative theory. Each method descends from a named problem, and reading the subject forward from those problems explains why its parts fit together.\n",{"path":17607,"title":17608,"module":6,"summary":6},"\u002Fdifferential-equations","Differential Equations",{"path":17610,"title":17611,"module":17612,"summary":17613},"\u002Frelativity\u002Ffoundations\u002Fspecial-relativity-postulates","The Postulates of Special Relativity","Foundations of Relativity","Newton's laws are the same in every inertial frame, but Maxwell's are not: the equations of electromagnetism single out one speed, c, and the nineteenth century read that as the speed of light relative to a medium, the ether. The Michelson-Morley experiment looked for Earth's motion through that medium and found nothing. Einstein's two postulates replace the ether, and their first consequence is that simultaneity is frame-dependent.\n",{"path":17615,"title":17616,"module":17612,"summary":17617},"\u002Frelativity\u002Ffoundations\u002Florentz-transformation-spacetime","The Lorentz Transformation and Spacetime","Requiring that a light sphere stay a light sphere in every inertial frame fixes the coordinate change between frames uniquely: the Lorentz transformation, with its factor gamma. Differentiating it gives relativistic velocity addition, which caps composed speeds at c. Plotting the same events on skewed spacetime axes turns the algebra into geometry, with calibration hyperbolae, an invariant interval, and a light cone that sorts events into past, future, and elsewhere.\n",{"path":17619,"title":17620,"module":17612,"summary":17621},"\u002Frelativity\u002Ffoundations\u002Ftime-dilation-length-contraction","Time Dilation, Length Contraction, and Paradoxes","A light clock and the constancy of c give the two headline effects directly: a moving clock runs slow by gamma, and a moving rod is short by the same factor. Cosmic-ray muons reaching sea level are the standing experimental proof. The relativistic Doppler effect adds the time-dilation factor to the classical shift, and the twin and pole-barn paradoxes dissolve once the relativity of simultaneity is taken seriously.\n",{"path":17623,"title":17624,"module":17612,"summary":17625},"\u002Frelativity\u002Ffoundations\u002Frelativistic-momentum-energy","Relativistic Momentum and Energy","Conserving momentum in every inertial frame forces the redefinition p = gamma m u, which diverges as the speed approaches c. Integrating the corresponding force gives the total energy E = gamma m c-squared, whose rest term m c-squared is Einstein's mass-energy equivalence. Energy and momentum join into a four-vector whose invariant length is the rest energy, giving E-squared = (pc)-squared + (m c-squared)-squared, massless particles, and nuclear binding energy.\n",{"path":17627,"title":17628,"module":17612,"summary":17629},"\u002Frelativity\u002Ffoundations\u002Fgeneral-relativity","A Taste of General Relativity","Einstein's happiest thought was that a freely falling observer feels no gravity: a uniform gravitational field is locally indistinguishable from an accelerating frame. That equivalence principle predicts that light bends near a mass, that clocks run slow deep in a gravitational well, that Mercury's orbit precesses, and that radar echoes are delayed. Every prediction has been confirmed, and pushing the redshift to its limit gives the black hole.\n",{"path":17631,"title":17632,"module":17633,"summary":17634},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fminkowski-spacetime-and-the-interval","Minkowski Spacetime and the Interval","Spacetime and the Lorentz Group","The Lorentz transformation of the foundations module is repackaged as the geometry of a four-dimensional space whose invariant is not a distance but the spacetime interval. Events, worldlines, and the metric signature define a causal structure that every observer shares. Proper time is the length of a timelike worldline, and the twin paradox becomes the statement that a straight worldline accumulates the most proper time.\n",{"path":17636,"title":17637,"module":17633,"summary":17638},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Ffour-vectors-and-index-notation","Four-Vectors and Index Notation","The index calculus that the rest of the course runs on. Contravariant and covariant components, the Minkowski metric as the machine that raises and lowers indices, and the Einstein summation convention are assembled into scalar products that are the same in every frame. The four-velocity and four-acceleration follow, together with the identity that the four-velocity has constant invariant length.\n",{"path":17640,"title":17641,"module":17633,"summary":17642},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fthe-lorentz-group-and-rapidity","The Lorentz Group and Rapidity","The Lorentz transformations are the linear maps that preserve the Minkowski metric, and they form the group O(1,3). Boosts are hyperbolic rotations parametrized by rapidity, which adds along a line where velocity does not. The boost and rotation generators fix the group's local structure; its four disconnected components are set by two signs; and two non-collinear boosts compose into a boost plus a rotation, the Wigner rotation behind Thomas precession.\n",{"path":17644,"title":17645,"module":17633,"summary":17646},"\u002Frelativity\u002Fspacetime-and-the-lorentz-group\u002Fdoppler-aberration-and-appearance","Doppler, Aberration, and Appearance","Light carries a null four-momentum, and boosting it produces every optical effect of relativity at once. The covariant Doppler formula follows from the transformation of frequency, aberration from the transformation of direction, and the headlight effect from the resulting concentration of light forward. The Terrell-Penrose result shows that a fast object photographs as rotated, not contracted.\n",{"path":17648,"title":17649,"module":17650,"summary":17651},"\u002Frelativity\u002Frelativistic-dynamics\u002Ffour-momentum-force-and-accelerated-motion","Four-Momentum, Four-Force, and Accelerated Motion","Relativistic Dynamics","The four-momentum packages energy and momentum into a single vector whose invariant length is the rest mass. Its proper-time derivative is the four-force, always orthogonal to the four-velocity, and a constant orthogonal four-force produces hyperbolic motion. Constant proper acceleration gives rapidity linear in proper time, the relativistic rocket equation, and the Rindler horizon behind an eternally accelerating observer.\n",{"path":17653,"title":17654,"module":17650,"summary":17655},"\u002Frelativity\u002Frelativistic-dynamics\u002Fparticle-decays-and-two-body-kinematics","Particle Decays and Two-Body Kinematics","Conservation of four-momentum fixes the kinematics of a decay from the masses alone. In the center-of-momentum frame a parent breaks into two daughters with equal and opposite momenta and energies set by the Kallen triangle function. Boosting to the lab opens the decay into a cone, and the invariant mass built from the daughters reconstructs the parent as a peak. Worked cases: the two-photon decay of the neutral pion and a heavy two-body hadronic decay.\n",{"path":17657,"title":17658,"module":17650,"summary":17659},"\u002Frelativity\u002Frelativistic-dynamics\u002Fcollisions-thresholds-and-the-cm-frame","Relativistic Collisions and Threshold Energies","Two-body collisions run on the same conserved four-momentum as decays. The invariant s sets the total energy available in the center-of-momentum frame and therefore the threshold for producing new particles. Fixed-target energy grows only as the square root of beam energy while a collider grows linearly, which is why colliders reach high energy. Compton scattering follows as a worked photon-electron collision giving the wavelength shift.\n",{"path":17661,"title":17662,"module":17650,"summary":17663},"\u002Frelativity\u002Frelativistic-dynamics\u002Fmandelstam-variables-and-invariants","Mandelstam Variables and Lorentz Invariants","For a two-to-two process the three Mandelstam invariants s, t, and u encode all the kinematics in frame-independent form. They obey a single linear constraint, the sum of the four squared masses, so only two are independent. s is the center-of-momentum energy squared, t and u are momentum transfers tied to the scattering angle, and crossing symmetry relates one amplitude across three channels through these variables.\n",{"path":17665,"title":17666,"module":17667,"summary":17668},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ffour-current-and-the-four-potential","The Four-Current and Four-Potential","Covariant Electromagnetism","Charge density and current combine into a single four-vector whose divergence is charge conservation. The scalar and vector potentials combine likewise into the four-potential, whose gauge freedom fixes to the Lorenz condition, reducing Maxwell's equations for the potentials to a single wave equation sourced by the four-current.\n",{"path":17670,"title":17671,"module":17667,"summary":17672},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fthe-electromagnetic-field-tensor","The Electromagnetic Field Tensor","The antisymmetric derivative of the four-potential is the field-strength tensor F, gauge invariant by construction, with the electric and magnetic fields as its components. Its dual exchanges E and B, and its two contractions form the Lorentz invariants that classify a field as electric, magnetic, or radiative in every frame.\n",{"path":17674,"title":17675,"module":17667,"summary":17676},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Ftransformation-of-electric-and-magnetic-fields","How E and B Transform","Transforming the field tensor under a boost gives explicit rules for the electric and magnetic fields: components along the motion are unchanged, transverse components mix and pick up a gamma. The field of a uniformly moving charge compresses transversely, and the force between a current and a moving charge shows that magnetism is the relativistic shadow of electrostatics.\n",{"path":17678,"title":17679,"module":17667,"summary":17680},"\u002Frelativity\u002Fcovariant-electrodynamics\u002Fcovariant-maxwell-and-the-stress-energy-tensor","Covariant Maxwell and the Stress–Energy Tensor","Maxwell's four equations collapse into two tensor equations, one sourced by the four-current and one an identity on the field strength, with charge conservation automatic. The Lorentz force becomes a four-vector law, and the field's energy, momentum, and stress assemble into a symmetric, conserved stress–energy tensor — the object that will source gravity.\n",{"path":17682,"title":17683,"module":17684,"summary":17685},"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-equivalence-principle-formalized","The Equivalence Principle","Curved Spacetime","The equality of gravitational and inertial mass promotes to a physical principle in three graded strengths — weak, Einstein, and strong. A freely falling laboratory is locally indistinguishable from an inertial frame, but the qualifier \"locally\" is essential: the size of the patch over which gravity vanishes is set by the tidal field, which no change of frame can remove. Tidal forces are the true, coordinate-independent signature of gravity, and they are what curvature will measure.\n",{"path":17687,"title":17688,"module":17684,"summary":17689},"\u002Frelativity\u002Fcurved-spacetime\u002Fmanifolds-vectors-and-the-metric","Manifolds, Vectors, and the Metric","A manifold is a space that looks locally like flat space, described by overlapping coordinate charts. Tangent vectors are directional derivatives with the coordinate basis vectors as partial-derivative operators; one-forms live in the dual space; and the metric tensor turns a coordinate line element into an invariant length. The 2-sphere and Rindler metrics serve as worked examples, including the coordinate singularities that are artefacts of the chart, not of the geometry.\n",{"path":17691,"title":17692,"module":17684,"summary":17693},"\u002Frelativity\u002Fcurved-spacetime\u002Fcovariant-derivative-and-christoffel-symbols","Parallel Transport and the Covariant Derivative","The ordinary derivative of a vector field is not a tensor, because it subtracts vectors living in different tangent spaces. A connection supplies the missing comparison: the covariant derivative adds Christoffel-symbol correction terms that cancel the coordinate artefacts. Requiring the connection to be torsion-free and to preserve the metric fixes the Christoffel symbols uniquely in terms of derivatives of the metric, giving the Levi-Civita connection that general relativity uses.\n",{"path":17695,"title":17696,"module":17684,"summary":17697},"\u002Frelativity\u002Fcurved-spacetime\u002Fgeodesics-and-the-geodesic-equation","Geodesics and the Newtonian Limit","Free fall is geodesic motion: a freely falling particle follows the straightest possible worldline, obtained either by parallel-transporting its own tangent vector or by extremizing proper time. Both routes give the geodesic equation. Affine parameters, and conserved quantities from symmetries via Killing vectors, make it solvable. In the weak-field slow-motion limit the geodesic equation reproduces Newton's law of gravity, fixing the time-time metric component as the Newtonian potential.\n",{"path":17699,"title":17700,"module":17684,"summary":17701},"\u002Frelativity\u002Fcurved-spacetime\u002Fcurvature-riemann-and-geodesic-deviation","Curvature and the Riemann Tensor","Curvature is the failure of parallel transport to commute: carrying a vector around an infinitesimal loop returns it rotated, and the rotation per unit area is the Riemann tensor. Its symmetries cut the components to twenty in four dimensions. Geodesic deviation makes it the equation of tidal forces, and its contractions — the Ricci tensor, the Ricci scalar, and the divergence-free Einstein tensor — assemble the objects the field equation is built from.\n",{"path":17703,"title":17704,"module":17684,"summary":17705},"\u002Frelativity\u002Fcurved-spacetime\u002Fthe-einstein-field-equations","The Einstein Field Equations","The field equation is assembled from a short list of requirements: a symmetric, divergence-free, second-order geometric tensor set proportional to the stress–energy tensor, with the coefficient fixed by the Newtonian limit. The cosmological constant is the one extra term the requirements allow. The Einstein–Hilbert action gives the same equation from a variational principle, and the coupled system closes the logic of the module: matter curves spacetime, and spacetime tells matter how to move.\n",{"path":17707,"title":17708,"module":17709,"summary":17710},"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fthe-schwarzschild-metric","The Schwarzschild Metric","The Schwarzschild Solution","The first exact solution of Einstein's equation follows from two assumptions, staticity and spherical symmetry, imposed on the vacuum outside a mass. Solving the vacuum field equations fixes two metric functions and produces the Schwarzschild geometry, whose one length scale is the Schwarzschild radius $r_s = 2GM\u002Fc^2$. Birkhoff's theorem shows this is the only spherical vacuum, and the far field reduces to Newtonian gravity.\n",{"path":17712,"title":17713,"module":17709,"summary":17714},"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Fgeodesics-and-orbits-in-schwarzschild","Orbits in the Schwarzschild Geometry","The two Killing symmetries of the Schwarzschild metric give a conserved energy and angular momentum per unit mass, reducing geodesic motion to a one-dimensional problem in an effective potential. The potential carries an extra attractive $1\u002Fr^3$ term absent from Newton's, which caps the centrifugal barrier, produces an innermost stable circular orbit at $6GM\u002Fc^2$, and makes bound orbits precess instead of closing.\n",{"path":17716,"title":17717,"module":17709,"summary":17718},"\u002Frelativity\u002Fthe-schwarzschild-solution\u002Flight-bending-and-null-geodesics","Null Geodesics and the Photon Sphere","Light follows null geodesics, governed by a photon effective potential with a single unstable maximum at $3GM\u002Fc^2$, the photon sphere. The impact parameter sorts rays into those that escape with a deflection and those captured, with the critical value $b_c = 3\\sqrt{3}\\,GM\u002Fc^2$ dividing them. A grazing ray bends by $4GM\u002F(c^2 b)$, twice the naive Newtonian value, and the critical impact parameter sets the edge of a black hole's shadow.\n",{"path":17720,"title":17721,"module":17722,"summary":17723},"\u002Frelativity\u002Ftests-of-general-relativity\u002Fperihelion-precession-of-mercury","The Perihelion Precession of Mercury","Tests of General Relativity","A single extra term in the Schwarzschild orbit equation, cubic in the inverse radius, keeps a bound orbit from closing. The perturbation advances the perihelion by 6πGM\u002F(c²a(1−e²)) per revolution, which for Mercury is 43 arcseconds per century — exactly the anomaly left after Newtonian planetary perturbations are subtracted. A note on frame dragging closes the lesson.\n",{"path":17725,"title":17726,"module":17722,"summary":17727},"\u002Frelativity\u002Ftests-of-general-relativity\u002Fdeflection-of-light-and-gravitational-lensing","Light Deflection and Gravitational Lensing","A light ray grazing the Sun bends by 4GM\u002F(c²b), exactly twice the value a Newtonian corpuscle would give; the extra factor is the curvature of space. The 1919 eclipse confirmed it. The same bending focuses light from distant sources into Einstein rings, multiple images, and microlensing brightenings, making lensing a direct probe of mass, including mass that emits no light.\n",{"path":17729,"title":17730,"module":17722,"summary":17731},"\u002Frelativity\u002Ftests-of-general-relativity\u002Fgravitational-redshift-and-shapiro-delay","Gravitational Redshift and the Shapiro Delay","A clock deeper in a gravitational well ticks slower, and a photon climbing out loses frequency by the ratio of the metric's time-time components. Pound and Rebka measured the 2.5×10⁻¹⁵ shift over a 22.5-metre tower. Radar signals grazing the Sun return late by about 250 microseconds, the Shapiro delay. Both probe the time part of the metric directly.\n",{"path":17733,"title":17734,"module":17722,"summary":17735},"\u002Frelativity\u002Ftests-of-general-relativity\u002Frelativity-in-technology-gps","Relativity and the Global Positioning System","A GPS satellite clock runs slow by 7 microseconds a day from its orbital speed and fast by 46 from its higher gravitational potential, a net gain of about 38 microseconds a day. Left uncorrected, the timing error would grow into kilometres of position error within a day and exceed navigation tolerance within minutes. The satellites carry a pre-launch frequency offset to cancel it.\n",{"path":17737,"title":17738,"module":17739,"summary":17740},"\u002Frelativity\u002Fblack-holes\u002Fhorizons-and-coordinate-singularities","Horizons and Coordinate Singularities","Black Holes","The Schwarzschild radius is a coordinate singularity, not a curvature singularity: the metric blows up there only because the static coordinates fail, while the geometry stays finite. Eddington–Finkelstein and Kruskal– Szekeres coordinates cross the horizon smoothly and show the light cones tipping toward the center. A freely falling observer reaches the true singularity at r=0 in finite proper time, while a distant observer sees the infall freeze and redden at the horizon.\n",{"path":17742,"title":17743,"module":17739,"summary":17744},"\u002Frelativity\u002Fblack-holes\u002Frotating-and-charged-black-holes","Rotating and Charged Black Holes","A stationary black hole is fixed by three numbers: mass, angular momentum, and charge. The Reissner–Nordström metric adds charge and splits the horizon in two; the Kerr metric adds rotation, drags inertial frames, and wraps the horizon in an ergosphere where nothing can stay still. Inside the ergosphere the Penrose process extracts rotational energy, and the no-hair theorem states that no other detail of the collapsed matter survives.\n",{"path":17746,"title":17747,"module":17739,"summary":17748},"\u002Frelativity\u002Fblack-holes\u002Fblack-hole-thermodynamics","Black-Hole Thermodynamics","The four laws of black-hole mechanics mirror the four laws of thermodynamics term for term, with horizon area playing the role of entropy and surface gravity the role of temperature. Hawking's calculation makes the analogy literal: a black hole radiates at a temperature set by its surface gravity, carries a real entropy proportional to its horizon area, and slowly evaporates. The thermal spectrum raises the information paradox.\n",{"path":17750,"title":17751,"module":17752,"summary":17753},"\u002Frelativity\u002Fgravitational-waves\u002Flinearized-gravity-and-wave-solutions","Linearized Gravity and Wave Solutions","Gravitational Waves","Weak gravity is a small perturbation of flat spacetime, and the linearized Einstein equation in the Lorenz gauge is an ordinary wave equation propagating at the speed of light. The trace-reversed perturbation carries the dynamics, residual gauge freedom fixes the transverse-traceless form, and the two physical polarizations deform a ring of freely falling masses into oscillating ellipses whose fractional size change is the strain.\n",{"path":17755,"title":17756,"module":17752,"summary":17757},"\u002Frelativity\u002Fgravitational-waves\u002Fgeneration-and-the-quadrupole-formula","The Quadrupole Formula","The retarded solution of the linearized field equation gives the field of a moving source, and conservation of mass and momentum forbids monopole and dipole radiation, leaving the mass quadrupole as the leading emitter. The quadrupole formula fixes the strain and the radiated luminosity, and applied to a compact binary it predicts the inspiral chirp of rising frequency and amplitude. The Hulse-Taylor pulsar's orbital decay confirmed it to a fraction of a percent.\n",{"path":17759,"title":17760,"module":17752,"summary":17761},"\u002Frelativity\u002Fgravitational-waves\u002Fdetection-ligo-and-the-first-events","LIGO and the First Detections","A gravitational wave is measured as a differential length change of the two arms of a kilometre-scale Michelson interferometer, a strain of order ten to the minus twenty-one that moves the mirrors by a fraction of a proton radius. GW150914 recorded the inspiral, merger, and ringdown of two black holes, fixing their masses and the energy radiated, and GW170817 with its coincident gamma-ray burst and kilonova opened multimessenger astronomy.\n",{"path":17763,"title":17764,"module":17765,"summary":17766},"\u002Frelativity\u002Fcosmological-bridge\u002Fthe-cosmological-principle-and-flrw-metric","The Cosmological Principle and the FLRW Metric","A Bridge to Cosmology","Homogeneity and isotropy restrict the spacetime of the universe to a single family of metrics: a flat cosmic-time slicing of spatial sections of constant curvature, scaled by a time-dependent factor a(t). This lesson builds the Friedmann–Lemaître–Robertson–Walker metric from those symmetries, separates comoving from proper distance, and derives cosmological redshift as the stretching of wavelengths with the scale factor.\n",{"path":17768,"title":17769,"module":17765,"summary":17770},"\u002Frelativity\u002Fcosmological-bridge\u002Ffriedmann-equations-and-cosmic-dynamics","The Friedmann Equations and Cosmic Dynamics","The Einstein equation applied to the FLRW metric with a perfect-fluid source yields the two Friedmann equations and the conservation law that ties them together. This lesson derives them, defines the critical density and the density parameters that fix the spatial geometry, works out how matter, radiation, and a cosmological constant dilute and drive the expansion, and hands off to a dedicated cosmology subject.\n",{"path":17772,"title":17773,"module":6,"summary":6},"\u002Frelativity","Relativity",{"path":17775,"title":17776,"module":6,"summary":6},"\u002Fphysical-computing","Physical Computing",{"path":17778,"title":17779,"module":17780,"summary":17781},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fblackbody-radiation-and-the-planck-quantum","Blackbody Radiation and the Planck Quantum","Origins of the Quantum","Millikan's oil-drop experiment fixed the electron charge as an indivisible unit, and the spectrum of thermal radiation forced a second, deeper quantum. Classical physics predicts an infinite energy density at short wavelengths; Planck removed the divergence by allowing a cavity oscillator to hold only energies that are integer multiples of hf, the first appearance of the quantum of action.\n",{"path":17783,"title":17784,"module":17780,"summary":17785},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-photoelectric-effect-and-the-photon","The Photoelectric Effect and the Photon","Light shone on a clean metal ejects electrons, but the details defied the wave theory: the electrons' maximum energy depends on the light's frequency, not its brightness, and there is a sharp threshold frequency below which nothing happens. Einstein resolved every anomaly by treating light as a stream of energy quanta hf, each absorbed whole by one electron, and Millikan's measurement of the stopping-potential slope confirmed h to a decade before anyone expected.\n",{"path":17787,"title":17788,"module":17780,"summary":17789},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fx-rays-and-the-compton-effect","X-Rays and the Compton Effect","X-rays are short-wavelength electromagnetic waves produced when fast electrons are braked in a target, and their diffraction by crystals lets Bragg's law measure atomic spacings. Compton then scattered X-rays off electrons and found the wavelength shifted by an amount that only a photon carrying momentum hf\u002Fc could explain, closing the case for the particle nature of light.\n",{"path":17791,"title":17792,"module":17780,"summary":17793},"\u002Fquantum-mechanics\u002Fold-quantum-theory\u002Fthe-old-quantum-theory-bohr-and-sommerfeld","The Old Quantum Theory: Bohr, Sommerfeld, and Correspondence","Between Bohr's 1913 atom and Schrödinger's 1926 equation, physics ran on a provisional recipe: keep classical orbits, but admit only those whose action integral is a whole multiple of Planck's constant. This lesson develops the Wilson-Sommerfeld phase-integral rule, applies it to the oscillator and to the elliptical Kepler orbits of hydrogen, derives Sommerfeld's relativistic fine structure and the quantization of orbit orientation, and shows how the correspondence principle fixed intensities and selection rules. The systematic failures — helium, line intensities, the anomalous Zeeman effect — mark exactly where a theory of orbits had to give way to a theory of waves.\n",{"path":17795,"title":17796,"module":17797,"summary":17798},"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fde-broglie-waves-and-electron-diffraction","De Broglie Waves and Electron Diffraction","The Wave Nature of Matter","In 1924 de Broglie proposed that every particle carries a wave of wavelength h\u002Fp. The hypothesis explains Bohr's quantized orbits as standing waves, and Davisson and Germer, then G. P. Thomson, confirmed it by diffracting electrons from crystals exactly as X-rays diffract. We derive the electron wavelength, work the Bragg analysis of the data, and give the relativistic form.\n",{"path":17800,"title":17801,"module":17797,"summary":17802},"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fwave-packets-and-the-probability-interpretation","Wave Packets and the Probabilistic Wave Function","A single de Broglie wave fills all space, but a particle is localized. Adding many waves of nearby wavelength builds a wave packet that is confined and moves at the group velocity, which equals the particle velocity. Born's rule reads the squared amplitude of the wave function as a probability density, the meaning confirmed by electron interference building up one detection at a time.\n",{"path":17804,"title":17805,"module":17797,"summary":17806},"\u002Fquantum-mechanics\u002Fmatter-waves\u002Fthe-uncertainty-principle","The Uncertainty Principle and Wave-Particle Duality","The packet relations delta-k delta-x about 1 become Heisenberg's principle once momentum is hbar times wave number: position and momentum cannot both be sharp, nor energy and time. The gamma-ray microscope shows the limit is physical, not technical. It fixes the zero-point energy of a confined particle, the size of the hydrogen atom, and the natural width of spectral lines, and it frames the wave-particle duality of all matter and radiation.\n",{"path":17808,"title":17809,"module":17810,"summary":17811},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-schrodinger-equation-in-one-dimension","The Schrödinger Equation in One Dimension","Wave Mechanics in One Dimension","The wave equation for matter cannot be derived; it is postulated and judged by experiment. We build the time-dependent Schrödinger equation from the de Broglie relations, read Born's probability rule off the complex wave function, and separate the time and space dependence to get the time-independent equation whose bound-state solutions are the stationary states. The five acceptability conditions on the wave function are what force energy to be quantized.\n",{"path":17813,"title":17814,"module":17810,"summary":17815},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-free-particle-and-wave-packet-dynamics","The Free Particle and Wave-Packet Dynamics","The free particle has no bound states: its stationary solutions are non-normalizable plane waves forming a continuum. Physical states are wave packets built by superposing them, and the superposition is a Fourier transform. We delta-normalize the plane waves, assemble a Gaussian packet, solve for its exact time evolution, and read off the two facts that reconcile the wave picture with mechanics: the packet moves at the group velocity ħk\u002Fm, the classical velocity, and it spreads because its component momenta travel at different speeds.\n",{"path":17817,"title":17818,"module":17810,"summary":17819},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fparticle-in-infinite-and-finite-square-wells","Particle in Infinite and Finite Square Wells","The infinite square well is the simplest bound-state problem: two boundary conditions quantize the energy into a ladder E_n = n² E_1, and the eigenfunctions are the standing waves of a string fixed at both ends. Relaxing the walls to a finite depth lets the wave function leak into the classically forbidden region, keeps the number of bound states finite, and turns the eigenvalue condition into a transcendental equation solved graphically.\n",{"path":17821,"title":17822,"module":17810,"summary":17823},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Foperators-expectation-values-and-the-harmonic-oscillator","Operators, Expectation Values, and the Harmonic Oscillator","Measurable quantities are extracted from the wave function as expectation values, and each observable is represented by an operator that acts between Ψ* and Ψ — position by multiplication, momentum by a derivative, energy by the Hamiltonian. Applied to the harmonic oscillator, the machinery yields evenly spaced levels E_n = (n+½)ℏω, Gaussian- times-Hermite eigenfunctions of definite parity, and the selection rule Δn = ±1.\n",{"path":17825,"title":17826,"module":17810,"summary":17827},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fthe-dirac-delta-potential","The Dirac-Delta Potential: A Single Bound State and Scattering","A potential concentrated at a single point is solvable in closed form and isolates the physics of matching a wave function across a discontinuity. Integrating the Schrödinger equation across the spike gives a jump condition on the derivative; the attractive delta well then supports exactly one bound state, of energy set by the strength alone, while the same spike scatters an incoming beam with a transmission that rises from zero to one. The attractive well and the repulsive barrier scatter identically yet only the well binds.\n",{"path":17829,"title":17830,"module":17810,"summary":17831},"\u002Fquantum-mechanics\u002Fwave-mechanics-1d\u002Fbarrier-penetration-and-quantum-tunneling","Barrier Penetration and Quantum Tunneling","Unbound states scatter rather than bind. A particle meeting a step is partly reflected even when it has more than enough energy to pass, and a particle meeting a barrier taller than its energy has a nonzero chance of appearing on the far side. Matching the wave function across the boundaries gives the reflection and transmission coefficients and the exponential tunneling probability that explains alpha decay, the scanning tunneling microscope, and the ammonia clock.\n",{"path":17833,"title":17834,"module":17835,"summary":17836},"\u002Fquantum-mechanics\u002Fformalism\u002Fhilbert-space-and-dirac-notation","Hilbert Space and Dirac Bra–Ket Notation","The Formalism of Quantum Mechanics","Wave mechanics is one representation of a deeper structure: quantum states are vectors in a complex inner-product space, and observables act on them as linear operators. We build that space from the axioms, introduce Dirac's kets and bras as vectors and the linear functionals that measure them, and identify the wavefunction as the components of an abstract state in the position basis. The resolution of the identity is the single algebraic tool that ties every basis, expansion, and matrix element together.\n",{"path":17838,"title":17839,"module":17835,"summary":17840},"\u002Fquantum-mechanics\u002Fformalism\u002Fobservables-hermitian-operators-and-eigenvalues","Observables, Hermitian Operators, and the Spectral Theorem","Every measurable quantity is represented by a Hermitian operator, and the reason is forced: a measurement needs real eigenvalues, orthogonal eigenvectors, and a complete eigenbasis, and Hermiticity delivers precisely those. We derive those properties from self-adjointness, state the spectral theorem, handle degeneracy, and show that two observables share an eigenbasis precisely when they commute — the algebraic condition behind compatible and incompatible measurements.\n",{"path":17842,"title":17843,"module":17835,"summary":17844},"\u002Fquantum-mechanics\u002Fformalism\u002Fthe-postulates-and-quantum-measurement","The Postulates and Quantum Measurement","With states as vectors and observables as Hermitian operators, the physical content of quantum mechanics reduces to a short list of postulates. We state them precisely, derive the Born probability rule for discrete and continuous spectra, work out projective collapse and its idempotence, compute expectation values and their variance, and state the measurement problem cleanly — the one place the postulates split unitary evolution from measurement without explaining the seam.\n",{"path":17846,"title":17847,"module":17835,"summary":17848},"\u002Fquantum-mechanics\u002Fformalism\u002Fposition-momentum-and-continuous-spectra","Position, Momentum, and Continuous Spectra","Position and momentum are the observables with no normalizable eigenstates: their spectra are continuous, their eigenkets are delta-normalized, and the two are Fourier conjugates. We derive the canonical commutator from the momentum operator, build the continuous-basis machinery (Dirac deltas replacing Kronecker deltas), show the position and momentum wavefunctions are a Fourier-transform pair, and compute expectation values in either representation.\n",{"path":17850,"title":17851,"module":17835,"summary":17852},"\u002Fquantum-mechanics\u002Fformalism\u002Fcommutators-and-the-generalized-uncertainty-principle","Commutators and the Generalized Uncertainty Principle","The commutator of two observables measures the obstruction to sharing an eigenbasis, and it bounds how sharply both can be known at once. We derive the generalized uncertainty relation from the Schwarz inequality, recover the position–momentum bound as a special case, characterize the minimum-uncertainty states that saturate it as Gaussians, and give the energy–time relation its correct reading as a lifetime bound rather than a commutator relation.\n",{"path":17854,"title":17855,"module":17835,"summary":17856},"\u002Fquantum-mechanics\u002Fformalism\u002Ftime-evolution-schrodinger-and-heisenberg-pictures","Time Evolution, Propagators, and the Heisenberg Picture","Time evolution is generated by the Hamiltonian and implemented by a unitary operator that preserves probability. We build that operator, expand a state in stationary states to see why probability densities freeze while phases wind, introduce the propagator, transfer the time dependence onto operators in the Heisenberg picture, and derive Ehrenfest's theorem — which recovers classical equations of motion for expectation values and identifies conserved quantities as observables commuting with the Hamiltonian.\n",{"path":17858,"title":17859,"module":17860,"summary":17861},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fladder-operators-and-the-number-states","Ladder Operators and the Number States","The Oscillator Algebraically, and Symmetry","The harmonic oscillator can be solved without touching a differential equation. Factoring the Hamiltonian into a lowering operator and its adjoint turns the spectrum into pure algebra: the commutator relation fixes the ladder, the vacuum condition fixes the ground state, and the energies fall out as equally spaced rungs. The same operators give the matrix elements of position and momentum for free.\n",{"path":17863,"title":17864,"module":17860,"summary":17865},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fcoherent-and-squeezed-states","Coherent and Squeezed States","A single number state never moves — its position expectation is pinned at the origin. The superposition that oscillates like a classical particle is the eigenstate of the annihilation operator: the coherent state. It is a displaced vacuum, carries Poissonian photon statistics, saturates the uncertainty bound, and traces a rigid Gaussian orbit in phase space. Squeezing deforms that circle, trading precision in one quadrature for noise in the other.\n",{"path":17867,"title":17868,"module":17860,"summary":17869},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fsymmetries-generators-and-conservation-laws","Symmetries, Generators, and Conservation Laws","Every continuous symmetry of a quantum system is a unitary operator built by exponentiating a Hermitian generator: momentum generates translations, angular momentum generates rotations, the Hamiltonian generates time evolution. When a generator commutes with the Hamiltonian, the transformation leaves the dynamics unchanged and the generator is conserved — the quantum form of Noether's theorem — and any symmetry that mixes states within a level forces degeneracy.\n",{"path":17871,"title":17872,"module":17860,"summary":17873},"\u002Fquantum-mechanics\u002Foscillator-and-symmetry\u002Fparity-time-reversal-and-discrete-symmetries","Parity, Time Reversal, and Discrete Symmetries","Parity and time reversal are symmetries no continuous generator can reach. Parity is a unitary involution whose eigenvalues label states even or odd, fixing the dipole selection rules. Time reversal is antiunitary: it conjugates i, flips momenta and spins, and for half-integer spin squares to minus one, which by Kramers' theorem makes every level of a time-reversal-invariant Hamiltonian at least doubly degenerate.\n",{"path":17875,"title":17876,"module":16715,"summary":17877},"\u002Fquantum-mechanics\u002Fangular-momentum\u002Forbital-angular-momentum-and-spherical-harmonics","Orbital Angular Momentum and Spherical Harmonics","Orbital angular momentum is the operator triple built from position and momentum. Its components fail to commute, so no state carries sharp values of more than one of them, but each commutes with the total square. Solving the common eigenvalue problem in spherical coordinates quantizes both the magnitude and the projection and produces the spherical harmonics, the angular part of every central-force wavefunction.\n",{"path":17879,"title":17880,"module":16715,"summary":17881},"\u002Fquantum-mechanics\u002Fangular-momentum\u002Fthe-angular-momentum-algebra","The Angular-Momentum Algebra and Ladder Operators","The eigenvalues of angular momentum follow from the commutation relations alone, with no reference to coordinates or wavefunctions. Raising and lowering operators built from the components generate finite multiplets, force the total quantum number to be a non-negative integer or half-integer, and fix the matrix elements of every component. The half-integer values excluded by orbital motion appear here, and they are what spin realizes.\n",{"path":17883,"title":17884,"module":16715,"summary":17885},"\u002Fquantum-mechanics\u002Fangular-momentum\u002Faddition-of-angular-momenta-and-clebsch-gordan","Addition of Angular Momenta and Clebsch–Gordan Coefficients","Two angular momenta combine into a total whose allowed magnitudes run from the difference to the sum of the parts in integer steps. The change from the uncoupled product basis to the coupled total-angular-momentum basis is carried out with the lowering operator and orthogonality, and its matrix of overlaps is the table of Clebsch–Gordan coefficients. Two spin-halves split into a triplet and a singlet, the prototype for every composite spin.\n",{"path":17887,"title":17888,"module":17889,"summary":17890},"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-schrodinger-equation-in-three-dimensions","The Schrödinger Equation in Three Dimensions","Central Potentials","A central potential depends only on the distance from a force center, so the three-dimensional Schrödinger equation separates in spherical coordinates. The angular factor is a spherical harmonic; the radial factor obeys a one-dimensional equation with an effective potential whose centrifugal barrier depends on the angular-momentum quantum number. The free particle and the spherical box fix the two limiting cases through the spherical Bessel functions.\n",{"path":17892,"title":17893,"module":17889,"summary":17894},"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-hydrogen-atom","The Hydrogen Atom","The Coulomb potential turns the radial equation into one whose bound states exist only for a discrete set of energies. A power-series solution truncated to keep the wavefunction normalizable forces the principal quantum number, and the energy comes out proportional to minus one over its square, recovering the Rydberg spectrum. The bound states are the associated Laguerre functions times spherical harmonics, and their energy depends on the principal number alone, giving an n-squared degeneracy larger than rotational symmetry can explain.\n",{"path":17896,"title":17897,"module":17889,"summary":17898},"\u002Fquantum-mechanics\u002Fcentral-potentials\u002Fthe-isotropic-oscillator-and-hidden-symmetry","The Isotropic Oscillator and Hidden Symmetry","The three-dimensional isotropic harmonic oscillator solves in both Cartesian and spherical bases, and the two solutions must agree on the degeneracy of every level. That agreement, and the accidental degeneracy of hydrogen, both come from a symmetry larger than rotation: the oscillator carries an SU(3) invariance built from a conserved quadrupole tensor, and the Coulomb problem carries an SO(4) invariance built from the conserved Runge–Lenz vector. These hidden symmetries pin the degeneracies that rotational invariance alone leaves unexplained.\n",{"path":17900,"title":17901,"module":17902,"summary":17903},"\u002Fquantum-mechanics\u002Fspin\u002Fspin-half-pauli-matrices-and-stern-gerlach","Spin-½, the Pauli Matrices, and Stern–Gerlach","Spin","A silver atom passing through an inhomogeneous magnetic field splits into two beams, not a smear. That single fact fixes the internal angular momentum of the electron to a two-valued quantity with no spatial wavefunction. We build the two-dimensional spin space, the Pauli matrices and their algebra, the spinor for measurement along an arbitrary axis, and the sequential Stern–Gerlach filters that expose measurement disturbance.\n",{"path":17905,"title":17906,"module":17902,"summary":17907},"\u002Fquantum-mechanics\u002Fspin\u002Fspin-in-a-magnetic-field-precession-and-resonance","Spin in a Magnetic Field: Precession and Resonance","A spin coupled to a magnetic field is the simplest nontrivial quantum dynamics. A static field makes the spin expectation precess on a cone at the Larmor frequency while the energy levels split linearly. Adding a weak oscillating field and passing to the rotating frame produces Rabi oscillations and a resonance lineshape — the physics of NMR and ESR, and the driven qubit.\n",{"path":17909,"title":17910,"module":17902,"summary":17911},"\u002Fquantum-mechanics\u002Fspin\u002Ftwo-level-systems-and-the-bloch-sphere","Two-Level Systems and the Bloch Sphere","Every two-state quantum system is a spin-½ in disguise. Its Hamiltonian is an effective magnetic field, its pure states are points on the Bloch sphere, and its unitary evolution is a rigid rotation of that sphere. The same structure produces avoided level crossings, the ammonia inversion doublet and its maser, and the qubit.\n",{"path":17913,"title":17914,"module":17915,"summary":17916},"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fidentical-particles-and-exchange-symmetry","Identical Particles and Exchange Symmetry","Identical Particles","Two electrons carry no label that distinguishes one from the other, and that bare fact reshapes the state space. The exchange operator that swaps particle labels commutes with any Hamiltonian built from identical particles, so its eigenvalue is conserved, and nature admits only its two extremes: totally symmetric states for bosons and totally antisymmetric states for fermions. The antisymmetry forces a statistical correlation, the exchange \"force,\" that keeps fermions apart and draws bosons together even with no interaction between them.\n",{"path":17918,"title":17919,"module":17915,"summary":17920},"\u002Fquantum-mechanics\u002Fidentical-particles\u002Fthe-pauli-principle-atoms-and-the-periodic-table","The Pauli Principle, Atoms, and the Periodic Table","Antisymmetry packaged as a Slater determinant turns the exclusion principle into an operating rule for building atoms. Helium shows the machinery in full: the electron-electron repulsion splits into a direct Coulomb integral and an exchange integral, and the exchange term alone pushes the spin-triplet (orthohelium) below the spin-singlet (parahelium) with no magnetic interaction in sight. Screening, the aufbau order, and Hund's rules then assemble the whole periodic table from the same antisymmetry.\n",{"path":17922,"title":17923,"module":17924,"summary":17925},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ftime-independent-perturbation-theory","Time-Independent Perturbation Theory","Approximation Methods for Bound States","Almost no realistic Hamiltonian can be solved exactly. Perturbation theory treats a hard Hamiltonian as a solvable one plus a small correction and expands the eigenvalues and eigenstates in powers of that correction. We derive the first- and second-order energy shifts and the first-order state correction for a nondegenerate level, expose the small-denominator failure that degeneracy forces, and fix it by diagonalizing the perturbation inside the degenerate subspace to find the \"good\" zeroth-order states.\n",{"path":17927,"title":17928,"module":17924,"summary":17929},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Ffine-structure-and-the-real-hydrogen-atom","Fine Structure and the Real Hydrogen Atom","The Bohr spectrum is only the leading term. Two relativistic corrections of order alpha-squared — the relativistic kinetic-energy correction and spin–orbit coupling, joined by the Darwin term for s states — split the hydrogen levels into fine structure that depends on the total angular momentum j. We derive each shift as a first-order perturbation, combine them into a formula depending only on n and j, and continue down the energy ladder to the Lamb shift and the hyperfine 21 cm line.\n",{"path":17931,"title":17932,"module":17924,"summary":17933},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-zeeman-and-stark-effects","The Zeeman and Stark Effects","An atom in an external field is a perturbation problem whose good basis depends on which interaction wins. A magnetic field competes with the internal spin–orbit coupling: the weak-field limit gives the anomalous Zeeman splitting set by the Landé g-factor, the strong-field limit gives the Paschen–Back pattern in the uncoupled basis, and the intermediate regime is a matrix diagonalization. An electric field gives a quadratic shift for the nondegenerate ground state and a linear splitting for the degenerate n = 2 level.\n",{"path":17935,"title":17936,"module":17924,"summary":17937},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-variational-method","The Variational Method","The expectation of the Hamiltonian in any trial state is an upper bound on the true ground-state energy. Minimizing that expectation over a parametrized family of trial functions turns the ground-state problem into ordinary calculus and needs no small parameter. We prove the bound, apply it to the helium atom with a screened effective charge, use a two-center trial to predict binding in the hydrogen molecular ion, and extend the method to excited states through orthogonality.\n",{"path":17939,"title":17940,"module":17924,"summary":17941},"\u002Fquantum-mechanics\u002Fapproximation-methods\u002Fthe-wkb-approximation","The WKB Approximation","When the potential varies slowly on the scale of the de Broglie wavelength, the wavefunction is locally a plane wave with a position-dependent wavelength. This semiclassical picture builds the wavefunction from the classical momentum, breaks down at the turning points where the momentum vanishes, and is repaired there by connection formulas. The result recovers the Bohr–Sommerfeld quantization rule with its half-integer correction and gives the exponential tunneling rate through a smooth barrier, the Gamow factor.\n",{"path":17943,"title":17944,"module":6,"summary":6},"\u002Fquantum-mechanics","Quantum Mechanics",{"path":17946,"title":17947,"module":17948,"summary":17949},"\u002Freal-analysis\u002Ffoundations\u002Fsets-logic-functions","Sets, Logic, and Functions","Foundations and the Real Number System","The working language of analysis: quantifiers and the proof patterns (contrapositive, contradiction, induction), sets and their operations, relations and equivalence classes, and functions with their images, injections, surjections, and bijections. Cardinality is measured by bijection, and Cantor's theorem that no set surjects onto its power set forces uncountable sets to exist.\n",{"path":17951,"title":17952,"module":17948,"summary":17953},"\u002Freal-analysis\u002Ffoundations\u002Fordered-fields-completeness","Ordered Fields and the Completeness Axiom","The real numbers are the unique ordered field with the least-upper-bound property. The field and order axioms, the exact failure of the rationals (no supremum for the set of rationals below √2), and completeness as the defining axiom of ℝ lead to the first consequences: the existence of √2, the Archimedean property, and the density of ℚ in ℝ.\n",{"path":17955,"title":17956,"module":17948,"summary":17957},"\u002Freal-analysis\u002Ffoundations\u002Fabsolute-value-bounds","Absolute Value, Bounded Sets, and Inequalities","The absolute value turns the order on ℝ into a notion of distance, with the triangle inequality as the estimate underlying most later proofs. Covered: its algebra, the triangle and reverse-triangle inequalities, and the extension of the sup\u002Finf vocabulary from sets to bounded functions.\n",{"path":17959,"title":17960,"module":17948,"summary":17961},"\u002Freal-analysis\u002Ffoundations\u002Fintervals-uncountability","Intervals, Uncountability, and Decimals","Intervals are classified, and ℝ is proved uncountable two ways: a nested-interval construction and the decimal diagonal argument. Decimal expansions are built as suprema of truncations, which pins the source of their non-uniqueness (the 0.4999… equals 0.5000… identity) and the identification of the rationals with the eventually-repeating expansions. The middle-thirds Cantor set is an uncountable set of measure zero.\n",{"path":17963,"title":17964,"module":17965,"summary":17966},"\u002Freal-analysis\u002Fsequences-series\u002Fsequences-limits","Sequences and Their Limits","Sequences and Series","A sequence is a function on the natural numbers; it converges to a limit when its terms eventually stay within any prescribed tolerance of that number. The epsilon-M definition fixes the order of the quantifiers, and from it the limit is unique, every convergent sequence is bounded, and only the tail matters. Divergence to plus or minus infinity records terms that outgrow every bound.\n",{"path":17968,"title":17969,"module":17965,"summary":17970},"\u002Freal-analysis\u002Fsequences-series\u002Flimit-laws-monotone","Limit Laws and Monotone Convergence","Limits commute with sums, products, quotients, roots, and absolute values and preserve non-strict inequalities, so a limit can be assembled from the limits of its parts without returning to epsilon and M. The squeeze lemma transfers a limit through two envelopes; the monotone convergence theorem produces a limit from boundedness alone; and the ratio test settles the geometric and factorial standard limits.\n",{"path":17972,"title":17973,"module":17965,"summary":17974},"\u002Freal-analysis\u002Fsequences-series\u002Flimsup-bolzano-weierstrass","Subsequences, Limit Superior, and Bolzano–Weierstrass","A bounded sequence need not converge, but it always has convergent subsequences, and its terms cluster between two extreme values. The limit superior and inferior are the limits of the tail suprema and infima; they always exist for a bounded sequence, coincide exactly when it converges, and are its largest and smallest subsequential limits. Bolzano–Weierstrass extracts a convergent subsequence from boundedness alone.\n",{"path":17976,"title":17977,"module":17965,"summary":17978},"\u002Freal-analysis\u002Fsequences-series\u002Fcauchy-completeness","Cauchy Sequences and the Completeness of the Reals","The Cauchy criterion tests convergence without knowing the limit: a sequence converges exactly when its terms eventually all lie within any tolerance of one another. Cauchy sequences are bounded, in the reals Cauchy and convergent are equivalent, and this completeness property is interchangeable with the least-upper-bound axiom — the single feature that separates the real line from the rationals.\n",{"path":17980,"title":17981,"module":17965,"summary":17982},"\u002Freal-analysis\u002Fsequences-series\u002Fseries-convergence","Series and Convergence Tests","A series converges when its sequence of partial sums does, so every fact about sequences transfers. Geometric and telescoping series sum in closed form; the n-th term test rejects series whose terms miss zero, though the harmonic series shows the converse fails; and the comparison test against the geometric and p-series benchmarks settles most nonnegative-term series.\n",{"path":17984,"title":17985,"module":17965,"summary":17986},"\u002Freal-analysis\u002Fsequences-series\u002Fabsolute-conditional-rearrangement","Absolute Convergence, the Ratio and Root Tests, and Rearrangements","Absolute convergence is the strong form of convergence that permits free manipulation; conditional convergence is fragile. Absolute convergence implies convergence, and the ratio and root tests detect it by comparison with the geometric series. The alternating series test supplies conditionally convergent series, Riemann's theorem rearranges any of them to any sum, and Mertens' theorem multiplies series when at least one converges absolutely.\n",{"path":17988,"title":17989,"module":17990,"summary":17991},"\u002Freal-analysis\u002Fmetric-spaces\u002Fmetric-spaces-norms","Metric Spaces, Norms, and Examples","Metric Spaces and Topology","A metric is a function $d(x,y)$ obeying four axioms: nonnegativity, identity of indiscernibles, symmetry, and the triangle inequality. The Euclidean, taxicab, sup, discrete, and great-circle metrics all qualify, as does the sup metric on $C[a,b]$. Every norm induces a metric, and strongly equivalent metrics share the same open sets.\n",{"path":17993,"title":17994,"module":17990,"summary":17995},"\u002Freal-analysis\u002Fmetric-spaces\u002Fopen-closed-sets","Open and Closed Sets, Interior, Closure","Open sets are those in which every point has room to move; closed sets are their complements. From the single ball construction come the topology axioms (arbitrary unions, finite intersections), the interior, closure, and boundary of a set, and the fact that openness is always relative to the ambient space.\n",{"path":17997,"title":17998,"module":17990,"summary":17999},"\u002Freal-analysis\u002Fmetric-spaces\u002Fconvergence-completeness","Convergence, Cauchy Sequences, and Completeness","The $\\varepsilon$-$N$ definition of a limit transfers verbatim to any metric space once $|x-y|$ is replaced by $d(x,y)$. Convergent sequences characterize closed sets and closures; Cauchy sequences and completeness capture spaces with no missing limits, with $\\mathbb{R}^n$ and $C[a,b]$ complete and $\\mathbb{Q}$ and $(0,1]$ not.\n",{"path":18001,"title":18002,"module":17990,"summary":18003},"\u002Freal-analysis\u002Fmetric-spaces\u002Fcompactness","Compactness","A set is compact if every open cover has a finite subcover. In a metric space this is equivalent to sequential compactness and to being complete and totally bounded. Compact sets are closed and bounded; the Heine–Borel theorem gives the converse in $\\mathbb{R}^n$ but nowhere else in general.\n",{"path":18005,"title":18006,"module":17990,"summary":18007},"\u002Freal-analysis\u002Fmetric-spaces\u002Fconnectedness","Connectedness","A space is connected when it cannot be split into two nonempty open pieces. The connected subsets of $\\mathbb{R}$ are precisely the intervals, path- connectedness gives a constructive sufficient condition, and connectedness is a topological invariant preserved by continuous maps, the fact behind the intermediate value theorem.\n",{"path":18009,"title":18010,"module":16409,"summary":18011},"\u002Freal-analysis\u002Fcontinuity\u002Flimits-of-functions","Limits of Functions","The limit of a function at a point is an epsilon–delta condition pinning one value L as the target of f(x) as x approaches c, mirroring the sequence definition with distance replacing index. It is stated only at cluster points of the domain, is unique when it exists, and reduces to sequential limits through the Heine criterion. The algebra of limits and one-sided limits follow from that reduction.\n",{"path":18013,"title":18014,"module":16409,"summary":18015},"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuous-functions","Continuous Functions","A function is continuous at c when its limit there equals its own value, lim f(x) = f(c). The epsilon–delta and sequential forms agree; sums, products, quotients, and compositions of continuous functions are continuous; and the failures split into jump, Dirichlet, popcorn, and removable types. The topological reading is that preimages of open sets are open.\n",{"path":18017,"title":18018,"module":16409,"summary":18019},"\u002Freal-analysis\u002Fcontinuity\u002Fevt-ivt","Extreme and Intermediate Value Theorems","On a closed bounded interval a continuous function attains an absolute maximum and minimum (the extreme value theorem, compactness preserved by continuity) and takes every value between its endpoint values (the intermediate value theorem, connectedness preserved). Both proofs run through Bolzano–Weierstrass and bisection, and yield root-finding, existence of k-th roots, and fixed-point theorems.\n",{"path":18021,"title":18022,"module":16409,"summary":18023},"\u002Freal-analysis\u002Fcontinuity\u002Funiform-continuity","Uniform Continuity","Uniform continuity strengthens continuity by demanding one delta that works at every point of the domain, not a delta re-chosen at each point. It separates x^2 on a compact interval from x^2 on the whole line and from 1\u002Fx near zero; continuity on a closed bounded interval is automatically uniform; uniformly continuous functions preserve Cauchy sequences and extend to endpoints; and Lipschitz continuity is the strongest of the three, through its secant-slope bound.\n",{"path":18025,"title":18026,"module":16409,"summary":18027},"\u002Freal-analysis\u002Fcontinuity\u002Fcontinuity-metric-spaces","Continuity on Metric Spaces","The epsilon–delta definition used only distances, so continuity transfers to maps between metric spaces by replacing absolute values with the two metrics. In this generality continuity still admits a sequential form, preserves compactness and connectedness, is uniform on a compact domain, and reads topologically as preimages of open sets being open, the formulation that defines homeomorphisms.\n",{"path":18029,"title":18030,"module":16409,"summary":18031},"\u002Freal-analysis\u002Fcontinuity\u002Flimits-infinity-monotone","Limits at Infinity and Monotone Functions","Treating infinity as a cluster point extends the epsilon–delta limit to x approaching plus or minus infinity, giving horizontal asymptotes and infinite limits. For monotone functions the one-sided limits always exist as suprema and infima, the discontinuities are jumps and at most countably many, the continuity is equivalent to the image being an interval, and a strictly monotone function always has a continuous inverse.\n",{"path":18033,"title":18034,"module":18035,"summary":18036},"\u002Freal-analysis\u002Fdifferentiation\u002Fthe-derivative","The Derivative","Differentiation","The derivative is the limit of the difference quotient, the slope the secant lines approach as the second point slides into the first. Differentiability forces continuity; linearity and the product, quotient, and chain rules follow from the definition; and a continuous function can fail to be differentiable, as the absolute value does at the origin.\n",{"path":18038,"title":18039,"module":18035,"summary":18040},"\u002Freal-analysis\u002Fdifferentiation\u002Fmean-value-theorem","The Mean Value Theorem","A relative extremum in the interior forces the derivative to vanish; Rolle's theorem and the mean value theorem turn that local fact into global control. The sign of the derivative fixes monotonicity, a bounded derivative yields a Lipschitz bound, and Darboux's theorem shows derivatives have the intermediate value property even where they are discontinuous.\n",{"path":18042,"title":18043,"module":18035,"summary":18044},"\u002Freal-analysis\u002Fdifferentiation\u002Ftaylors-theorem","Taylor's Theorem","Taylor's theorem generalizes the mean value theorem: an n-times differentiable function is matched near a point by a degree-n polynomial, with a Lagrange remainder that names the error exactly through one higher derivative. Iterating the mean value theorem proves it; the second-derivative test is the order-one case; and a smooth non-analytic bump separates a Taylor series from the function it fails to represent.\n",{"path":18046,"title":18047,"module":18035,"summary":18048},"\u002Freal-analysis\u002Fdifferentiation\u002Finverse-function-1d","The Inverse Function Theorem in One Variable","A nonzero derivative certifies a local inverse and fixes its slope. A strictly monotone differentiable function has a differentiable inverse whose derivative is the reciprocal of the original; the inverse function theorem removes the monotonicity hypothesis, and the reciprocal formula constructs nth roots and the logarithm's derivative, failing exactly where the derivative vanishes.\n",{"path":18050,"title":18051,"module":18052,"summary":18053},"\u002Freal-analysis\u002Friemann-integration\u002Fdarboux-integral","Partitions, Darboux Sums, and Integrability","The Riemann Integral","The Riemann integral is defined by trapping the area under a bounded function between under- and over-estimates. Partitions cut the domain into strips; lower and upper Darboux sums bracket the area; refining a partition tightens the bracket. A function is integrable exactly when the bracket can be made arbitrarily thin, and the tagged Riemann-sum limit gives the same number.\n",{"path":18055,"title":18056,"module":18052,"summary":18057},"\u002Freal-analysis\u002Friemann-integration\u002Fintegrability-classes","Which Functions Are Integrable","The Cauchy criterion certifies whole classes of functions as integrable. Continuous functions are integrable because uniform continuity makes every oscillation cap small; monotone functions are integrable because their caps telescope to a single total jump; bounded functions with finitely many discontinuities are integrable by isolating the bad points. The Dirichlet function fails, and the Lebesgue criterion names the exact boundary.\n",{"path":18059,"title":18060,"module":18052,"summary":18061},"\u002Freal-analysis\u002Friemann-integration\u002Fproperties-of-the-integral","Properties of the Integral","The integral is a linear, order-preserving, additive operator on the integrable functions. It splits across subintervals, respects inequalities, bounds the size of a function by the integral of its absolute value, and preserves products. The mean value theorem for integrals identifies the integral with an attained average height on a fixed rectangle.\n",{"path":18063,"title":16464,"module":18052,"summary":18064},"\u002Freal-analysis\u002Friemann-integration\u002Ffundamental-theorem","The fundamental theorem ties the integral to the derivative in two forms. The evaluation form computes a definite integral from any antiderivative; the differentiation form shows the area function has derivative equal to the integrand at points of continuity. Together they make differentiation and integration inverse operations, and yield integration by parts and change of variables.\n",{"path":18066,"title":18067,"module":18052,"summary":18068},"\u002Freal-analysis\u002Friemann-integration\u002Flog-exp-improper","The Logarithm, Exponential, and Improper Integrals","The integral defines transcendental functions. The logarithm is the area under 1\u002Ft, the exponential is its inverse, and their calculus properties follow from the fundamental theorem. Improper integrals extend integration to unbounded intervals and unbounded integrands as limits of proper integrals, with a p-test, a comparison test, absolute versus conditional convergence, and the integral test linking integrals to series.\n",{"path":18070,"title":18071,"module":18072,"summary":18073},"\u002Freal-analysis\u002Ffunction-sequences\u002Fpointwise-uniform-convergence","Pointwise and Uniform Convergence","Sequences and Series of Functions","A sequence of functions has two natural notions of limit. Pointwise convergence fixes each input and takes the limit of numbers; uniform convergence demands one rate that works for every input at once. The uniform norm turns the second into a statement about a single sequence of numbers, and the uniform Cauchy criterion and the Weierstrass M-test let us certify it.\n",{"path":18075,"title":18076,"module":18072,"summary":18077},"\u002Freal-analysis\u002Ffunction-sequences\u002Finterchange-of-limits","Interchange of Limits: Continuity, Integration, Differentiation","Passing to a limit inside a continuity statement, an integral, or a derivative is an interchange of two limits, and the two limits do not always commute. Uniform convergence licenses the first two swaps: the uniform limit of continuous functions is continuous, and the limit of the integrals is the integral of the limit. Differentiation needs uniform convergence of the derivatives, and counterexamples show why each hypothesis is required.\n",{"path":18079,"title":18080,"module":18072,"summary":18081},"\u002Freal-analysis\u002Ffunction-sequences\u002Fpower-series-weierstrass","Power Series and the Weierstrass Approximation Theorem","A power series converges uniformly on every closed subinterval inside its radius of convergence, together with all of its derivatives. That makes it continuous, differentiable, and integrable term by term, so a power series defines an infinitely differentiable function. The Weierstrass approximation theorem then shows that polynomials come uniformly close to any continuous function on a closed bounded interval.\n",{"path":18083,"title":18084,"module":18072,"summary":18085},"\u002Freal-analysis\u002Ffunction-sequences\u002Fpicard-ode","Picard's Existence and Uniqueness Theorem","The Banach fixed-point theorem says a contraction of a complete metric space has exactly one fixed point, found by iterating from any start. Applied to the space of continuous functions with the uniform norm, it proves Picard's theorem: a first-order differential equation with a Lipschitz right-hand side has a unique local solution. Picard iteration constructs that solution explicitly, and worked examples show the Lipschitz condition is not optional.\n",{"path":18087,"title":18088,"module":18089,"summary":18090},"\u002Freal-analysis\u002Fseveral-variables\u002Fdifferentiability-rn","The Derivative of a Map ℝⁿ → ℝᵐ","Functions of Several Variables (Introduction)","The derivative of a map between Euclidean spaces is the linear transformation of vanishing relative error, unique when it exists and represented in coordinates by the Jacobian matrix of partial derivatives. Differentiability forces continuity through a local Lipschitz bound. Existence of the partial derivatives alone does not suffice; continuity of the partials does.\n",{"path":18092,"title":18093,"module":18089,"summary":18094},"\u002Freal-analysis\u002Fseveral-variables\u002Fgradient-chain-rule","Directional Derivatives, the Gradient, and the Chain Rule","The directional derivative measures the rate of change of a scalar field along a chosen heading and equals the derivative applied to that direction. The gradient collects these into a vector that points along steepest ascent and sits orthogonal to level sets. The chain rule composes derivatives by multiplying Jacobians, and a mean value theorem holds for scalar fields but fails for vector-valued maps.\n",{"path":18096,"title":18097,"module":18089,"summary":18098},"\u002Freal-analysis\u002Fseveral-variables\u002Fhigher-derivatives-taylor-extrema","Higher Derivatives, Taylor's Theorem, and Extrema","Iterating the derivative gives a symmetric second derivative, the Hessian, whose mixed partials agree when they are continuous. Taylor's theorem expands a smooth map to any order with a Lagrange-type remainder, and at a critical point the definiteness of the Hessian decides between a local minimum, a local maximum, and a saddle.\n",{"path":18100,"title":18101,"module":18089,"summary":18102},"\u002Freal-analysis\u002Fseveral-variables\u002Finverse-implicit-theorems","The Inverse and Implicit Function Theorems","A nonlinear map with a nonsingular Jacobian is locally invertible, with the inverse's derivative given by the inverse matrix. The contraction mapping principle supplies the local inverse; the implicit function theorem then solves a system for some variables in terms of the rest whenever the relevant Jacobian block is invertible. Worked coordinate changes show both theorems in use.\n",{"path":18104,"title":18105,"module":18089,"summary":18106},"\u002Freal-analysis\u002Fseveral-variables\u002Fmultiple-integrals","Multiple Integrals","The Riemann integral of a bounded function over a closed rectangle in Euclidean space is built from Darboux upper and lower sums on a grid of subrectangles, with the same squeeze criterion that governs the one-variable integral. Continuous integrands are integrable, and a set of content zero can be ignored. Fubini's theorem evaluates a multiple integral as an iterated one in either order, and the indicator trick extends the theory to regions bounded by curves.\n",{"path":18108,"title":18109,"module":6,"summary":6},"\u002Freal-analysis","Real Analysis",{"path":18111,"title":18112,"module":16062,"summary":18113},"\u002Fabstract-algebra\u002Ffoundations\u002Fsets-functions-relations","Sets, Functions, and Equivalence Relations","Algebra is built on three prior notions: the set, the map between sets, and the equivalence relation that reorganizes a set into disjoint classes. Sets, maps (injective, surjective, bijective), fibers and preimages, and the correspondence between equivalence relations and partitions — the one structural fact reused in every later quotient construction.\n",{"path":18115,"title":18116,"module":16062,"summary":18117},"\u002Fabstract-algebra\u002Ffoundations\u002Fintegers-and-modular-arithmetic","The Integers and Modular Arithmetic","The integers carry the template every ring later imitates: well-ordering drives induction, induction drives the division algorithm, and division drives the Euclidean algorithm, gcd, Bézout's identity, and unique factorization into primes. Quotienting by congruence mod n builds the first finite arithmetic, Z\u002FnZ, whose invertible elements form the group of units.\n",{"path":18119,"title":18120,"module":18121,"summary":18122},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fgroup-axioms-and-first-examples","Group Axioms and First Examples","Groups and Symmetry","A group is a set with one associative operation that has an identity and inverses. We state the axioms, prove that the identity, inverses, and cancellation behave as expected, define the order of a group and of an element, and catalogue the running examples: the integers, the additive group of residues mod n, and the multiplicative group of units mod n.\n",{"path":18124,"title":18125,"module":18121,"summary":18126},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fdihedral-and-symmetric-groups","Dihedral and Symmetric Groups","The dihedral group D_{2n} is the symmetries of a regular n-gon, generated by a rotation r and a reflection s subject to three relations. The symmetric group S_n is all permutations of n objects, written in cycle notation. Orders, generators and relations, cycle decomposition, the order of a permutation from its cycle type, and the parity that splits S_n in half.\n",{"path":18128,"title":18129,"module":18121,"summary":18130},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fmatrix-and-quaternion-groups","Matrix and Quaternion Groups","Invertible matrices over a field form the general linear group GL_n(F), with the determinant-one matrices as the subgroup SL_n(F). Over a finite field the order of GL_n(F) has a clean product formula. The quaternion group Q_8 is a second small nonabelian group, distinct from the dihedral group of the same order; its multiplication and subgroup structure sharpen the contrast between the two.\n",{"path":18132,"title":18133,"module":18121,"summary":18134},"\u002Fabstract-algebra\u002Fgroups-and-symmetry\u002Fhomomorphisms-and-group-actions","Homomorphisms, Isomorphisms, and Actions","A homomorphism is a map between groups that respects the operation; an isomorphism is a bijective one, making two groups the same up to relabeling. The kernel and image measure how far a homomorphism is from injective and surjective. A group action realizes a group as permutations of a set, and actions correspond exactly to homomorphisms into a symmetric group, with orbits and stabilizers as the first tools for counting.\n",{"path":18136,"title":18137,"module":18138,"summary":18139},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fsubgroups-and-substructures","Subgroups and Their Substructures","Subgroups and Quotients","A subgroup is a subset that is a group under the inherited operation. One test decides it: nonempty and closed under the map $(x,y) \\mapsto xy^{-1}$. From an arbitrary subset $A$ we build the centralizer, normalizer, and center, and from an action the stabilizer and kernel, all of them subgroups nested in a fixed chain inside $G$.\n",{"path":18141,"title":18142,"module":18138,"summary":18143},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcyclic-groups","Cyclic Groups","A cyclic group is generated by one element. Two facts organize the whole theory: the order of an element equals the order of the subgroup it generates, and cyclic groups of equal order are isomorphic, so $\\mathbb{Z}$ and $\\mathbb{Z}\u002Fn\\mathbb{Z}$ are the only ones. From there the generators ($\\varphi(n)$ of them), the subgroups (one per divisor of $n$), and a fast exponentiation algorithm all follow.\n",{"path":18145,"title":18146,"module":18138,"summary":18147},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fgeneration-and-subgroup-lattices","Generation and the Lattice of Subgroups","The subgroup generated by a subset $A$ is the smallest subgroup containing it, described top-down as an intersection and bottom-up as the set of words in $A$ and its inverses. Collecting all subgroups and ordering them by containment produces the subgroup lattice, whose Hasse diagram shows the joins, meets, and containment relations among all subgroups.\n",{"path":18149,"title":18150,"module":18138,"summary":18151},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcosets-lagrange-and-normal-subgroups","Cosets, Lagrange, and Normal Subgroups","The left cosets of a subgroup partition a group into equal-sized blocks, so the order of a subgroup divides the order of the group: Lagrange's theorem. When the blocks can be multiplied consistently — exactly when the subgroup is normal — they form the quotient group $G\u002FN$. Fermat's and Euler's theorems fall out as index computations.\n",{"path":18153,"title":18154,"module":18138,"summary":18155},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fisomorphism-theorems","The Isomorphism Theorems","Four theorems relate homomorphisms, quotients, and subgroup lattices. The first identifies the image of a homomorphism with the quotient by its kernel; the second and third compute quotients built from two subgroups and quotients of quotients; the fourth matches the subgroups of $G\u002FN$ with the subgroups of $G$ lying above $N$. Together they make quotient groups computable.\n",{"path":18157,"title":18158,"module":18138,"summary":18159},"\u002Fabstract-algebra\u002Fsubgroups-and-quotients\u002Fcomposition-series-and-the-alternating-group","Composition Series and the Alternating Group","A composition series breaks a finite group into simple quotient factors, and Jordan-Hölder says those factors are unique up to order. This turns classification into two problems: list the simple groups, and describe how to reassemble them. The sign homomorphism splits $S_n$ into even and odd permutations, defining the alternating group $A_n$, simple for $n \\ge 5$.\n",{"path":18161,"title":18162,"module":18163,"summary":18164},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Factions-and-cayleys-theorem","Actions, Orbits, and Cayley's Theorem","Group Actions and Sylow Theory","A group action turns abstract elements into permutations of a set. The action splits the set into orbits, and the orbit-stabilizer theorem ties each orbit's size to the index of a stabilizer. Applied to a group acting on itself by left multiplication, this gives Cayley's theorem: every group is a group of permutations.\n",{"path":18166,"title":18167,"module":18163,"summary":18168},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fconjugation-and-the-class-equation","Conjugation and the Class Equation","A group acts on itself by conjugation, and the orbits are the conjugacy classes. Orbit-stabilizer turns the resulting partition into the class equation, which forces every group of prime-power order to have a nontrivial center. Conjugacy in the symmetric group is cycle type, and Burnside's lemma counts orbits by averaging fixed points.\n",{"path":18170,"title":18171,"module":18163,"summary":18172},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fsylow-theorems","The Sylow Theorems","Lagrange's theorem forbids subgroups whose order fails to divide the group order; Sylow's theorems supply a partial converse for prime powers. A Sylow p-subgroup always exists, all of them are conjugate, and their count satisfies two congruence-and-divisibility constraints tight enough to prove many groups non-simple from their order alone.\n",{"path":18174,"title":18175,"module":18163,"summary":18176},"\u002Fabstract-algebra\u002Fgroup-actions-and-sylow\u002Fautomorphisms-and-simple-groups","Automorphisms and Simplicity of Aₙ","Conjugation makes a group act on itself and on its normal subgroups by automorphisms, giving the inner automorphism group G\u002FZ(G) and the embedding of N(H)\u002FC(H) into Aut(H). Characteristic subgroups are those every automorphism fixes, and the automorphism group of a cyclic group is its unit group. The lesson closes by proving the alternating group Aₙ is simple for n ≥ 5.\n",{"path":18178,"title":18179,"module":18180,"summary":18181},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fdirect-products-and-finite-abelian-groups","Direct Products and Finite Abelian Groups","Products and Group Structure","The direct product assembles a larger group from componentwise copies of smaller ones, and a recognition theorem reverses the process when two normal subgroups meet trivially and span the group. The Fundamental Theorem of Finitely Generated Abelian Groups then classifies every such group by two equivalent invariants, invariant factors and elementary divisors.\n",{"path":18183,"title":18184,"module":18180,"summary":18185},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fsemidirect-products","Semidirect Products","The semidirect product relaxes the direct product by requiring only one factor to be normal, with the other acting on it through a homomorphism into its automorphism group. This single twisting map lets abelian pieces assemble into non-abelian groups, realizes the dihedral groups as $\\mathbb{Z}_n \\rtimes \\mathbb{Z}_2$, and, with a recognition theorem, classifies groups of several small orders.\n",{"path":18187,"title":18188,"module":18180,"summary":18189},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fnilpotent-and-solvable-groups","p-Groups, Nilpotent, and Solvable Groups","Finite p-groups have nontrivial center, and iterating the center upward builds the nilpotent groups, which decompose as the direct product of their Sylow subgroups. Iterating the commutator downward builds the solvable groups, whose factors are abelian. The chain cyclic, abelian, nilpotent, solvable orders these classes, and A_5 breaks the last link.\n",{"path":18191,"title":18192,"module":18180,"summary":18193},"\u002Fabstract-algebra\u002Fproducts-and-group-structure\u002Fclassifying-small-groups","Classifying Groups of Small Order","With Sylow's theorem to force normal subgroups, direct and semidirect products to assemble them, and presentations to name the result, every group up to order fifteen can be listed explicitly. Free groups make presentations precise: generators with no relations, from which any group is a quotient by the normal closure of its relations.\n",{"path":18195,"title":18196,"module":18197,"summary":18198},"\u002Fabstract-algebra\u002Fring-theory\u002Frings-definitions-and-examples","Rings: Definitions and Examples","Ring Theory","A ring carries two operations: an abelian group under addition and an associative multiplication linked by the distributive laws. The named special cases — commutative rings, integral domains, division rings, and fields — differ only in how their multiplication behaves. Standard examples include quadratic integer rings, polynomial rings, matrix rings, and group rings.\n",{"path":18200,"title":18201,"module":18197,"summary":18202},"\u002Fabstract-algebra\u002Fring-theory\u002Fideals-quotients-and-homomorphisms","Ideals, Quotient Rings, and Homomorphisms","Ring homomorphisms have kernels that absorb multiplication; such subsets are ideals, and every ideal is the kernel of the projection onto a quotient ring. The quotient construction yields the ring isomorphism theorems and classifies ideals by their quotients: R\u002FI is a field exactly when I is maximal, an integral domain exactly when I is prime.\n",{"path":18204,"title":18205,"module":18197,"summary":18206},"\u002Fabstract-algebra\u002Fring-theory\u002Ffractions-and-the-chinese-remainder-theorem","Fields of Fractions and the CRT","Rings of fractions invert a multiplicatively closed set, enlarging an integral domain into its field of fractions the way Z becomes Q. The Chinese Remainder Theorem splits a quotient by comaximal ideals into a direct product, generalizing Z\u002FmnZ ≅ Z\u002FmZ × Z\u002FnZ and explaining why the Euler function is multiplicative.\n",{"path":18208,"title":18209,"module":18210,"summary":18211},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Feuclidean-domains-pids-ufds","Euclidean Domains, PIDs, and UFDs","Factorization and Polynomial Rings","Three classes of integral domain, ordered by how much of elementary arithmetic survives: Euclidean domains carry a division algorithm, principal ideal domains make every ideal a single multiple, and unique factorization domains factor every element into irreducibles in one way. We prove the chain ED implies PID implies UFD, the classes are separated by explicit counterexamples, and irreducible and prime coincide exactly in a UFD.\n",{"path":18213,"title":18214,"module":18210,"summary":18215},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fpolynomial-rings-over-fields","Polynomial Rings over Fields","When the coefficients form a field, polynomial long division works exactly as it does over the rationals, and it works with a unique quotient and remainder. That single fact makes F[x] a Euclidean domain, hence a PID and a UFD: every ideal is the multiples of one polynomial, roots correspond to linear factors, and F[x]\u002F(f) is a field precisely when f is irreducible.\n",{"path":18217,"title":18218,"module":18210,"summary":18219},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Fgauss-lemma-and-unique-factorization","Gauss's Lemma and Unique Factorization","A UFD is not a field, so its polynomial ring is not a PID — yet unique factorization survives the passage from R to R[x]. Gauss's lemma supplies the passage: a polynomial that factors over the fraction field already factors over R, once content is factored out. This gives the theorem that R[x] is a UFD whenever R is, so Z[x] and Q[x,y] factor uniquely even though neither is a PID.\n",{"path":18221,"title":18222,"module":18210,"summary":18223},"\u002Fabstract-algebra\u002Ffactorization-and-polynomials\u002Firreducibility-criteria-and-groebner","Irreducibility Criteria and Gröbner Bases","Deciding whether a given polynomial is irreducible, and computing in multivariate polynomial rings. In one variable: the rational root test, reduction modulo a prime, and Eisenstein's criterion. In several variables, where division fails, a monomial order gives leading terms, a Gröbner basis restores a well-defined remainder, and Buchberger's algorithm computes it.\n",{"path":18225,"title":18226,"module":18227,"summary":18228},"\u002Fabstract-algebra\u002Fmodule-theory\u002Fintroduction-to-modules","Introduction to Modules","Module Theory","A module is an abelian group on which a ring acts, generalizing both vector spaces (when the ring is a field) and abelian groups (when the ring is the integers). Submodules, homomorphisms, quotients, and the isomorphism theorems carry over from groups, and an F[x]-module is the same datum as a vector space with a chosen linear operator — the correspondence behind the canonical forms.\n",{"path":18230,"title":18231,"module":18227,"summary":18232},"\u002Fabstract-algebra\u002Fmodule-theory\u002Ffree-modules-and-direct-sums","Generation, Direct Sums, and Free Modules","A generating set spans a module by R-linear combinations; a direct sum decomposes it into independent pieces; a free module has a basis and the universal property that a homomorphism is determined by arbitrary values on that basis. Rank is well defined over a commutative ring, torsion blocks a basis, and every module is a quotient of a free one — a presentation by generators and relations.\n",{"path":18234,"title":18235,"module":18227,"summary":18236},"\u002Fabstract-algebra\u002Fmodule-theory\u002Ftensor-products-and-exact-sequences","Tensor Products and Exact Sequences","The tensor product builds a module in which elements of two modules can be multiplied, characterized by a universal property turning bilinear maps into linear ones; extension of scalars is its guiding case. Exact sequences track how a module is assembled from a submodule and a quotient, when that assembly splits, and which modules — projective, injective, flat — make the Hom and tensor functors preserve exactness.\n",{"path":18238,"title":18239,"module":18227,"summary":18240},"\u002Fabstract-algebra\u002Fmodule-theory\u002Fvector-spaces-and-linear-maps","Vector Spaces and Linear Maps","A vector space is a module over a field, and the field hypothesis removes every pathology a general module can have: every vector space is free, so it has a basis, a well-defined dimension, and a coordinate isomorphism with F^n. Linear maps become matrices, change of basis becomes similarity, every space pairs with a dual of the same dimension, and the determinant is the unique alternating multilinear normalized form.\n",{"path":18242,"title":18243,"module":18244,"summary":18245},"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fstructure-theorem-over-pids","The Structure Theorem for Modules over a PID","Modules over PIDs and Canonical Forms","Every finitely generated module over a principal ideal domain splits as a free part plus a direct sum of cyclic torsion pieces, in two canonical ways: invariant factors, tied together by a divisibility chain, and elementary divisors, one prime power at a time. Existence follows from the stacked-basis theorem, both lists are unique, and the case $R = \\mathbb{Z}$ is the classification of finitely generated abelian groups.\n",{"path":18247,"title":18248,"module":18244,"summary":18249},"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Frational-canonical-form","Rational Canonical Form","A linear operator turns its vector space into a module over the polynomial ring $F[x]$, with $x$ acting as the operator. The structure theorem's invariant factors then become polynomials, each cyclic summand becomes a companion matrix, and the block-diagonal assembly is the rational canonical form. It is unique, it is computed inside the base field, and two matrices are similar exactly when their rational canonical forms agree.\n",{"path":18251,"title":18252,"module":18244,"summary":18253},"\u002Fabstract-algebra\u002Fmodules-over-pids\u002Fjordan-canonical-form","Jordan Canonical Form","When the base field contains all the eigenvalues, the elementary divisors of an operator are powers of linear polynomials, and each cyclic summand becomes a Jordan block: an eigenvalue on the diagonal with ones just above it. Stacking the blocks gives the Jordan canonical form, unique up to reordering, as close to diagonal as the operator allows. Diagonalizability reads off the minimal polynomial, and the block sizes are counted by ranks of powers of the operator minus the eigenvalue.\n",{"path":18255,"title":18256,"module":18257,"summary":18258},"\u002Fabstract-algebra\u002Ffield-theory\u002Ffield-extensions-and-algebraic-elements","Field Extensions and Algebraic Elements","Field Theory","A field extension makes a larger field K into a vector space over a smaller field F, and its degree [K:F] is that dimension. Adjoining a root of an irreducible polynomial builds a simple extension F(α) isomorphic to F[x]\u002F(m), whose degree is the degree of the minimal polynomial. The tower law makes these degrees multiply, which turns algebra over fields into bookkeeping with integers.\n",{"path":18260,"title":18261,"module":18257,"summary":18262},"\u002Fabstract-algebra\u002Ffield-theory\u002Fstraightedge-and-compass-constructions","Straightedge-and-Compass Constructions","The lengths a straightedge and compass can build from a unit form a field closed under square roots, and every constructible number lies in a tower of quadratic extensions. So its degree over the rationals is a power of two. That single obstruction settles three problems the Greeks left open: doubling the cube, trisecting a general angle, and squaring the circle are all impossible.\n",{"path":18264,"title":18265,"module":18257,"summary":18266},"\u002Fabstract-algebra\u002Ffield-theory\u002Fsplitting-fields-and-algebraic-closure","Splitting Fields and Algebraic Closure","The splitting field of a polynomial is the smallest extension in which it factors into linear pieces, obtained by adjoining all its roots. Every polynomial has one, its degree is at most n factorial, and any two splitting fields are isomorphic. Pushing this to all polynomials at once gives the algebraic closure, a field in which every polynomial splits and which is unique up to isomorphism.\n",{"path":18268,"title":18269,"module":18257,"summary":18270},"\u002Fabstract-algebra\u002Ffield-theory\u002Fseparable-and-cyclotomic-extensions","Separable Extensions and Cyclotomic Fields","A polynomial is separable when its roots are distinct, detected by whether it shares a factor with its formal derivative. Over perfect fields — characteristic zero and finite fields — every irreducible is separable, and the existence and uniqueness of the finite fields follow. Cyclotomic polynomials package the roots of unity by order, are irreducible over the rationals, and give the cyclotomic field its degree phi(n).\n",{"path":18272,"title":18273,"module":18274,"summary":18275},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fthe-galois-correspondence","The Galois Correspondence","Galois Theory","Galois theory attaches to a field extension its group of symmetries and shows that, for the right extensions, the subgroups of that group are in exact order-reversing correspondence with the intermediate fields. The automorphism group, Artin's theorem, the characterization of Galois extensions, and the Fundamental Theorem together turn questions about fields into questions about finite groups.\n",{"path":18277,"title":18278,"module":18274,"summary":18279},"\u002Fabstract-algebra\u002Fgalois-theory\u002Ffinite-fields","Finite Fields","Every finite field has prime-power order, is the splitting field of $x^{p^n} - x$, and is unique up to isomorphism. Its extension over the prime field is Galois with cyclic group generated by the Frobenius map $x \\mapsto x^p$, so the Galois correspondence reduces the subfield lattice to the divisor lattice of $n$. Möbius inversion counts the irreducible polynomials of each degree, and cyclic error-correcting codes are one application.\n",{"path":18281,"title":18282,"module":18274,"summary":18283},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fcyclotomic-and-abelian-extensions","Cyclotomic and Abelian Extensions","The Galois group of the $n$th cyclotomic field over $\\mathbb{Q}$ is the unit group $(\\mathbb{Z}\u002Fn\\mathbb{Z})^\\times$, which makes cyclotomic fields the worked catalogue of abelian extensions of $\\mathbb{Q}$. The isomorphism identifies subfields with subgroups, realizes every finite abelian group as a Galois group over $\\mathbb{Q}$, and leads to Kronecker–Weber. Composites of Galois extensions and the primitive element theorem supply the machinery.\n",{"path":18285,"title":18286,"module":18274,"summary":18287},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fgalois-groups-of-polynomials","Galois Groups of Polynomials","Ordering the roots of a separable polynomial embeds its Galois group in the symmetric group $S_n$, and the group is transitive exactly when the polynomial is irreducible. The discriminant decides membership in $A_n$; for cubics and quartics the resolvent cubic pins the group down; and reduction modulo a prime produces elements of prescribed cycle type, the standard tool for computing Galois groups over $\\mathbb{Q}$.\n",{"path":18289,"title":18290,"module":18274,"summary":18291},"\u002Fabstract-algebra\u002Fgalois-theory\u002Fsolvability-by-radicals-and-the-quintic","Solvability by Radicals and the Quintic","A polynomial is solvable by radicals exactly when its Galois group is solvable. Cyclic extensions are radical extensions once roots of unity are present, which turns a radical tower into a solvable subnormal series. Since $S_n$ is solvable only for $n \\le 4$, the general quintic has no radical formula, and an explicit quintic with Galois group $S_5$ has roots provably not expressible in radicals.\n",{"path":18293,"title":18294,"module":18295,"summary":18296},"\u002Fabstract-algebra\u002Fcapstone\u002Fcommutative-algebra-and-algebraic-geometry","A Glimpse of Commutative Algebra and Algebraic Geometry","Capstone: Where Algebra Goes Next","Commutative algebra reads geometry off the ring of polynomial functions. The dictionary runs through Noetherian rings and the ascending chain condition, Hilbert's Basis Theorem, affine algebraic sets and the two maps connecting ideals to zero sets, radicals, the Zariski topology, and Hilbert's Nullstellensatz, which over an algebraically closed field makes radical ideals and algebraic sets the same object.\n",{"path":18298,"title":18299,"module":18295,"summary":18300},"\u002Fabstract-algebra\u002Fcapstone\u002Frepresentation-and-character-theory","A Glimpse of Representation and Character Theory","Representation theory studies a group by the ways it can act linearly on a vector space. Representations are equivalent to modules over the group ring; Maschke's theorem gives complete reducibility, the Wedderburn consequences bound the irreducible degrees, and character theory reduces a representation to a trace invariant governed by the orthogonality relations and displayed in the character table of a small group.\n",{"path":18302,"title":18303,"module":6,"summary":6},"\u002Fabstract-algebra","Abstract Algebra",{"path":18305,"title":18306,"module":18307,"summary":18308},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fatomic-spectra-rutherford","Atomic Spectra and Rutherford's Nucleus","Early Atomic Models and the Old Quantum Theory","Atoms emit light only at sharp, reproducible wavelengths, and by 1890 those wavelengths were captured by the Rydberg-Ritz formula. Neither empirical regularity had a mechanical explanation. Rutherford's alpha-scattering experiment supplied the missing structure: the atom's positive charge and nearly all its mass sit in a tiny central nucleus, with the electrons far outside.\n",{"path":18310,"title":18311,"module":18307,"summary":18312},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-model-hydrogen","The Bohr Model of Hydrogen","Bohr grafted three quantum postulates onto Rutherford's nuclear atom: certain orbits do not radiate, radiation accompanies a jump between them, and quantization must match classical physics for large orbits. Quantizing the angular momentum fixes the orbit radii and energies, reproduces the Rydberg-Ritz formula, and predicts the Rydberg constant from fundamental constants alone.\n",{"path":18314,"title":18315,"module":18307,"summary":18316},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fx-ray-spectra-franck-hertz","X-Ray Spectra and the Franck-Hertz Experiment","Two 1913-14 experiments confirmed the Bohr-Rutherford atom independently of optical spectra. Moseley found that the square root of a characteristic X-ray frequency is linear in atomic number, fixing Z as nuclear charge and ordering the periodic table. Franck and Hertz measured discrete atomic energy levels directly by scattering electrons through a mercury vapor.\n",{"path":18318,"title":18319,"module":18307,"summary":18320},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fbohr-sommerfeld-old-quantum-theory","The Bohr-Sommerfeld Old Quantum Theory","Bohr fixed the hydrogen levels with a single quantum number by quantizing angular momentum. Sommerfeld replaced that ad hoc rule with a general prescription: quantize the action of each separable coordinate. The rule produces elliptical orbits, a second (azimuthal) quantum number, space quantization, and — once the relativistic mass variation is included — a fine-structure splitting that matches experiment to order alpha squared.\n",{"path":18322,"title":18323,"module":18307,"summary":18324},"\u002Fatomic-physics\u002Fearly-models-and-old-quantum-theory\u002Fold-quantum-theory-limits-wkb","Limits of the Old Quantum Theory and the WKB Bridge","The old quantum theory works only where the classical motion is separable into independent periodic coordinates. It fails for helium, forbids the correct zero angular momentum of the hydrogen ground state, and misses the half-integer in the oscillator and in molecular spectra. The WKB quantization condition, derived from the Schrodinger equation, is the modern descendant of the Sommerfeld rule and repairs the half-integer through the Maslov correction.\n",{"path":18326,"title":18327,"module":18328,"summary":18329},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fschrodinger-3d-hydrogen","The Schrödinger Equation in Three Dimensions and Hydrogen","The Quantum Hydrogen Atom","Extending the Schrödinger equation to three dimensions and separating it in spherical coordinates produces three ordinary differential equations, one per coordinate. Their boundary conditions generate the quantum numbers n, ℓ, and mℓ, quantize the angular momentum to √(ℓ(ℓ+1))ℏ with projections mℏ, and fix the bound-state energies of hydrogen at −Z²(13.6 eV)\u002Fn².\n",{"path":18331,"title":18332,"module":18328,"summary":18333},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fhydrogen-wave-functions","Hydrogen Wave Functions and Orbitals","The hydrogen wave functions factor into a radial part Rₙℓ(r) and an angular spherical harmonic Yℓm(θ,φ). Squaring gives the probability cloud; the radial distribution P(r) = r²|ψ|² peaks at the Bohr radius for the ground state and at the Bohr orbits for excited states. The angular part fixes the s, p, and d orbital shapes that govern chemical bonding.\n",{"path":18335,"title":18336,"module":18328,"summary":18337},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fradial-equation-in-full","Solving the Radial Equation in Full","The hydrogen radial equation is solved from the differential equation up. The substitution u = rR turns it into a one-dimensional problem with a centrifugal barrier; matching the asymptotic behaviour at the origin and at infinity peels off the factors r^(ℓ+1) and e^(−r\u002Fna₀); a Frobenius series for the remainder must terminate, and that termination condition yields the quantization n ≥ ℓ+1 with E = −Z²Ry\u002Fn². The surviving polynomials are the associated Laguerre functions, whose degree n−ℓ−1 counts the radial nodes.\n",{"path":18339,"title":18340,"module":18328,"summary":18341},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fsymmetry-degeneracy-runge-lenz","Accidental Degeneracy and the Runge-Lenz Symmetry","Hydrogen energies depend only on n, so states of different ℓ at the same n are degenerate. This is not a coincidence but the mark of a hidden symmetry: the quantum Runge-Lenz vector is conserved for the 1\u002Fr potential alone, and together with angular momentum it generates the group SO(4). The Casimir invariant of that group reproduces E = −Z²Ry\u002Fn² and its representations count the n² states. Any departure from 1\u002Fr breaks the symmetry and lifts the ℓ-degeneracy.\n",{"path":18343,"title":18344,"module":18328,"summary":18345},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fexpectation-values-virial","Expectation Values, the Virial Theorem, and Scaling","The radial matrix elements ⟨r^k⟩ of hydrogenic states are the raw material of every later correction. This lesson derives ⟨1\u002Fr⟩ from the virial theorem, builds the full family ⟨r⟩, ⟨r²⟩, ⟨1\u002Fr²⟩, ⟨1\u002Fr³⟩ from Kramers' recursion and the Feynman-Hellmann theorem, and reads off their scaling with n, ℓ, and Z. The virial balance ⟨T⟩ = −½⟨V⟩ = −E fixes the energy budget of every bound state.\n",{"path":18347,"title":18348,"module":18328,"summary":18349},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Fquantum-defects-alkali-spectra","Quantum Defects and Alkali Spectra","An alkali atom is one valence electron outside a closed-shell core, and to a good approximation it is hydrogen with a modified quantum number. Core penetration makes low-ℓ states more bound than the Coulomb formula predicts, and the shortfall is captured by a single number per ℓ, the quantum defect δℓ. The spectrum then follows the Rydberg formula with n replaced by the effective n − δℓ, and the sodium D-line doublet is the worked case.\n",{"path":18351,"title":18352,"module":18328,"summary":18353},"\u002Fatomic-physics\u002Fquantum-hydrogen-atom\u002Frydberg-atoms","Rydberg Atoms","A Rydberg atom is an atom excited to a very high principal quantum number, and every hydrogenic property becomes exaggerated by a power of n. Size grows as n², binding falls as n⁻², radiative lifetime lengthens as n³, and the static polarizability explodes as n⁷. The levels crowd toward the ionization limit, and the enormous dipole interaction between two Rydberg atoms produces the blockade that underlies neutral-atom quantum computing.\n",{"path":18355,"title":18356,"module":18357,"summary":18358},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Frelativistic-kinetic-correction","The Relativistic Kinetic-Energy Correction","Fine Structure and the Dirac Atom","The Bohr energies treat the electron as slowly moving, but its speed is of order αc, so the kinetic energy needs a relativistic correction. Expanding √(p²c²+m²c⁴) to order (v\u002Fc)² produces the perturbation −p⁴\u002F8m³c², whose first-order shift on a hydrogenic state is evaluated with the trick p²=2m(E−V). The result depends on n and ℓ, is smaller than the gross structure by α²≈5×10⁻⁵, and is one of the three pieces that combine into the fine-structure formula.\n",{"path":18360,"title":18361,"module":18357,"summary":18362},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fspin-orbit-thomas-precession","Spin-Orbit Coupling and Thomas Precession","In the electron's rest frame the nucleus orbits it, and the resulting current produces a magnetic field that couples to the electron's spin moment. The interaction is ξ(r) L·S, with ξ built from the Coulomb potential and the radial expectation ⟨1\u002Fr³⟩. A relativistic subtlety, Thomas precession, halves the naive coefficient because the electron's rest frame is accelerating. The result splits each ℓ≥1 level into a j=ℓ±½ doublet and makes (n, ℓ, j, mⱼ) the good quantum numbers.\n",{"path":18364,"title":18365,"module":18357,"summary":18366},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdarwin-term-fine-structure-formula","The Darwin Term and the Fine-Structure Formula","The third fine-structure correction, the Darwin term, is a contact interaction proportional to ∇²V that acts only on s-states, physically a smearing of the electron over a Compton wavelength. Adding the relativistic, spin-orbit, and Darwin shifts, the ℓ-dependence cancels and the total collapses to a formula in n and j alone. The n=2 shell splits into 2S₁\u002F₂, 2P₁\u002F₂, 2P₃\u002F₂, with the two j=½ levels exactly degenerate, a coincidence the Dirac theory explains.\n",{"path":18368,"title":18369,"module":18357,"summary":18370},"\u002Fatomic-physics\u002Ffine-structure-and-the-dirac-atom\u002Fdirac-equation-hydrogen","The Dirac Equation for Hydrogen","The fine-structure formula was assembled from three perturbations; the Dirac equation produces it in one stroke and exactly. A first-order relativistic wave equation forces a four-component spinor, from which spin s=½, the g-factor of 2, the spin-orbit term, and antiparticles all emerge automatically. Its exact Coulomb spectrum depends only on n and j, and expanding in Zα reproduces the perturbative result, including the 2S₁\u002F₂–2P₁\u002F₂ degeneracy that sets up the Lamb shift.\n",{"path":18372,"title":18373,"module":18374,"summary":18375},"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Flamb-shift-qed","The Lamb Shift and QED Radiative Corrections","QED Corrections and Hyperfine Structure","The Dirac equation makes the 2S₁\u002F₂ and 2P₁\u002F₂ levels of hydrogen exactly degenerate. Lamb and Retherford measured a splitting of about 1058 MHz that the Dirac theory cannot produce. The gap comes from the electron's coupling to the quantized electromagnetic field: self-energy, vacuum polarization, and the anomalous magnetic moment. Welton's vacuum-fluctuation estimate reproduces the size and shows why the effect lands almost entirely on s-states, and the same radiative corrections make hydrogen the most stringent test of QED.\n",{"path":18377,"title":18378,"module":18374,"summary":18379},"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fhyperfine-structure-21cm","Hyperfine Structure and the 21 cm Line","The proton carries a magnetic moment, and it interacts with the magnetic field the electron produces at the nucleus. For s-states that interaction is the Fermi contact term, proportional to the electron density at the origin and to the dot product of the nuclear and electronic spins. Coupling I and J into F = I + J splits each level by a Landé interval rule; in hydrogen's ground state it produces the F = 0\u002FF = 1 doublet whose 1420 MHz, 21 cm transition maps neutral hydrogen across the galaxy.\n",{"path":18381,"title":18382,"module":18374,"summary":18383},"\u002Fatomic-physics\u002Fqed-corrections-and-hyperfine-structure\u002Fnuclear-effects-isotope-shift","Nuclear Size, Moments, and Isotope Shifts","A real nucleus has a finite size, a mass that changes between isotopes, and, when its spin is at least one, an electric quadrupole moment. Each leaves a fingerprint in the atomic spectrum: the volume shift from s-electrons sampling the charge distribution, the mass and field isotope shifts that separate on a King plot, the quadrupole interaction that breaks the Landé interval rule, and the hyperfine anomaly from the magnetization distribution. Atomic spectroscopy reads nuclear properties out of these shifts.\n",{"path":18385,"title":18386,"module":18387,"summary":18388},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fperiodic-table-atomic-spectra","The Periodic Table and Atomic Spectra","Many-Electron Atoms","Identical electrons demand antisymmetric wave functions, which is the Pauli exclusion principle: no two electrons share all four quantum numbers. Filling shells in order of increasing energy — shifted by penetration and shielding — builds the periodic table and its recurring ionization pattern. Selection rules govern optical spectra, and an external field splits lines by the Zeeman effect.\n",{"path":18390,"title":18391,"module":18387,"summary":18392},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fcentral-field-self-consistent","The Central-Field Approximation and the Self-Consistent Field","The N-electron Hamiltonian does not separate because every pair of electrons repels. The central-field approximation replaces that pairwise repulsion with an averaged spherical potential each electron feels, restoring hydrogen-like orbitals labelled by n and ℓ. The Thomas-Fermi statistical model fixes the shape of the screened charge from Fermi-gas thermodynamics; the Hartree self-consistent field determines it exactly by iterating orbitals against the potential they generate until the two agree.\n",{"path":18394,"title":18395,"module":18387,"summary":18396},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fidentical-particles-hartree-fock","Exchange, Slater Determinants, and Hartree-Fock","A product wave function ignores that electrons are identical fermions. Enforcing antisymmetry writes the state as a Slater determinant, which vanishes whenever two electrons share a spin-orbital — the exclusion principle made algebraic. The energy of a determinant carries a new term with no classical analogue, the exchange integral, nonzero only for parallel spins; it lowers the energy of aligned electrons and carves a Fermi hole around each one. Adding the exchange operator to the mean field gives the Hartree-Fock equations, and what they still miss defines the correlation energy.\n",{"path":18398,"title":18399,"module":18387,"summary":18400},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhelium-two-electron-atom","Helium: the Prototype Two-Electron Atom","Helium is the smallest atom the Schrödinger equation cannot solve exactly, and the smallest that shows every many-electron effect. Ignoring the electron repulsion overbinds the ground state by 30 eV; first-order perturbation theory and a one-parameter variational calculation with an effective charge close most of the gap. The excited configurations split into para (singlet) and ortho (triplet) states separated by the exchange integral, with the triplet lower — and the absence of a 1s² triplet is the Pauli principle in its plainest form.\n",{"path":18402,"title":18403,"module":18387,"summary":18404},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fls-jj-coupling-term-symbols","LS and jj Coupling; Term Symbols","A configuration is not a single energy level. The residual electrostatic repulsion and the spin-orbit interaction split it, and which one dominates fixes the coupling scheme. In light atoms the electrostatic term wins: orbital and spin angular momenta couple separately into L and S, then into J, giving Russell- Saunders term symbols. In heavy atoms spin-orbit wins and each electron's j forms first. The Pauli principle prunes the allowed terms of equivalent electrons, the Landé interval rule spaces the fine-structure multiplet, and the scheme crosses over from LS to jj down a column.\n",{"path":18406,"title":18407,"module":18387,"summary":18408},"\u002Fatomic-physics\u002Fmany-electron-atoms\u002Fhund-rules-ground-terms","Hund's Rules and Ground-State Terms","A configuration allows several terms; Hund's three rules pick the ground one. Maximize the spin S first, then the orbital L, then set J to |L−S| for a less-than-half shell and L+S for a more-than-half shell. The first two rules come from exchange lowering the energy of apart-kept electrons; the third comes from the sign of the spin-orbit coupling, which flips as a shell passes half-filling and turns the multiplet from normal to inverted. Worked ground terms for carbon, nitrogen, oxygen, and iron show the rules in action.\n",{"path":18410,"title":18411,"module":18412,"summary":18413},"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fzeeman-effect","The Zeeman Effect","Atoms in External Fields","A magnetic field couples to the atom through its magnetic moment, splitting each level into equally spaced sublevels labelled by the projection of the total angular momentum. When spin is present the spacing is not the classical one: it carries the Landé g-factor, a projection of the spin and orbital moments onto the total angular momentum. We derive the weak-field Hamiltonian from minimal coupling, evaluate the shift with the projection theorem, and read off the polarization of the emitted components.\n",{"path":18415,"title":18416,"module":18412,"summary":18417},"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fpaschen-back-intermediate","The Paschen-Back and Intermediate-Field Regimes","When the magnetic interaction grows past the fine-structure coupling, spin and orbital angular momentum decouple and precess independently about the field. The anomalous Zeeman pattern reverts to a simple triplet, the Paschen-Back effect. Between the two limits neither coupling dominates and the level positions follow from diagonalizing the combined spin-orbit and Zeeman Hamiltonian. We build the two-by-two problem for a single valence electron, solve it in closed form, and show both limits emerge from one expression.\n",{"path":18419,"title":18420,"module":18412,"summary":18421},"\u002Fatomic-physics\u002Fatoms-in-external-fields\u002Fstark-effect-polarizability","The Stark Effect and Field Ionization","An electric field shifts atomic levels by coupling to the electron's position. Parity forbids a first-order shift for a non-degenerate state, so most atoms respond only at second order through their polarizability, a quadratic Stark shift. Hydrogen is the exception: its accidental degeneracy admits a permanent dipole and a linear shift, cleanest in parabolic coordinates. At large fields the Coulomb well develops a saddle, and Rydberg states field-ionize at a threshold that falls as the fourth power of the principal quantum number.\n",{"path":18423,"title":18424,"module":18425,"summary":18426},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Ftime-dependent-perturbation-golden-rule","Time-Dependent Perturbation Theory and the Golden Rule","Radiative Transitions and Spectral Lines","An atom in a weak oscillating field makes transitions between its stationary states. First-order time-dependent perturbation theory gives the transition amplitude as a Fourier component of the perturbation at the Bohr frequency, and the resulting probability is a sinc-squared resonance that sharpens as the field acts longer. For a two-level system the same coupling produces Rabi oscillations; for a transition into a continuum the long-time limit collapses the sinc-squared into a delta function and yields Fermi's golden rule, a constant transition rate set by the coupling strength and the density of final states.\n",{"path":18428,"title":18429,"module":18425,"summary":18430},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fdipole-approximation-einstein-coefficients","The Dipole Approximation and Einstein Coefficients","The coupling between an atom and light is the interaction of the electron with the electromagnetic field. Because an optical wavelength dwarfs the atom, the spatial variation of the field across the atom can be dropped, leaving the electric-dipole interaction and its matrix element. That matrix element defines the oscillator strength, which obeys the Thomas-Reiche-Kuhn sum rule. Einstein's three rate coefficients (absorption, stimulated emission, spontaneous emission) follow from detailed balance with thermal radiation, fixing the ratio of spontaneous to stimulated rates and its steep growth with frequency.\n",{"path":18432,"title":18433,"module":18425,"summary":18434},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Fselection-rules-forbidden-transitions","Selection Rules and Forbidden Transitions","The dipole matrix element vanishes for most pairs of states, and the pattern of which survive is the set of selection rules. Parity forces the orbital angular momentum to change by one; the angular integral of three spherical harmonics restricts the magnetic quantum number to change by zero or one; the photon's spin restricts the total angular momentum. When the dipole element vanishes, higher multipoles (magnetic dipole and electric quadrupole) can still drive the transition at rates smaller by powers of the fine-structure constant, and states with no allowed decay become metastable.\n",{"path":18436,"title":18437,"module":18425,"summary":18438},"\u002Fatomic-physics\u002Fradiative-transitions-and-line-shapes\u002Flifetimes-and-line-shapes","Lifetimes, Line Widths, and Line Shapes","A spectral line is never infinitely sharp. The finite lifetime of the excited state gives every line a natural Lorentzian width set by the total decay rate, the Fourier transform of an exponentially damped emission. Thermal motion adds a Gaussian Doppler width that usually dominates in a gas; collisions add a further Lorentzian pressure width; the observed profile is the Voigt convolution of the Gaussian and Lorentzian parts. Strong driving fields broaden the line further through saturation. Each mechanism has a distinct dependence on temperature, density, and intensity that lets it be identified and, where possible, removed.\n",{"path":18440,"title":18441,"module":18442,"summary":18443},"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Flaser-principles","Population Inversion, Gain, and the Laser","Lasers and Spectroscopy","A laser is an optical amplifier placed inside a resonant cavity. Amplification requires that stimulated emission outrun absorption, which requires more atoms in the upper level than the lower one — a population inversion that the Einstein relations forbid in thermal equilibrium and that no two-level pump can produce. Three- and four-level schemes reach it by routing atoms through auxiliary states. The gain coefficient sets how strongly a weak beam grows, the cavity fixes the threshold and selects a comb of longitudinal modes, and gain saturation clamps the steady-state inversion at its threshold value.\n",{"path":18445,"title":18446,"module":18442,"summary":18447},"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fspectroscopy-techniques","Spectroscopic Techniques and Frequency Combs","A tunable laser turns spectroscopy from photographing a spectrum into interrogating a single transition, but at room temperature the Doppler width buries the natural linewidth under a thousandfold-broader Gaussian. Saturated absorption and two-photon spectroscopy defeat the first-order Doppler shift by selecting the zero-velocity class or cancelling the shift between counter-propagating photons, recovering natural-width features. Laser-induced fluorescence pushes sensitivity to single atoms, and the optical frequency comb converts an optical frequency into a countable radio-frequency beat, giving absolute frequency measurement across the visible spectrum.\n",{"path":18449,"title":18450,"module":18442,"summary":18451},"\u002Fatomic-physics\u002Flasers-and-spectroscopy\u002Fline-catalog-nist-asd","Reading Real Spectra with the NIST Database","Every quantity computed in this course — energy levels, transition frequencies, oscillator strengths, lifetimes — is tabulated for real atoms in the NIST Atomic Spectra Database. This lesson reads that data as physics: how levels are labelled by term symbols and energies in wavenumbers, how a transition list encodes wavelength, Einstein coefficient, and line strength, how a Grotrian diagram is reconstructed from the tables, and how a measured spectrum is matched to catalog lines. The residual between computed and tabulated positions is the running score of atomic theory.\n",{"path":18453,"title":18454,"module":18455,"summary":18456},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Flaser-cooling-doppler","Laser Cooling and Optical Molasses","Modern Atomic Physics","A near-resonant laser beam pushes an atom because every absorbed photon delivers one unit of momentum and the subsequent spontaneous emission averages to zero. Two counter-propagating red-detuned beams turn that push into friction: the Doppler shift brings a moving atom closer to resonance with the beam it moves against, so the net force opposes the velocity. Six beams give optical molasses in three dimensions. The random recoil of spontaneous emission heats against the friction, and the balance sets the Doppler cooling limit. Adding a magnetic-field gradient makes the force position-dependent as well, giving the magneto-optical trap.\n",{"path":18458,"title":18459,"module":18455,"summary":18460},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fsub-doppler-trapping","Sub-Doppler Cooling and Atom Traps","Optical molasses cools multilevel atoms below the Doppler limit. A polarization gradient plus optical pumping makes an atom repeatedly climb a light-shift hill and be pumped to the valley, losing kinetic energy each cycle — Sisyphus cooling. The floor is the recoil limit, one photon momentum of residual motion. Below it, cooling must avoid scattering photons: conservative magnetic and optical-dipole traps hold the atoms while forced evaporation removes the hot tail, driving the phase-space density up toward quantum degeneracy.\n",{"path":18462,"title":18463,"module":18455,"summary":18464},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Fbose-einstein-condensation","Bose-Einstein Condensation of Atomic Gases","Below a critical temperature a gas of identical bosons places a macroscopic fraction of its atoms in the single lowest-energy state. The transition occurs when the thermal de Broglie wavelength grows to the interparticle spacing, so the phase- space density reaches order unity. The critical temperature follows from the Bose-Einstein distribution and the density of states, the condensate fraction grows as one minus (T\u002FTc) to the three-halves, and the condensate reveals itself in time-of-flight as a sharp bimodal peak in the momentum distribution. The 1995 rubidium and sodium experiments realized it in dilute trapped gases.\n",{"path":18466,"title":18467,"module":18455,"summary":18468},"\u002Fatomic-physics\u002Fmodern-atomic-physics\u002Foptical-clocks-precision","Optical Atomic Clocks and Precision Measurement","An atomic clock counts the oscillations of a field locked to an atomic transition. The cesium microwave standard defines the second through the 9.19 GHz ground-state hyperfine transition, interrogated by Ramsey's separated-oscillatory-field method whose fringe width is set by the free-precession time. Optical clocks replace the microwave transition with an optical one five orders of magnitude higher in frequency, raising the quality factor and the fractional stability in proportion. Lattice and single-ion clocks reach fractional uncertainties near ten-to-the-minus- eighteen by trapping the atoms at a magic wavelength that cancels the light shift, and at that level they measure the gravitational redshift over centimetres of height.\n",{"path":18470,"title":18471,"module":6,"summary":6},"\u002Fatomic-physics","Atomic Physics",{"path":18473,"title":18474,"module":6,"summary":6},"\u002Fdatabases","Databases",{"path":18476,"title":18477,"module":16062,"summary":18478},"\u002Fcategory-theory\u002Ffoundations\u002Fwhat-is-a-category","Categories, Objects, and Arrows","A category is objects, arrows between them, a rule for composing arrows, and an identity arrow on every object, subject to associativity and the unit laws. The axioms mention no elements: arrows need not be functions, and an object is known only through the arrows into and out of it. Isomorphism, commutative diagrams, duality, and the terminal object are the first consequences.\n",{"path":18480,"title":18481,"module":16062,"summary":18482},"\u002Fcategory-theory\u002Ffoundations\u002Fexamples-of-categories","A Zoo of Categories","The axioms admit two very different kinds of model: large categories of structured sets and their structure-preserving maps (Set, Mon, Grp, Top, Vect), and small categories that are themselves single algebraic objects — a monoid as a one-object category, a poset as a thin category. The awkward cases Rel and Pfn have sets as objects but relations and partial functions as arrows, and a typed programming language presents its types and programs as a category.\n",{"path":18484,"title":18485,"module":16062,"summary":18486},"\u002Fcategory-theory\u002Ffoundations\u002Fspecial-morphisms","Isomorphisms, Monos, and Epis","Injectivity and surjectivity mention elements, so a general category re-expresses them by cancellation: monomorphisms cancel on the left, epimorphisms on the right. Sections and retractions are the split versions with an explicit one-sided inverse. Mono plus epi does not force an isomorphism, and subobjects are equivalence classes of monos into a fixed object.\n",{"path":18488,"title":18489,"module":16062,"summary":18490},"\u002Fcategory-theory\u002Ffoundations\u002Ffunctors","Functors: Maps Between Categories","A functor sends objects to objects and arrows to arrows while preserving composition and identities. Covariant and contravariant functors, the standard stock (forgetful, free, hom, and powerset), and the classification by faithfulness, fullness, and essential surjectivity all follow. Functors compose, so categories and functors form a category themselves.\n",{"path":18492,"title":18493,"module":16062,"summary":18494},"\u002Fcategory-theory\u002Ffoundations\u002Fnatural-transformations","Natural Transformations and Functor Categories","A natural transformation is a map between two parallel functors: one component arrow per object, subject to a commuting square for every arrow of the source. Naturality is verified for the determinant, the double dual, and list operations; functors and natural transformations form the functor category [C, D]; and vertical and horizontal composition satisfy the Godement interchange law.\n",{"path":18496,"title":18497,"module":16062,"summary":18498},"\u002Fcategory-theory\u002Ffoundations\u002Fsize-and-set-theory","Size: Small, Large, Locally Small","The objects of Set do not form a set, and pretending otherwise reproduces the classical paradoxes. Classes make the small\u002Flarge distinction precise, with locally small and essentially small as the intermediate notions. Cantor's theorem shows Set and its algebraic relatives are large, and the function-based axiomatization of sets is the one category theory prefers to ZFC.\n",{"path":18500,"title":18501,"module":18502,"summary":18503},"\u002Fcategory-theory\u002Funiversal-properties\u002Funiversal-properties","Universal Properties, Initial and Terminal Objects","Universal Properties and Basic Constructions","A universal property characterizes an object by a for-all\u002Fexists-unique condition on the arrows into or out of it, and any two objects satisfying the same property are isomorphic by a unique isomorphism. Initial and terminal objects are the simplest cases; the free vector space, the discrete topology, and the ring of integers show the pattern at work.\n",{"path":18505,"title":18506,"module":18502,"summary":18507},"\u002Fcategory-theory\u002Funiversal-properties\u002Fproducts-and-coproducts","Products and Coproducts","The product of two objects is a wedge of projections through which every other wedge factors uniquely; the coproduct is the dual, built from injections. In Set these are the cartesian product and the disjoint union, in a poset the meet and join, and in abelian groups the two coincide. The mediating-arrow discipline established here is the template for all limits.\n",{"path":18509,"title":18510,"module":18502,"summary":18511},"\u002Fcategory-theory\u002Funiversal-properties\u002Fconstructions-on-categories","Opposite, Product, Slice, and Comma Categories","Categories are themselves mathematical structures, and the standard algebraic constructions apply: opposites, products, subcategories, slices, and the comma category that subsumes them. The opposite category yields the duality principle, halving the subject's proofs; slice and comma categories repackage every universal property as an initial or terminal object.\n",{"path":18513,"title":18514,"module":18515,"summary":18516},"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Frepresentable-functors","Hom-Functors and Representables","Representables and the Yoneda Lemma","Fixing an object A of a locally small category produces a set-valued functor, the hom-functor A(A,-), that records every map out of A. A functor is representable when it is naturally isomorphic to such a hom-functor. We define the covariant and contravariant hom-functors, collect the standard representables (identity, forgetful, powerset), and read maps as generalized elements of varying shape.\n",{"path":18518,"title":18519,"module":18515,"summary":18520},"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-lemma","The Yoneda Lemma","The Yoneda lemma computes the natural transformations out of a representable presheaf: they form a set in natural bijection with X(A). The proof fixes a single degree of freedom, the image of the identity arrow, and shows naturality forces everything else. We prove the bijection, verify naturality in both variables, and read off that a natural transformation out of a representable is just one element.\n",{"path":18522,"title":18523,"module":18515,"summary":18524},"\u002Fcategory-theory\u002Frepresentables-yoneda\u002Fyoneda-consequences","The Yoneda Embedding and Its Uses","Three corollaries turn the Yoneda lemma into working machinery. A representation of a presheaf is the same thing as a universal element; the Yoneda embedding of a category into its presheaf category is full and faithful; and two objects are isomorphic exactly when their representables are. Together they justify constructing arrows by constructing natural transformations between hom-functors, and they contain Cayley's theorem as the one-object case.\n",{"path":18526,"title":18527,"module":18528,"summary":18529},"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits","Cones and Limits","Limits and Colimits","A diagram is a functor from a small shape category; a cone over it is an object with compatible legs to every node; and a limit is the terminal cone, the one every other cone factors through uniquely. Products and terminal objects reappear as limits over particular shapes, and the whole construction is unique up to a single isomorphism.\n",{"path":18531,"title":18532,"module":18528,"summary":18533},"\u002Fcategory-theory\u002Flimits-colimits\u002Fproducts-equalizers-pullbacks","Equalizers and Pullbacks","The equalizer of a parallel pair is the universal arrow that makes the two composites agree; the pullback of a cospan is the universal commutative square. In Set they are solution sets and fibered products, every equalizer is monic, monics are stable under pullback, and products plus equalizers together generate all limits.\n",{"path":18535,"title":18536,"module":18528,"summary":18537},"\u002Fcategory-theory\u002Flimits-colimits\u002Fcolimits","Colimits: Coproducts, Coequalizers, Pushouts","Colimits are limits in the opposite category: cocones replace cones, and the universal cocone is initial rather than terminal. Coproducts glue objects side by side, coequalizers impose relations and produce quotients, pushouts glue along a shared part, and in Set every colimit is a quotient of a disjoint union. Directed colimits admit a clean elementwise description.\n",{"path":18539,"title":18540,"module":18528,"summary":18541},"\u002Fcategory-theory\u002Flimits-colimits\u002Fcomputing-limits","Computing Limits in Concrete Categories","In Set the limit of any diagram is the set of threads: choice functions through the nodes that commute with every edge. In Pos, Mon, and Top the recipe is the same limit downstairs plus the unique structure that makes the projections structure-preserving — pointwise order, componentwise operations, the topology generated by the projections. The pattern is what \"the forgetful functor creates limits\" means concretely.\n",{"path":18543,"title":18544,"module":18528,"summary":18545},"\u002Fcategory-theory\u002Flimits-colimits\u002Flimits-and-functors","Preservation, Reflection, and Creation of Limits","A functor preserves limits if it sends limit cones to limit cones, reflects them if it recognizes them, and creates them if limits downstairs lift uniquely upstairs. Representable functors preserve all limits, forgetful functors from algebra create them, and limits in functor categories are computed pointwise, one evaluation at a time.\n",{"path":18547,"title":18548,"module":18549,"summary":18550},"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions","Adjoint Functors via Hom-Set Bijections","Adjunctions","An adjunction is a natural bijection between two hom-sets: maps out of $F(A)$ in one category correspond to maps into $G(B)$ in the other. We give the definition, spell out the naturality axioms that make the correspondence compatible with composition, and work the flagship examples — free vector spaces, free groups, discrete and indiscrete topologies, and currying.\n",{"path":18552,"title":18553,"module":18549,"summary":18554},"\u002Fcategory-theory\u002Fadjunctions\u002Funits-and-counits","Units, Counits, and the Triangle Identities","The whole hom-set bijection of an adjunction is generated by two natural transformations: the unit, obtained by transposing identity maps on one side, and the counit, by transposing them on the other. Two triangle identities are all they must satisfy, and any pair satisfying them determines a unique adjunction. The same correspondence specializes to order-preserving maps between posets and to free constructions.\n",{"path":18556,"title":18557,"module":18549,"summary":18558},"\u002Fcategory-theory\u002Fadjunctions\u002Fadjunctions-via-universal-arrows","Adjunctions from Universal Arrows","The unit component at a single object is an initial object of a comma category, and this universal property alone rebuilds the whole adjunction. A functor has a left adjoint exactly when every object admits such a universal arrow, and the left adjoint is assembled from them one object at a time. We prove the equivalence of all three formulations of adjointness.\n",{"path":18560,"title":18561,"module":18549,"summary":18562},"\u002Fcategory-theory\u002Fadjunctions\u002Ffree-forgetful-adjunctions","Free Constructions and Free–Forgetful Adjunctions","Free monoids, free groups, and free vector spaces are left adjoints to forgetful functors, and the universal mapping property is all one needs to prove it. Some forgetful functors also have right adjoints (co-free constructions like the indiscrete topology), producing three-functor chains. Contravariant adjunctions, symmetric in their two functors, close the lesson with the pattern behind duality and representation theorems.\n",{"path":18564,"title":18565,"module":18566,"summary":18567},"\u002Fcategory-theory\u002Fadjoints-limits\u002Flimits-via-adjoints","Limits as Adjoints and as Representables","Adjoints, Representables, and Limits Together","A cone on a diagram is a natural transformation from a constant diagram, so a limit is a representation of the cone functor and, equivalently, a value of the right adjoint to the diagonal functor. We prove both rephrasings, derive uniqueness and functoriality of limits from them, and record the dual statement that a colimit is the left adjoint to the diagonal.\n",{"path":18569,"title":18570,"module":18566,"summary":18571},"\u002Fcategory-theory\u002Fadjoints-limits\u002Fpresheaf-limits-colimits","Limits and Colimits of Presheaves","Representables preserve limits, and limits in a functor category are computed one object at a time, so a presheaf category is complete and cocomplete with all its structure inherited pointwise from Set. The Yoneda embedding then preserves limits but not colimits, and the density theorem repairs the colimit side: every presheaf is a canonical colimit of representables.\n",{"path":18573,"title":18574,"module":18566,"summary":18575},"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoints-preserve-limits","Right Adjoints Preserve Limits (RAPL)","A functor with a left adjoint preserves every limit that exists, and dually a functor with a right adjoint preserves colimits. The proof is a four-line chain of natural isomorphisms through the adjunction and the continuity of representables. The theorem yields product-and-exponential arithmetic in Set, another proof that limits commute with limits, and a standard test for proving that a functor has no adjoint.\n",{"path":18577,"title":18578,"module":18566,"summary":18579},"\u002Fcategory-theory\u002Fadjoints-limits\u002Fadjoint-functor-theorem","The Adjoint Functor Theorem","RAPL makes limit preservation necessary for having a left adjoint; the adjoint functor theorems identify when it is sufficient. For ordered sets no extra hypothesis is needed. In general the candidate adjoint is a limit over a comma category that may be large, and the general adjoint functor theorem tames it with a weakly initial set. We prove GAFT in full and apply it to free groups and, through the special adjoint functor theorem, the Stone–Čech compactification.\n",{"path":18581,"title":18582,"module":18583,"summary":18584},"\u002Fcategory-theory\u002Fmonads-algebras\u002Fmonads","Monads from Adjunctions","Monads and Algebras","A monad on a category is an endofunctor equipped with a unit and a multiplication satisfying associativity and unit laws — the data of a monoid, written internally to the category of endofunctors. Every adjunction induces one, and the list, exception, and state constructions that model computational effects are all monads on Set.\n",{"path":18586,"title":18587,"module":18583,"summary":18588},"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-eilenberg-moore","Algebras for a Monad","An algebra for a monad is an object with a structure map that interacts correctly with the unit and multiplication. The algebras form the Eilenberg–Moore category, whose free–forgetful adjunction induces the monad back; a comparison functor relates any other inducing adjunction to it, and for the list monad the algebras are exactly monoids.\n",{"path":18590,"title":18591,"module":18583,"summary":18592},"\u002Fcategory-theory\u002Fmonads-algebras\u002Fkleisli-and-programming","The Kleisli Category and Monads in Programming","The Kleisli category of a monad has the same objects as the base but takes arrows A to TB, composed by mapping and flattening. These arrows are effectful programs, Kleisli composition is the bind of functional programming, and the Kleisli adjunction is the initial resolution of the monad, with Eilenberg–Moore at the terminal end.\n",{"path":18594,"title":18595,"module":18583,"summary":18596},"\u002Fcategory-theory\u002Fmonads-algebras\u002Falgebras-for-endofunctors","Algebras for an Endofunctor and Recursion","Dropping the monad laws leaves algebras for a bare endofunctor, whose initial objects are the least fixed points of the functor by Lambek's lemma. The natural numbers, lists, and trees are initial algebras; the unique map out of an initial algebra is the fold of functional programming; and the Smyth–Plotkin fixed-point technique builds Scott domains the same way.\n",{"path":18598,"title":18599,"module":18600,"summary":18601},"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Fcartesian-closed-categories","Cartesian Closed Categories","Cartesian Closed Categories and Typed Lambda Calculus","A cartesian closed category has a terminal object, binary products, and for every pair of objects an exponential object that internalizes the hom-set as an object of the category. The defining data is an evaluation arrow and a currying operation, packaged by the adjunction between product-with-A and exponential-by-A. Set, Boolean and Heyting algebras, functor categories, and Cat are all cartesian closed.\n",{"path":18603,"title":18604,"module":18600,"summary":18605},"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Flambda-calculus-correspondence","Typed Lambda Calculus and CCCs","The typed lambda calculus and the cartesian closed category are two presentations of the same theory. Types become objects, terms with one free variable become arrows, product types become products, and function types become exponentials, with abstraction matching currying and application matching evaluation. Building the category of a lambda theory and the internal language of a category are mutually inverse up to equivalence.\n",{"path":18607,"title":18608,"module":18600,"summary":18609},"\u002Fcategory-theory\u002Fcartesian-closed-lambda\u002Ffixed-points-and-recursion","Fixed Points in Cartesian Closed Categories","The untyped lambda calculus has a fixed-point combinator; the typed calculus cannot, and Lawvere's fixed-point theorem explains why: any point-surjection onto an exponential forces every endomap to have a fixed point, which is the abstract form of Cantor's diagonal argument. Recursion is recovered instead by restricting to omega-complete partially ordered objects, where every continuous endomap has a least fixed point built by iterating from bottom. This gives While loops a semantics.\n",{"path":18611,"title":18612,"module":6,"summary":6},"\u002Fcategory-theory","Category Theory",{"path":18614,"title":17256,"module":18615,"summary":18616},"\u002Fdeep-learning\u002Fmathematical-background\u002Flinear-algebra-for-deep-learning","Mathematical Background","Every quantity a network touches is a tensor, and every layer is a matrix acting on one. This lesson compiles the linear algebra deep learning actually uses: products and norms, the system $Ax=b$ and when it is solvable, the two decompositions (eigen and SVD) that diagonalize a transformation, and the pseudoinverse that solves what cannot be solved exactly. It then derives PCA as the worked example that ties it all together.\n",{"path":18618,"title":18619,"module":18615,"summary":18620},"\u002Fdeep-learning\u002Fmathematical-background\u002Fprobability-and-information-theory","Probability & Information Theory","This lesson assembles the probabilistic vocabulary a network is trained in (random variables, densities, the chain rule, expectation and covariance, the handful of distributions that recur everywhere) and then the information theory that turns a probabilistic model into a loss: self-information, entropy, and the KL divergence whose asymmetry is the cross-entropy objective itself.\n",{"path":18622,"title":18623,"module":18615,"summary":18624},"\u002Fdeep-learning\u002Fmathematical-background\u002Fnumerical-computation","Numerical Computation","Machine learning runs on finite-precision arithmetic, where every number is approximated and every operation rounds. This lesson sets the numerical ground rules: overflow and underflow and the standard stabilizations, the condition number that measures how much a problem amplifies error, and the gradient-based optimization (first and second order, constrained and unconstrained) that every training loop runs.\n",{"path":18626,"title":16615,"module":18615,"summary":18627},"\u002Fdeep-learning\u002Fmathematical-background\u002Fcalculus","This lesson assembles the differential calculus used in training networks: the gradient and directional derivative, the Jacobian and Hessian, and the chain rule in scalar, vector, and matrix form. From the chain rule it derives back-propagation as a single sweep over the computational graph, tabulates the matrix-calculus identities that recur in layer gradients, reads optimization off a second-order Taylor expansion, and ends with why reverse-mode automatic differentiation is the algorithm every framework runs.\n",{"path":18629,"title":18630,"module":16062,"summary":18631},"\u002Fdeep-learning\u002Ffoundations\u002Fwhat-is-deep-learning","What Is Deep Learning?","Deep learning is representation learning by composition: stack simple differentiable layers, define a loss, and let gradient descent discover the features a human would otherwise have to engineer by hand. We set up the whole vocabulary (model, loss, optimizer, data), the training loop that ties them together, and the three reasons the approach became practical.\n",{"path":18633,"title":18634,"module":16062,"summary":18635},"\u002Fdeep-learning\u002Ffoundations\u002Fmachine-learning-refresher","A Machine-Learning Refresher","The statistical framework the networks live in: data drawn from an unknown distribution, a loss to minimize, and the central question of generalization: will it work on data we have not seen? We set up empirical risk, capacity, the bias–variance tradeoff, and maximum likelihood.\n",{"path":18637,"title":18638,"module":16062,"summary":18639},"\u002Fdeep-learning\u002Ffoundations\u002Flinear-models-and-the-perceptron","Linear Models & the Perceptron","The simplest learners (linear regression, logistic regression, the perceptron) already contain the whole template: a weighted sum, a loss, a gradient step. They also fail on the XOR problem, which no linear model can solve — the limitation that motivates deep learning.\n",{"path":18641,"title":18642,"module":18643,"summary":18644},"\u002Fdeep-learning\u002Fneural-networks\u002Fthe-multilayer-perceptron","The Multilayer Perceptron","Neural Networks","Stacking linear layers with a nonlinearity between them removes the limitation that stopped the perceptron. We build the multilayer perceptron in explicit matrix form (the forward pass, its dimensions, a worked XOR network with concrete weights) and prove why the nonlinearity is essential: without it the deepest stack collapses to a single hyperplane.\n",{"path":18646,"title":18647,"module":18643,"summary":18648},"\u002Fdeep-learning\u002Fneural-networks\u002Factivation-functions","Activation Functions","The activation is the only nonlinear part of a layer, and the reason depth adds expressive power. We catalog the standard hidden units (sigmoid, tanh, ReLU and its descendants, plus GELU, softplus, swish and maxout), derive each unit's derivative in full, make the vanishing-gradient problem quantitative with the chain-rule product, work numeric examples, and explain why the saturating units gave way to ReLU and why ReLU's own dead-unit failure gave way to Leaky\u002FPReLU\u002FELU\u002FGELU.\n",{"path":18650,"title":18651,"module":18643,"summary":18652},"\u002Fdeep-learning\u002Fneural-networks\u002Funiversal-approximation","Universal Approximation","One hidden layer with a non-polynomial activation can approximate any continuous function on a compact set to arbitrary accuracy: the universal approximation theorem. We prove it constructively (two sigmoids make a bump; sums of bumps make any curve), then show the limitation: existence is not efficiency. Depth-separation results exhibit functions a deep net represents with $O(n)$ units that a shallow net needs $\\exp(n)$ units to match.\n",{"path":18654,"title":18655,"module":18643,"summary":18656},"\u002Fdeep-learning\u002Fneural-networks\u002Fbackpropagation","Backpropagation","Backpropagation is the chain rule run backward over a computational graph. We formalize the graph, derive the four backprop equations for an MLP, present the forward and backward passes as algorithms, and work a tiny two-layer net by hand with explicit numbers. The result: one scalar loss, reverse-mode autodiff, and a gradient for every parameter at twice the cost of a forward pass.\n",{"path":18658,"title":18659,"module":18643,"summary":18660},"\u002Fdeep-learning\u002Fneural-networks\u002Floss-functions-and-output-units","Loss Functions & Output Units","The last layer is where a network's hidden representation meets the task. Choosing an output unit and a loss is not two independent choices; maximum likelihood fixes the pair. We derive the standard couplings (linear\u002FMSE, sigmoid\u002FBCE, softmax\u002Fcross-entropy), show why softmax and cross-entropy were built to cancel into the residual $\\hat y - y$, and prove why squared error is the wrong loss for a saturating classifier.\n",{"path":18662,"title":18663,"module":18664,"summary":18665},"\u002Fdeep-learning\u002Foptimization\u002Fgradient-descent-and-sgd","Gradient Descent & SGD","Optimization","Training is descent on the empirical risk: step the parameters against the gradient. We derive the minibatch gradient as an unbiased estimator whose variance falls as $1\u002FB$, derive the learning-rate ceiling from the smoothness-stability bound $\\eta \u003C 2\u002FL$, and lay out the schedules (step, exponential, cosine, warmup) that anneal it over training.\n",{"path":18667,"title":18668,"module":18664,"summary":18669},"\u002Fdeep-learning\u002Foptimization\u002Fmomentum-and-adaptive-methods","Momentum & Adaptive Methods","Plain gradient descent zig-zags across ravines and moves slowly along flat valleys, because one global learning rate cannot suit a surface with wildly different curvature in different directions. Two fixes address the two problems: momentum accumulates a velocity that damps the oscillation and accelerates the drift, and adaptive methods give every parameter its own learning rate scaled by the history of its gradients. Adam fuses both, and is the default optimizer of modern deep learning.\n",{"path":18671,"title":18672,"module":18664,"summary":18673},"\u002Fdeep-learning\u002Foptimization\u002Finitialization","Weight Initialization","The initial weights determine whether training can succeed before the first gradient step. Initialize every weight equal and all hidden units compute the same function forever; initialize too small or too large and the signal vanishes or explodes as it crosses depth. A single variance condition, $n_{\\text{in}}\\mathrm{Var}(W)=1$, fixes both, and reading it off the forward and backward passes yields Xavier and He initialization directly.\n",{"path":18675,"title":18676,"module":18664,"summary":18677},"\u002Fdeep-learning\u002Foptimization\u002Fthe-optimization-landscape","The Optimization Landscape","The loss of a deep network is a non-convex surface in millions of dimensions, so local search carries no global guarantee, yet it works. We classify critical points by the eigenvalues of the Hessian, show that in high dimension nearly all of them are saddle points rather than bad local minima, and read off the practical terrain — plateaus, cliffs, ill-conditioning, and the sharp-versus-flat distinction that ties the geometry of a minimum to how well it generalizes.\n",{"path":18679,"title":18680,"module":18664,"summary":18681},"\u002Fdeep-learning\u002Foptimization\u002Fsecond-order-and-approximate-methods","Second-Order & Approximate Methods","Newton's method reads the curvature of the loss off its Hessian and jumps to the minimum of the local quadratic in a single step, rescaling away the ill-conditioning that slows first-order descent. We derive it, then explain the three obstacles that keep it out of deep learning: a $d \\times d$ Hessian for $d$ in the billions, an attraction to saddle points, and minibatch noise. The alternative is approximation (conjugate gradients, BFGS and L-BFGS, the natural gradient and Hessian-free methods), each buying some of Newton's curvature information without ever forming or inverting $H$.\n",{"path":18683,"title":18684,"module":18685,"summary":18686},"\u002Fdeep-learning\u002Fregularization\u002Fregularization-overview","Regularization Overview","Regularization","Regularization is any modification to a learning algorithm meant to lower test error at the possible expense of training error. We derive the bias–variance decomposition that explains why it helps, set up the two parameter-norm penalties, $L^2$ weight decay and $L^1$, derive their update rules and eigenbasis shrinkage, show geometrically why $L^1$ alone produces sparse weights (soft-thresholding), distinguish weight decay from loss-added $L^2$ under AdamW, and read both penalties through the two lenses that recur across the chapter: a norm-ball constraint via KKT, and a prior via MAP estimation.\n",{"path":18688,"title":18689,"module":18685,"summary":18690},"\u002Fdeep-learning\u002Fregularization\u002Fdropout-and-data-augmentation","Dropout & Data Augmentation","Two of the most effective regularizers add no penalty term at all; they perturb the computation instead. Dropout multiplies hidden units by a random Bernoulli mask, training an exponential ensemble of thinned subnetworks that share weights; inverted scaling collapses that ensemble into one cheap forward pass at test time. Data augmentation enlarges the training set with label-preserving transforms, injecting the invariances the task demands, and noise injection (input, weight, label smoothing, Mixup) generalizes the same idea into a continuous family.\n",{"path":18692,"title":18693,"module":18685,"summary":18694},"\u002Fdeep-learning\u002Fregularization\u002Fearly-stopping-and-parameter-sharing","Early Stopping & Parameter Sharing","Two cheap regularizers that cost no extra term in the loss. Early stopping treats training time itself as a hyperparameter (watch the validation curve, halt at its minimum, keep the best checkpoint), and for a quadratic objective it is provably equivalent to $L^2$ weight decay. Parameter sharing goes the other way: it constrains many weights to be _equal_, the prior behind every convolution and every recurrent step, and the reason a CNN has orders of magnitude fewer parameters than the dense net it replaces.\n",{"path":115,"title":18696,"module":18685,"summary":18697},"Normalization","Normalization layers standardize activations to zero mean and unit variance inside the network, then hand the model a learnable scale and shift to undo the constraint when it pays to. Batch normalization does this across the batch and must keep separate train-time and test-time statistics; layer, instance, and group norm change only the axes they average over. The result is faster, better-conditioned optimization and a free dose of regularizing batch noise.\n",{"path":18699,"title":18700,"module":15125,"summary":18701},"\u002Fdeep-learning\u002Farchitectures\u002Fconvolutional-networks","Convolutional Networks","A convolutional network replaces the dense layer's all-to-all weight matrix with a small kernel slid across the input. Three structural commitments (sparse connectivity, parameter sharing, and translation equivariance) collapse the parameter count by orders of magnitude and bake the right prior for images directly into the architecture. We derive the convolution arithmetic, the output geometry, pooling, and the receptive field, then assemble the canonical stack.\n",{"path":18703,"title":18704,"module":15125,"summary":18705},"\u002Fdeep-learning\u002Farchitectures\u002Fcnn-architectures","CNN Architectures","Six landmark networks, each contributing exactly one idea: LeNet's conv-pool stack, AlexNet's ReLU-and-dropout scale, VGG's $3\\times3$ uniformity, Inception's multi-scale module, ResNet's residual skip, and DenseNet's dense connectivity. The common thread is the degradation problem (why plain deeper nets train worse, not just overfit) and the residual block that solved it by keeping a $+1$ path open for the gradient.\n",{"path":18707,"title":18708,"module":15125,"summary":18709},"\u002Fdeep-learning\u002Farchitectures\u002Frecurrent-networks","Recurrent Networks","A recurrent network folds a sequence into a fixed-size hidden state, reusing one set of weights at every time step, the architectural prior that the same rule applies wherever it lands in time. Unrolling the recurrence exposes a deep feed-forward graph; backpropagation through it sums gradient contributions across all steps and chains a product of Jacobians, and that product is why long-range gradients vanish or explode. That failure motivates gated architectures.\n",{"path":18711,"title":18712,"module":15125,"summary":18713},"\u002Fdeep-learning\u002Farchitectures\u002Flstm-and-gru","LSTM & GRU","A plain recurrent network propagates its hidden state through a repeated weight-matrix multiply, and the Jacobian product that results vanishes or explodes long before a useful gradient can reach the early steps. Gated RNNs fix this with an additive memory path: a cell state that is carried forward almost unchanged, past which the gradient flows along a near-identity highway. We derive that highway, give the full LSTM and GRU equations, and compare the two.\n",{"path":17,"title":18715,"module":15125,"summary":18716},"Attention & Transformers","Attention replaces fixed wiring with content-based routing: every position reads from every other through a soft, learned dot-product lookup. We derive scaled dot-product attention and its $\\sqrt{d_k}$ correction, build it into multi-head self-attention, inject order with positional encodings, and stack the whole thing into the Transformer block that displaced recurrence and convolution alike.\n",{"path":15127,"title":5,"module":15125,"summary":15143},{"path":14484,"title":14485,"module":15125,"summary":18719},"The Transformer makes no assumption about what a token represents. This part follows the architecture out of language: image patches feed a plain encoder (the Vision Transformer), the decoder-only half scales into the GPT line of large language models, and one substrate covers translation, retrieval, and multimodal grounding. We work the ViT patch arithmetic and a GPT parameter count by hand, then close on the empirical scaling laws — power-law loss, the Chinchilla compute-optimal balance, and emergent behavior — that made scale the dominant lever.\n",{"path":18721,"title":18722,"module":15125,"summary":18723},"\u002Fdeep-learning\u002Farchitectures\u002Fgraph-neural-networks","Graph Neural Networks","A graph neural network learns on data with no grid and no canonical ordering: atoms in a molecule, users in a social network, road segments in a map. The unifying idea is message passing — each node repeatedly aggregates its neighbors' states and updates its own — built to respect the one symmetry graphs demand, permutation equivariance. We derive the message-passing framework, specialize it into GCN, GraphSAGE, GAT, and GIN, read off graph-level outputs, and bound what message passing can and cannot tell apart.\n",{"path":18725,"title":18726,"module":15125,"summary":18727},"\u002Fdeep-learning\u002Farchitectures\u002Fstate-space-models","State-Space Models and Mamba","A state-space model carries a continuous linear hidden state through a sequence, and that linearity buys two equivalent algorithms from one set of weights: a recurrence that runs in linear time with constant memory, and a global convolution that trains in parallel. Long-range memory comes from how the transition matrix is initialized (HiPPO) and parameterized (S4's diagonal-plus-low-rank form). Mamba breaks the convolution on purpose, making the parameters input-dependent so the model can select what to remember, recovered at speed by a hardware-aware parallel scan.\n",{"path":18729,"title":18730,"module":18731,"summary":18732},"\u002Fdeep-learning\u002Ftheory\u002Fgeneralization-theory","Generalization Theory","Theory & Frontiers","Classical learning theory bounds the gap between training and test error by a model's capacity (VC dimension, Rademacher complexity), and predicts that a model with more parameters than data should overfit catastrophically. Modern networks do the opposite: they interpolate, even fit pure noise, and still generalize. We derive the classical bounds, work the bias-variance decomposition, show why the bounds go vacuous, and survey what replaced them: double descent, the interpolation threshold, margin and norm-based bounds, and the implicit bias of the optimizer itself.\n",{"path":18734,"title":18735,"module":18731,"summary":18736},"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-robustness","Adversarial Robustness","A trained network can be fooled by a perturbation too small for a human to see: add a carefully aimed vector of magnitude $\\epsilon$ to a correctly classified image and the prediction flips. We derive the fast gradient sign method as the first-order-optimal step inside an $L_\\infty$ ball, explain the linearity hypothesis that makes high-dimensional models so easy to push around, build up to projected gradient descent, and frame adversarial training as a min-max robust-optimization problem with its own accuracy cost. Defenses beyond training continue in the next lesson.\n",{"path":18738,"title":18739,"module":18731,"summary":18740},"\u002Fdeep-learning\u002Ftheory\u002Fadversarial-defenses","Adversarial Defenses","Defending a network against an adversary is far harder than attacking one. This lesson covers the defense side: certified guarantees via randomized smoothing, the transferability that makes black-box attacks possible, and the recurring failure of gradient masking, where a defense hides the attacker's gradient instead of moving the decision boundary. It ends with the adaptive-attack discipline (BPDA, EOT, transfer) that every robustness claim must be tested against.\n",{"path":18742,"title":18743,"module":18731,"summary":18744},"\u002Fdeep-learning\u002Ftheory\u002Fbayesian-and-ensemble-methods","Bayesian & Ensemble Methods","A trained network returns a single point prediction and, with the softmax, a confidence, but that confidence is usually miscalibrated, collapsing to near- certainty even on inputs the model has never seen. This lesson covers uncertainty estimation for networks: the two kinds of uncertainty, the Bayesian posterior over weights and its tractable stand-ins (MC dropout, deep ensembles), and how to check whether a model's reported confidences match observed frequencies.\n",{"path":18746,"title":18747,"module":18731,"summary":18748},"\u002Fdeep-learning\u002Ftheory\u002Fdeep-equilibrium-models","Deep Equilibrium Models","A deep network need not be a fixed stack of layers; it can be a single weight-tied layer iterated to convergence, its output defined implicitly as the fixed point $z^\\star = f_\\theta(z^\\star, x)$. The forward pass becomes root-finding and the backward pass becomes implicit differentiation, so training costs O(1) memory regardless of effective depth. We derive both passes from the implicit function theorem and close the course on defining a layer by a fixed-point condition rather than an explicit stack.\n",{"path":18750,"title":18751,"module":18752,"summary":18753},"\u002Fdeep-learning\u002Fgenerative-models\u002Flinear-factor-models","Linear Factor Models","Generative Models","The simplest generative models share one template: a latent variable drawn from a fixed prior, run through a linear decoder, plus noise. Probabilistic PCA, factor analysis, independent component analysis, and sparse coding are all this template with a different prior on the latents and a different noise model. We derive each marginal, see why ICA needs non-Gaussianity to identify its sources, and show how sparse coding learns Gabor-like dictionary atoms.\n",{"path":18755,"title":18756,"module":18752,"summary":18757},"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoencoders","Autoencoders","An autoencoder is a network trained to copy its input to its output through a narrow channel; the useful product is the bottleneck representation $h$, not the reconstruction. We derive the undercomplete autoencoder and prove its linear case recovers PCA, then trade the bottleneck for explicit regularization (sparse, denoising, contractive) and show how a denoising autoencoder learns the low-dimensional manifold the data lives on.\n",{"path":18759,"title":18760,"module":18752,"summary":18761},"\u002Fdeep-learning\u002Fgenerative-models\u002Fvariational-autoencoders","Variational Autoencoders","An autoencoder compresses, but its latent space has gaps: sample a point between two encodings and the decoder produces noise. The variational autoencoder fixes this by training a probabilistic encoder against a prior, so the latent space becomes a smooth, samplable density. We derive the evidence lower bound it maximizes, the reparameterization trick that lets gradients flow through a random sample, and the closed-form Gaussian regularizer that pulls the posterior toward the prior.\n",{"path":18763,"title":18764,"module":18752,"summary":18765},"\u002Fdeep-learning\u002Fgenerative-models\u002Fgenerative-adversarial-networks","Generative Adversarial Networks","A generative adversarial network trains two networks against each other: a generator that turns noise into samples, and a discriminator that tries to tell real data from forgeries. The game has a clean theory: the optimal discriminator is a likelihood ratio, and at equilibrium the generator minimizes the Jensen–Shannon divergence to the data, with a global optimum exactly when its distribution matches the data. We derive that result, fix the saturating loss that breaks training, and catalogue the failure modes (mode collapse, instability, vanishing gradients) and the architectural fixes.\n",{"path":18767,"title":18768,"module":18752,"summary":18769},"\u002Fdeep-learning\u002Fgenerative-models\u002Fautoregressive-and-normalizing-flows","Autoregressive Models & Normalizing Flows","Two families that provide exact likelihoods, each at a cost. Autoregressive models factor the joint by the probability chain rule and learn each conditional with a masked network: exact $\\log p(x)$, but sampling proceeds one coordinate at a time. Normalizing flows push a simple base density through an invertible map and read $\\log p(x)$ off the change-of-variables formula, trading architectural freedom for a cheap Jacobian determinant via triangular coupling layers.\n",{"path":18771,"title":18772,"module":18752,"summary":18773},"\u002Fdeep-learning\u002Fgenerative-models\u002Fenergy-based-and-boltzmann-machines","Energy-Based & Boltzmann Machines","Energy-based models replace an explicit density with a scalar energy and a Boltzmann normalization, $p(x) = e^{-E(x)}\u002FZ$: simple to specify, but with an intractable partition function $Z$. The Boltzmann machine and its restricted variant make the energy bilinear so the hidden units factorize, and contrastive divergence sidesteps $Z$ by replacing the model expectation with a few Gibbs steps started at the data. We close on the undirected deep models (DBNs and DBMs) and how they differ from the directed VAE.\n",{"path":18775,"title":18776,"module":18752,"summary":18777},"\u002Fdeep-learning\u002Fgenerative-models\u002Fdiffusion-and-score-based-models","Diffusion and Score-Based Models","Corrupt a data point with Gaussian noise in small steps until only noise remains, then train a network to undo one step at a time. We derive the forward process and its closed-form marginal, reduce the variational bound to the single noise-prediction objective that makes diffusion trainable, and show the score-matching view that unifies it with Langevin sampling and the continuous SDE. The lesson closes with DDIM fast sampling, classifier-free guidance, and the latent diffusion that powers modern text-to-image systems.\n",{"path":18779,"title":18780,"module":18781,"summary":18782},"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fstructured-probabilistic-models","Structured Probabilistic Models","Probabilistic Methods","A joint distribution over $n$ variables is a table with exponentially many entries; nobody can store it, fit it, or sample from it directly. Structure fixes this: a graph whose missing edges encode conditional independencies that factor the joint into small local pieces. We build the two dialects, directed (Bayesian networks) and undirected (Markov random fields), read independence off the graph, and connect the machinery to the latent-variable and energy-based models that power deep generative learning.\n",{"path":18784,"title":18785,"module":18781,"summary":18786},"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fmonte-carlo-and-mcmc","Monte Carlo & MCMC","Most quantities of interest in a probabilistic model are integrals nobody can compute in closed form: expectations, marginals, partition functions. Monte Carlo replaces the integral with an average over samples; importance sampling reweights samples from a tractable proposal; and when even sampling the target is hard, Markov-chain Monte Carlo builds a chain whose stationary distribution _is_ the target. We derive Metropolis–Hastings and Gibbs, analyze mixing, and close on the partition-function gradient that powers energy-based learning.\n",{"path":18788,"title":18789,"module":18781,"summary":18790},"\u002Fdeep-learning\u002Fprobabilistic-methods\u002Fapproximate-inference","Approximate Inference","In a latent-variable model the quantity we need, the posterior $p(h\\mid v)$ over hidden causes, is almost never computable, because its normalizer is an intractable sum over configurations. Approximate inference reframes the problem as optimization: maximize the evidence lower bound, a tractable functional whose gap to the true log-evidence equals a KL divergence. From that single bound fall expectation–maximization, mean-field variational inference, MAP, and the learned encoders behind variational autoencoders.\n",{"path":18792,"title":18793,"module":18794,"summary":18795},"\u002Fdeep-learning\u002Fpractical\u002Fpractical-methodology","Practical Methodology","Practical Deep Learning","Knowing the algorithms is half the job; the other half is a disciplined loop. Fix a goal and a metric, stand up an end-to-end baseline, then read the train\u002Fvalidation gap to decide whether the next move is more data or a bigger model. We detail that loop: choosing metrics under class imbalance, default baselines by data type, extrapolating the data a target needs, and guarding the data pipeline against the leaks and label bugs that corrupt every gradient. Hyperparameter tuning, debugging, and deployment continue in the sequel.\n",{"path":18797,"title":18798,"module":18794,"summary":18799},"\u002Fdeep-learning\u002Fpractical\u002Fhyperparameters-and-debugging","Hyperparameters & Debugging","The tuning half of the methodology loop. The learning rate is the one hyperparameter that dominates, so we tune it first, on a log scale, coarse to fine, and prefer random search to grid when only a few dials matter. Then an ordered debugging playbook — overfit one batch, check the loss at initialization against ln C, watch the gradient norm, gradient-check against centered finite differences — and, after launch, monitoring for train-test skew and distribution drift with confidence-based abstention.\n",{"path":18801,"title":18802,"module":18794,"summary":18803},"\u002Fdeep-learning\u002Fpractical\u002Frepresentation-learning","Representation Learning","A good representation makes a hard task easy by changing coordinates: it disentangles the factors of variation, spends its bits as a distributed code, and respects the low-dimensional manifold the data lives on. We make those three properties precise, recover the manifold hypothesis, and close on the first method that turned them into training practice — greedy layer-wise unsupervised pretraining — before the sequel picks up how the field learned to reuse those features.\n",{"path":18805,"title":18806,"module":18794,"summary":18807},"\u002Fdeep-learning\u002Fpractical\u002Ftransfer-learning","Transfer Learning","A representation learned once can be reused everywhere. We cover the main mechanisms of reuse: feature extraction versus fine-tuning, the generic-to-specific gradient of features that sets the freeze boundary, the learning-rate discipline that keeps borrowed weights from being erased, domain adaptation when only the input distribution shifts, and the modern arc from supervised transfer to self-supervised foundation models.\n",{"path":18809,"title":18810,"module":18794,"summary":18811},"\u002Fdeep-learning\u002Fpractical\u002Fapplications","Applications","We survey large-scale training (the hardware, the two axes of parallelism, mixed precision, and the compression tricks that shrink a model after it is trained), then specialize the same gradient loop to vision, language, speech, and recommendation. Each domain is a different prior bolted onto one optimizer: convolutional invariance for pixels, distributed word vectors for tokens, sequence transduction for audio, low-rank factorization for the user–item matrix.\n",{"path":18813,"title":18814,"module":18794,"summary":18815},"\u002Fdeep-learning\u002Fpractical\u002Fmodel-compression-and-distillation","Model Compression and Distillation","A trained network and a deployable one are rarely the same object. This lesson is the toolkit for closing that gap: knowledge distillation transfers a large teacher's soft, information-rich logits into a small student; pruning deletes the weights that contribute least; quantization swaps 32-bit floats for 8- or 4-bit integers; and low-rank factorization replaces a fat matrix with two thin ones. We derive each method, show what it costs in accuracy, and lay out which combinations win on which hardware.\n",{"path":18817,"title":18818,"module":18794,"summary":18819},"\u002Fdeep-learning\u002Fpractical\u002Fmeta-learning-and-few-shot","Meta-Learning and Few-Shot Learning","A deep network trained on one example per class overfits. Meta-learning targets this few-shot regime by training across a distribution of tasks so that a new task is learnable from a handful of examples. We formalize the $N$-way $K$-shot episode, then derive the two dominant families: metric methods that learn an embedding where distance classifies (Prototypical Networks), and optimization methods that learn an initialization a few gradient steps can adapt (MAML). We close on the link to transfer learning and to the in-context few-shot behavior of large language models.\n",{"path":18821,"title":18822,"module":18823,"summary":18824},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Flarge-language-models","Large Language Models","Large Models & Agents","A large language model is a decoder-only Transformer trained on one objective, next-token prediction, then scaled until new behavior appears. This first part builds the object itself: the equivalence between next-token prediction and lossless compression, subword tokenization (BPE, WordPiece, Unigram, SentencePiece) worked on a real sentence, the four pretraining objectives and the attention masks that distinguish them, and the three model families (encoder-only, decoder-only, encoder--decoder) with their parameter budgets. Scaling, decoding, the KV cache, and alignment continue in part two.\n",{"path":18826,"title":18827,"module":18823,"summary":18828},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fscaling-inference-and-alignment","Scaling, Inference, and Alignment of Language Models","Once a language model is built, three questions remain: how does it improve as it grows, how is it decoded and served affordably, and how is a raw next-token predictor turned into an assistant. We derive the Kaplan power laws and the Chinchilla compute-optimal balance, trace emergent abilities and in-context learning, catalog the decoding strategies from greedy to nucleus sampling, work the KV cache that makes generation quadratic instead of cubic, cover parameter-efficient adaptation by low-rank updates (LoRA), and close on the alignment stack: instruction tuning, RLHF, and DPO.\n",{"path":18830,"title":18831,"module":18823,"summary":18832},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fseq2seq-pretraining-and-bart","Denoising Sequence-to-Sequence Pretraining: BART","BERT corrupts and reconstructs; GPT predicts the next token. Sequence-to-sequence pretraining unifies both by training a full encoder–decoder as a denoising autoencoder: corrupt the text with a noise function, then reconstruct the original through a bidirectional encoder and an autoregressive decoder. This first part derives the denoising objective, catalogs BART's five noise functions (with a worked Poisson-infilling budget), proves BART specializes to both BERT and GPT, and traces a dimension-annotated forward pass through its encoder--decoder. T5, PEGASUS, fine-tuning, and decoding continue in part two.\n",{"path":18834,"title":18835,"module":18823,"summary":18836},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ftext-to-text-transfer-and-conditional-generation","Text-to-Text Transfer and Conditional Generation","BART reconstructs a corrupted document; T5 pushes the same denoising idea into a single interface where every task is a string-to-string map. This second part covers T5's span corruption with sentinel tokens (with a worked token budget), PEGASUS's summarization-matched gap sentences and the MASS midpoint, supervised fine-tuning and beam-search decoding with a length penalty, the exposure-bias failure modes of autoregressive decoding, and a theorem showing why a bidirectional encoder--decoder strictly dominates a decoder-only model when the output is conditioned on a full input.\n",{"path":18838,"title":18839,"module":18823,"summary":18840},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fspeech-and-audio-models","Speech Recognition: Front-Ends and Alignment","Speech is a long, high-rate sequence whose label is short and unaligned, so the whole subject turns on bridging that mismatch. This first part builds the spectral front-ends that compress a waveform into frames (STFT, mel spectrogram, MFCC, with a worked frame-count), derives CTC's marginalization over alignments and its forward-backward recursion with a two-frame numeric example, and contrasts it with attention-based seq2seq (LAS) and the RNN transducer. Self-supervised and weakly-supervised models, and text-to-speech, continue in part two.\n",{"path":18842,"title":18843,"module":18823,"summary":18844},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fself-supervised-speech-and-synthesis","Self-Supervised Speech Models and Synthesis","The recognition front-ends and alignment losses of part one all need transcribed audio, which is scarce. This second part removes that dependence: wav2vec 2.0 learns speech representations from unlabeled audio by a masked contrastive objective, HuBERT swaps the contrast for masked prediction of clustered units, and Whisper trades curation for scale with weakly-supervised web audio and a multitask token interface. We close with text-to-speech (the same length mismatch run backwards) and a tour of speech foundation models, discrete audio codecs, and neural TTS.\n",{"path":18846,"title":18847,"module":18823,"summary":18848},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fai-agents","AI Agents: Tools and Reasoning","A language model that only emits text is a function from prompt to prompt; an agent closes the loop, letting that model act on an environment, read back the result, and decide again. This first part formalizes the agent as a policy over interaction histories, builds out tool calling and the executor trust boundary, the ReAct interleaving of reasoning and action (with concrete traces), and search over thoughts: chain-of-thought, self-consistency, least-to-most, and Tree of Thoughts. Memory, retrieval, reflection, and multi-agent orchestration continue in part two.\n",{"path":18850,"title":18851,"module":18823,"summary":18852},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fagent-memory-retrieval-and-orchestration","Agent Memory, Retrieval, and Orchestration","An agent's reasoning and tool use only matter if it can remember what it learned and coordinate work larger than one context window. This second part builds the systems around the loop: short-term scratchpad versus long-term vector store, retrieval-augmented generation with a worked softmax over passage scores, reflection (Reflexion, Self-Refine), and multi-agent orchestration. It closes on the failure modes that bound agents — invalid tool calls, horizon-error compounding, context overflow, non-terminating loops — and the benchmarks that score the full loop.\n",{"path":18854,"title":18855,"module":18823,"summary":18856},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmixture-of-experts","Mixture-of-Experts","A mixture-of-experts layer replaces one feed-forward network with many and a router that sends each token to only a few of them, so the parameter count and the per-token compute become separate dials. We derive the gated output, sparse top-$k$ routing softmax, the load-balancing loss that stops the router from collapsing onto a single expert, and expert\u002Ftoken capacity with dropping, then work the dimension-annotated tensor shapes and FLOP arithmetic. We trace the architectures from the sparsely-gated LSTM through GShard, Switch Transformer, and Mixtral, cover distributed expert parallelism, and close on the training dynamics, failure modes, and serving costs of a sparse model.\n",{"path":18858,"title":18859,"module":18823,"summary":18860},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Fmultimodal-models","Multimodal Contrastive Learning","A multimodal model places images, text, and audio in one representation space, so a picture and its caption land close together. This first part builds the contrastive route: the shared embedding space and its residual modality gap, the Vision Transformer image encoder (patch embedding, CLS token, position embeddings, with shapes), the symmetric InfoNCE loss that trains the CLIP dual encoder from a batch similarity matrix (with a worked numeric step), and zero-shot classification as a softmax over class-prompt embeddings. Fusion and vision-language models continue in part two.\n",{"path":18862,"title":18863,"module":18823,"summary":18864},"\u002Fdeep-learning\u002Flarge-models-and-agents\u002Ffusion-and-vision-language-models","Fusion and Vision-Language Models","A contrastive model compares modalities but never lets one read another. This second part builds the fusion route: early, late, and cross-attention fusion, then the three designs that connect a frozen vision encoder to a frozen language model — Flamingo's zero-initialized gated cross-attention, BLIP-2's Q-Former, and LLaVA's linear projector. We work the token-budget arithmetic that separates them, name the object-hallucination and fine-detail failure modes, cover the contrastive-then- instruction-tune recipe and its retrieval\u002Fcaptioning\u002FVQA benchmarks, and close on natively multimodal models.\n",{"path":18866,"title":18867,"module":18868,"summary":18869},"\u002Fdeep-learning\u002Freinforcement-learning\u002Ffoundations-of-reinforcement-learning","Foundations of Reinforcement Learning","Reinforcement Learning","Reinforcement learning is the third paradigm: an agent learns to act by interacting with an environment that returns rewards, not labels. We formalize the interaction as a Markov decision process, define the value functions that rank states and actions, and derive the Bellman expectation and optimality equations that every method downstream solves. Dynamic programming gives the exact answer when the model is known, and its convergence rests on a single fact: the Bellman operator is a contraction.\n",{"path":18871,"title":18872,"module":18868,"summary":18873},"\u002Fdeep-learning\u002Freinforcement-learning\u002Fmodel-free-prediction-and-control","Model-Free Prediction and Control","When the dynamics are unknown, an agent cannot plan against a model; it must learn directly from sampled experience. We build prediction and control from two estimators of the same return: Monte Carlo averages whole episodes, while temporal-difference learning bootstraps from its own next estimate. We trace the bias-variance contrast between them, derive SARSA and Q-learning as the on-policy and off-policy forms of control, unify everything through n-step returns and eligibility traces, and close on the deadly triad that makes off-policy bootstrapping with function approximation diverge.\n",{"path":18875,"title":18876,"module":18868,"summary":18877},"\u002Fdeep-learning\u002Freinforcement-learning\u002Fdeep-q-networks","Deep Q-Networks","A Deep Q-Network replaces the tabular action-value function with a neural approximator $Q(s,a;\\theta)$ and trains it by regression toward a bootstrapped target. Naive online Q-learning with a network diverges, so DQN adds two stabilizers: an experience-replay buffer that decorrelates samples, and a periodically-frozen target network that holds the regression target still. We derive the loss, give the full algorithm and the Atari pipeline, and then layer on Double DQN, the dueling split, prioritized replay, and the Rainbow combination.\n",{"path":18879,"title":18880,"module":18868,"summary":18881},"\u002Fdeep-learning\u002Freinforcement-learning\u002Fpolicy-gradients-and-actor-critic","Policy Gradients and Actor-Critic Methods","Value-based reinforcement learning learns what each state is worth and acts greedily; policy-gradient methods skip the detour and optimize a parameterized policy directly by ascending the gradient of expected return. The policy gradient theorem makes this tractable through the log-derivative trick, turning an intractable gradient of an expectation into an expectation of a gradient. REINFORCE realizes the idea but suffers high variance; baselines, the advantage function, and actor-critic learning reduce it, and trust-region methods (TRPO, PPO) keep each update from destroying the policy it just learned.\n",{"path":18883,"title":18884,"module":18868,"summary":18885},"\u002Fdeep-learning\u002Freinforcement-learning\u002Frl-from-human-feedback","Reinforcement Learning from Human Feedback","Many objectives we want from a model, that it be helpful and harmless, are hard to write down but easy to judge by comparison. RLHF turns that asymmetry into a training signal: fit a reward model to pairwise human preferences under the Bradley-Terry likelihood, then fine-tune the policy to maximize that reward under a KL penalty toward a reference. We derive the reward loss, the KL-regularized RL objective and its closed-form optimum, then show how DPO inverts that optimum to collapse the whole pipeline into one supervised log-sigmoid loss, and survey IPO, KTO, RLAIF, and GRPO.\n",{"path":18887,"title":15047,"module":6,"summary":6},"\u002Fdeep-learning",{"path":18889,"title":18890,"module":16806,"summary":18891},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fequilibrium-state-variables-zeroth-law","Equilibrium, State Variables, and the Zeroth Law","Thermodynamics describes a many-body system by a handful of macroscopic variables and the equilibrium relations among them. This lesson fixes the vocabulary: systems and the walls that separate them, state variables versus path-dependent process quantities, quasi-static and reversible idealizations, and the zeroth law, whose transitivity of thermal equilibrium is what lets temperature exist as a number. The ideal-gas thermometer turns that number into a scale, and an equation of state ties the variables into a surface.\n",{"path":18893,"title":18894,"module":16806,"summary":18895},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Ffirst-law-heat-and-work","The First Law: Internal Energy, Heat, and Work","The first law is energy conservation for a system that exchanges energy as both heat and work. Internal energy is a state function with an exact differential; heat and work are path-dependent process quantities. This lesson states $\\d U=\\delta Q+\\delta W$, computes compression work as an area on the $P$–$V$ plane, defines the heat capacities $C_V$ and $C_P$ and the enthalpy that makes $C_P$ natural, and works the isothermal and adiabatic processes of an ideal gas, including the adiabat $PV^\\gamma=\\text{const}$.\n",{"path":18897,"title":18898,"module":16806,"summary":18899},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fsecond-law-entropy-and-the-carnot-bound","The Second Law, Carnot Cycles, and Entropy","The second law forbids the free conversion of heat into work. This lesson states the Kelvin and Clausius forms, proves them equivalent, and analyzes the Carnot cycle to get the efficiency bound $1-T_c\u002FT_h$. Carnot's theorem makes that bound universal and defines the thermodynamic temperature scale. The Clausius inequality $\\oint \\delta Q\u002FT\\le 0$ then constructs entropy as a state function, $\\d S=\\delta Q_{\\rm rev}\u002FT$, whose non-decrease in isolated systems is the arrow of time.\n",{"path":18901,"title":18902,"module":16806,"summary":18903},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fthermodynamic-potentials-and-maxwell-relations","Thermodynamic Potentials and Maxwell Relations","The fundamental relation $\\d U=T\\,\\d S-P\\,\\d V+\\mu\\,\\d N$ packages the first and second laws into one exact differential. Legendre transforms swap each conjugate pair to produce the Helmholtz, enthalpy, Gibbs, and grand potentials, each minimized under its own natural variables. Equality of mixed second partials of these potentials gives the Maxwell relations, which convert unmeasurable entropy derivatives into measurable ones from the equation of state.\n",{"path":18905,"title":18906,"module":16806,"summary":18907},"\u002Fstatistical-mechanics\u002Fthermodynamics\u002Fstability-response-functions-and-the-third-law","Response Functions, Stability, and the Third Law","Response functions — heat capacities, compressibilities, thermal expansion — are the second derivatives of the potentials and the quantities an experiment actually measures. This lesson derives the general relation $C_P-C_V=TV\\alpha^2\u002F\\kappa_T$, shows that convexity of the potentials forces the stability conditions $C_V>0$ and $\\kappa_T>0$, and states the third law: entropy approaches a constant as $T\\to0$, so heat capacities and expansion coefficients vanish there and absolute zero is unattainable.\n",{"path":18909,"title":18910,"module":18911,"summary":18912},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fclassical-statistics-and-equipartition","Classical Statistics and Equipartition","Microstates, Phase Space, and Statistical Entropy","A liter of gas holds on the order of a trillion trillion molecules, far too many to track by their equations of motion. Classical statistical mechanics replaces the trajectories with a single probability law, the Boltzmann distribution, and reads the measurable properties of matter off it: the Maxwell speed distribution, the average energy per degree of freedom, and the heat capacities of gases and solids — together with the low-temperature failures that forced the quantum revision.\n",{"path":18914,"title":18915,"module":18911,"summary":18916},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fphase-space-and-liouvilles-theorem","Phase Space, Trajectories, and Liouville's Theorem","A classical system of N particles is one point in a 6N-dimensional phase space, and its evolution is a single trajectory driven by Hamilton's equations. This lesson builds that geometric picture, introduces the phase-space density of an ensemble, and proves Liouville's theorem: the density is carried by the flow as an incompressible fluid, so phase-space volume is conserved. The stationary densities of equilibrium follow as functions of the conserved quantities alone.\n",{"path":18918,"title":18919,"module":18911,"summary":18920},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fensembles-and-the-equal-probability-postulate","Ensembles and the Postulate of Equal a Priori Probabilities","An ensemble is a probability distribution over the microstates of a system. This lesson states the single postulate on which equilibrium statistical mechanics rests — that an isolated system in equilibrium is equally likely to be in any of its accessible microstates — and works out its consequences: the accessible phase-space volume, the overwhelming dominance of the most probable macrostate as the particle number grows, and the ergodic hypothesis that lets a time average be replaced by an ensemble average.\n",{"path":18922,"title":18923,"module":18911,"summary":18924},"\u002Fstatistical-mechanics\u002Ffoundations\u002Fstatistical-entropy-boltzmann-and-gibbs","Statistical Entropy: Boltzmann and Gibbs","Entropy is the logarithm of the number of accessible microstates. This lesson builds the two statistical entropies — Boltzmann's S = k ln Omega for an isolated system and Gibbs's S = -k sum p ln p for any ensemble — proves they agree for a uniform distribution, and connects both to Shannon's measure of missing information. The second law emerges as the drift toward maximum multiplicity, and maximizing the Gibbs entropy under constraints previews the canonical distribution.\n",{"path":18926,"title":18927,"module":18928,"summary":18929},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fmicrocanonical-ensemble-and-entropy","The Microcanonical Ensemble and Statistical Entropy","The Microcanonical Ensemble","An isolated system holds its energy, volume, and particle number fixed, and the fundamental postulate assigns equal probability to every microstate on its energy shell. This lesson builds the microcanonical distribution, defines the enclosed phase-space volume $\\Gamma(E)$, the surface density of states $\\omega(E)=\\d\\Gamma\u002F\\d E$, and the shell count $\\Omega(E)$, shows their logarithms agree to $O(\\ln N)$ for large $N$, and reads the Boltzmann entropy $S=k\\ln\\Omega$ off the count. The measure factors $h^{3N}$ and $N!$ enter here and make $S$ extensive.\n",{"path":18931,"title":18932,"module":18928,"summary":18933},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fequilibrium-conditions-temperature-pressure-chemical-potential","Thermal, Mechanical, and Diffusive Equilibrium","Two isolated subsystems that can exchange energy, volume, or particles reach equilibrium at the partition that maximizes their combined entropy. Setting the derivative of the total entropy to zero identifies the statistical definitions $1\u002FT=(\\partial S\u002F\\partial E)$, $P\u002FT=(\\partial S\u002F\\partial V)$, and $-\\mu\u002FT=(\\partial S\u002F\\partial N)$, shows heat flows from hot to cold as an entropy increase, and recovers the fundamental relation $\\d S=(\\d E+P\\,\\d V-\\mu\\,\\d N)\u002FT$ from pure counting.\n",{"path":18935,"title":18936,"module":18928,"summary":18937},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Fideal-gas-phase-space-and-the-sackur-tetrode-entropy","The Ideal Gas, Phase-Space Volume, and the Sackur–Tetrode Entropy","The monatomic ideal gas is the first system whose microcanonical count can be done in closed form. The momentum integral is the volume of a $3N$-dimensional ball of radius $\\sqrt{2mE}$, the configuration integral is $V^N$, and together they give the Sackur–Tetrode entropy $S=Nk[\\ln(V\u002FN\\lambda^3)+5\u002F2]$ with the thermal wavelength $\\lambda=h\u002F\\sqrt{2\\pi mkT}$. The formula matches the measured entropy of helium, fixes the classical regime $n\\ll n_Q$, and shows why the $N!$ is needed for extensivity.\n",{"path":18939,"title":18940,"module":18928,"summary":18941},"\u002Fstatistical-mechanics\u002Fmicrocanonical\u002Ftwo-state-systems-paramagnets-and-negative-temperature","Two-State Systems, Paramagnets, and Negative Temperature","The ideal two-state paramagnet has a multiplicity counted by the binomial coefficient, an entropy that is an inverted dome in the energy, and a temperature read from the slope $1\u002FT=\\partial S\u002F\\partial E$. Because the energy is bounded above, the slope changes sign past the entropy maximum: a population-inverted spin system has a negative absolute temperature, which is hotter than any positive temperature. Nuclear-spin experiments and lasers realize the inverted state.\n",{"path":18943,"title":18944,"module":18945,"summary":18946},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fcanonical-ensemble-and-the-boltzmann-distribution","The Canonical Ensemble and the Boltzmann Distribution","The Canonical Ensemble","A system held at fixed temperature by contact with a heat reservoir is described by the canonical ensemble. Expanding the reservoir entropy to first order in the system energy gives the Boltzmann distribution $p_i\\propto e^{-\\beta E_i}$, and the same law follows from maximizing the Gibbs entropy at fixed mean energy. Both routes identify $\\beta=1\u002Fk_BT$ and fix the probability of every microstate from the temperature alone.\n",{"path":18948,"title":18949,"module":18945,"summary":18950},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fpartition-function-and-the-helmholtz-free-energy","The Partition Function and the Helmholtz Free Energy","The normalizing sum of the Boltzmann distribution, the partition function $Z=\\sum_i e^{-\\beta E_i}$, is a generating function for the thermodynamics. The mean energy is $-\\partial\\ln Z\u002F\\partial\\beta$, and the Gibbs entropy of the canonical distribution collapses to the bridge relation $F=-k_BT\\ln Z$. From $F$ every thermodynamic quantity follows by differentiation, and $Z$ factorizes over independent degrees of freedom.\n",{"path":18952,"title":18953,"module":18945,"summary":18954},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fenergy-fluctuations-and-ensemble-equivalence","Energy Fluctuations and the Equivalence of Ensembles","In the canonical ensemble the energy fluctuates, and the second derivative of $\\ln Z$ gives its variance. The fluctuation–response identity $\\langle\\Delta E^2\\rangle = k_BT^2C_V$ ties the spread of the energy to the heat capacity, and the relative fluctuation falls as $1\u002F\\sqrt{N}$. In the thermodynamic limit the canonical energy distribution is a sharp spike, and the canonical and microcanonical ensembles predict the same thermodynamics.\n",{"path":18956,"title":18957,"module":18945,"summary":18958},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fthe-einstein-solid-and-harmonic-systems","Harmonic Systems: The Einstein Solid and Vibrational Heat Capacity","A quantum harmonic oscillator has a geometric partition function summed in closed form, giving a mean energy $\\hbar\\omega(\\tfrac12+\\langle n\\rangle)$ with the Bose occupation factor. Modeling a solid as $3N$ independent oscillators yields a heat capacity that rises from zero and saturates at the Dulong–Petit value $3Nk_B$. The Einstein temperature sets the crossover, and the model's exponential low-temperature falloff, too steep against the observed $T^3$, motivates the Debye theory.\n",{"path":18960,"title":18961,"module":18945,"summary":18962},"\u002Fstatistical-mechanics\u002Fcanonical\u002Fparamagnetism-and-the-schottky-anomaly","Paramagnetism, Two-Level Systems, and the Schottky Anomaly","A magnetic moment in a field is a two-level system whose partition function is a hyperbolic cosine. The magnetization of a spin-$\\tfrac12$ paramagnet is $N\\mu\\tanh(\\mu B\u002Fk_BT)$, generalizing to the Brillouin function for spin $J$; it gives Curie's law $\\chi\\propto 1\u002FT$ at high temperature and saturates at low temperature. A finite level gap produces the Schottky heat-capacity peak, and the temperature dependence of the entropy on the field is the basis of adiabatic demagnetization cooling.\n",{"path":18964,"title":18965,"module":18966,"summary":18967},"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fideal-gas-partition-function-and-the-gibbs-paradox","The Ideal Gas Partition Function and the Gibbs Paradox","The Classical Ideal Gas","The classical monatomic ideal gas built from the partition function. The single-particle sum is $z_1=V\u002F\\lambda^3$ with the thermal de Broglie wavelength $\\lambda$; the $N$-particle partition function is $z_1^N\u002FN!$, and the $N!$ is forced by indistinguishability. From $Z$ the ideal-gas law, $U=\\tfrac32 Nk_BT$, and the Sackur–Tetrode entropy follow. The $N!$ makes the entropy extensive and resolves the Gibbs paradox: mixing identical gases produces no entropy change.\n",{"path":18969,"title":18970,"module":18966,"summary":18971},"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fequipartition-and-the-virial-theorem","Equipartition and the Virial Theorem","The equipartition theorem derived from the canonical ensemble: every phase-space coordinate that enters the Hamiltonian quadratically carries a mean energy $\\tfrac12 k_BT$. The generalized form $\\langle x_i\\,\\partial H\u002F\\partial x_j\\rangle = k_BT\\,\\delta_{ij}$ contains equipartition and the classical virial theorem as special cases. Equipartition fixes the classical heat capacities, fails by quantum freeze-out when a level gap exceeds $k_BT$, and shifts for a relativistic gas whose energy is linear rather than quadratic in momentum.\n",{"path":18973,"title":18974,"module":18966,"summary":18975},"\u002Fstatistical-mechanics\u002Fclassical-gas\u002Fmolecular-gases-rotation-and-vibration","Molecular Gases: Rotational and Vibrational Degrees of Freedom","The internal partition function of a diatomic gas factorizes into translational, rotational, vibrational, and electronic parts. The rigid rotor gives a rotational temperature $\\theta_{\\rm rot}$; the harmonic bond gives a vibrational temperature $\\theta_{\\rm vib}$. Each mode contributes to the heat capacity only above its characteristic temperature, producing the diatomic $C_V$ staircase from $\\tfrac32 R$ to $\\tfrac52 R$ to $\\tfrac72 R$. Homonuclear molecules carry a symmetry number, and hydrogen splits into ortho and para species.\n",{"path":18977,"title":18978,"module":18979,"summary":18980},"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fgrand-canonical-ensemble-and-the-grand-partition-function","The Grand Canonical Ensemble","Grand Canonical Ensemble","When a system exchanges both energy and particles with a reservoir, the reservoir fixes its temperature and its chemical potential. Expanding the reservoir entropy to first order in the exchanged energy and particle number gives the Gibbs factor $e^{-\\beta(E-\\mu N)}$, and summing it over every microstate of every particle number gives the grand partition function $\\Xi$. The grand potential $\\Phi = -k_BT\\ln\\Xi = -PV$ generates the mean particle number, energy, entropy, and pressure by differentiation.\n",{"path":18982,"title":18983,"module":18979,"summary":18984},"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fchemical-potential-fugacity-and-number-fluctuations","Chemical Potential, Fugacity, and Number Fluctuations","The chemical potential is the energy to add one particle at fixed entropy and volume, equal to the slope of the free energy in the particle number. For the classical ideal gas $\\mu=k_BT\\ln(n\\lambda^3)$ is large and negative, and the fugacity $z=n\\lambda^3$ is small. The grand ensemble makes the particle number fluctuate; its variance $\\langle\\Delta N^2\\rangle=k_BT(\\partial N\u002F\\partial\\mu)$ equals $k_BT\\,N^2\\kappa_T\u002FV$, tying density fluctuations to the isothermal compressibility. Equality of $\\mu$ is the condition for diffusive equilibrium and phase coexistence.\n",{"path":18986,"title":18987,"module":18979,"summary":18988},"\u002Fstatistical-mechanics\u002Fgrand-canonical\u002Fensemble-summary-and-the-thermodynamic-web","The Three Ensembles and the Thermodynamic Web","The microcanonical, canonical, and grand canonical ensembles hold different variables fixed and generate different potentials — the entropy $S$, the Helmholtz free energy $F$, and the grand potential $\\Phi$ — linked by Legendre transforms that trade each fixed variable for its conjugate. Each successive ensemble lets one more quantity fluctuate. In the thermodynamic limit the three agree, the relative fluctuations vanishing as $1\u002F\\sqrt{N}$; the ideal gas gives the same equation of state in all three. The choice of ensemble is a matter of convenience, set by which sum is easiest.\n",{"path":18990,"title":18991,"module":18992,"summary":18993},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fquantum-statistics-bose-einstein-and-fermi-dirac","Quantum Statistics — Bose-Einstein and Fermi-Dirac","Quantum Statistics","Quantum particles of the same kind are genuinely indistinguishable: no label survives an overlap of their wave functions. Counting states with that constraint replaces the Boltzmann distribution with two quantum laws — the Bose-Einstein distribution for integer-spin particles, which clump into shared states, and the Fermi-Dirac distribution for half-integer-spin particles, which exclude one another. Both reduce to Boltzmann in the dilute, hot limit, and a de Broglie criterion says exactly when.\n",{"path":18995,"title":18996,"module":18992,"summary":18997},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fderiving-the-quantum-distributions","Deriving the Quantum Distributions from the Grand Ensemble","The Bose-Einstein and Fermi-Dirac distributions follow from one observation: in the occupation-number representation the single-particle modes are independent, so the grand partition function factorizes into one factor per mode. A boson mode sums a geometric series over all occupancies; a fermion mode sums two terms. Differentiating each factor gives the mean occupation $1\u002F(e^{\\beta(\\varepsilon-\\mu)}\\mp 1)$, the Maxwell-Boltzmann limit when occupancies are small, and the occupation fluctuations that distinguish bunching from anti-bunching.\n",{"path":18999,"title":19000,"module":18992,"summary":19001},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fthe-classical-limit-and-quantum-concentration","The Classical Limit and Quantum Concentration","When every single-particle level is nearly empty, both quantum distributions collapse to the Maxwell-Boltzmann form, and the fugacity equals the ratio of the number density to the quantum concentration $n_Q = 1\u002F\\lambda^3$. The gas is classical when $n \\ll n_Q$, degenerate when $n \\gtrsim n_Q$. The chemical potential is large and negative in the classical regime and rises through zero as the gas degenerates. The leading quantum correction to the ideal-gas law is a second virial term that lowers the pressure for bosons and raises it for fermions — a statistical attraction and repulsion with no interaction behind it.\n",{"path":19003,"title":19004,"module":18992,"summary":19005},"\u002Fstatistical-mechanics\u002Fquantum-statistics\u002Fideal-quantum-gases-general-framework","Ideal Quantum Gases: The General Framework","Every ideal quantum gas is handled by one calculation. The sum over single-particle modes becomes an energy integral weighted by a density of states $g(\\varepsilon)\\propto\\varepsilon^{1\u002F2}$, and the number and pressure reduce to the Bose and Fermi functions $g_\\nu(z)$ and $f_\\nu(z)$ of the fugacity. An integration by parts fixes $PV=\\tfrac23 U$ for a nonrelativistic gas and $PV=\\tfrac13 U$ for an ultrarelativistic one, independent of statistics. Specializing the density of states and the chemical potential then produces the photon gas, phonons, the Bose gas, and the Fermi gas as four branches of the same framework.\n",{"path":19007,"title":19008,"module":19009,"summary":19010},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-and-the-fermion-gas","Bose-Einstein Condensation and the Fermion Gas","Bosonic Systems","Below a critical temperature a boson gas drops a macroscopic fraction of its particles into the single ground state — Bose-Einstein condensation, the mechanism behind superfluid helium and the dilute-atom condensates cooled to nanokelvin. The same statistics applied to a photon gas reproduces Planck's blackbody spectrum. Fermions do the opposite: forbidden from sharing states, they fill every level up to the Fermi energy, and that filled sea governs the electrons in metals and the pressure that holds up a white dwarf.\n",{"path":19012,"title":19013,"module":19009,"summary":19014},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthe-photon-gas-and-plancks-radiation-law","The Photon Gas and Planck's Radiation Law","Electromagnetic radiation in equilibrium with cavity walls is a gas of non-conserved bosons, and non-conservation forces the chemical potential to zero. Counting standing-wave modes with two polarizations and weighting each by the Bose occupation gives the Planck spectral energy density. Its low-frequency tail reproduces the classical Rayleigh-Jeans law and the ultraviolet catastrophe; the Bose factor cuts the divergence off at high frequency and the peak obeys Wien's displacement law.\n",{"path":19016,"title":19017,"module":19009,"summary":19018},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fblackbody-thermodynamics-and-radiation-pressure","Blackbody Thermodynamics and Radiation Pressure","Integrating the Planck spectrum over all frequencies gives the total energy density proportional to the fourth power of temperature — the Stefan-Boltzmann law — and the isotropy of a relativistic gas fixes the radiation pressure at one third of the energy density. From the free energy follow the entropy and heat capacity, both proportional to T cubed, and the adiabatic law for radiation. The results govern the pressure inside stars and the cooling of the cosmic microwave background as the universe expands.\n",{"path":19020,"title":19021,"module":19009,"summary":19022},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fphonons-and-the-debye-model","Phonons and the Debye Model","The vibrations of a crystal lattice are quantized into phonons — bosons of zero chemical potential, counted exactly like cavity photons but with three polarizations, a finite sound speed, and a total of 3N modes. The Debye model replaces the true dispersion by a linear one cut off at a frequency that enforces that count. It gives the correct low-temperature T-cubed heat capacity the Einstein model missed and recovers the Dulong-Petit value at high temperature.\n",{"path":19024,"title":19025,"module":19009,"summary":19026},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fbose-einstein-condensation-derived","Bose-Einstein Condensation Derived","For a gas of conserved bosons the excited states can hold only a finite number of particles at fixed temperature, set by the Bose function at unit fugacity. When the total exceeds that ceiling the surplus collapses into the single ground state, which the continuum density-of-states integral misses and which must be restored by hand. This fixes the critical temperature, the condensate fraction, and the fact that a uniform gas condenses only in three or more dimensions.\n",{"path":19028,"title":19029,"module":19009,"summary":19030},"\u002Fstatistical-mechanics\u002Fbose-systems\u002Fthermodynamics-of-the-bose-gas-and-superfluidity","Thermodynamics of the Bose Gas and Superfluidity","The energy and pressure of the ideal Bose gas follow from the Bose function at the order above the density, and below the critical temperature the pressure depends on temperature alone because the condensate carries none. The heat capacity rises to a cusp at the transition. Real superfluid helium departs from the ideal gas because interactions matter: the Landau criterion ties frictionless flow to the phonon-roton excitation spectrum, and the two-fluid model carries a second sound.\n",{"path":19032,"title":19033,"module":19034,"summary":19035},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fthe-ideal-fermi-gas-at-zero-temperature","The Ideal Fermi Gas at Zero Temperature","Degenerate Fermi Gas","At absolute zero a gas of non-interacting fermions fills every single-particle state up to the Fermi energy and leaves the rest empty, a filled Fermi sphere in momentum space. This lesson computes the Fermi momentum, energy, and temperature from the density, the density of states, the total ground-state energy, and the degeneracy pressure that grows as $n^{5\u002F3}$. Numerical Fermi energies for metals set the scale: they are electron-volts, so room temperature is deep in the degenerate regime.\n",{"path":19037,"title":19038,"module":19034,"summary":19039},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fsommerfeld-expansion-and-electrons-in-metals","The Sommerfeld Expansion and Electrons in Metals","Turning on a small temperature blurs the Fermi step over a shell of width $k_BT$ around $\\epsilon_F$. The Sommerfeld expansion turns integrals over the Fermi function into a power series in $(k_BT\u002F\\epsilon_F)^2$, giving the shift of the chemical potential and a heat capacity linear in $T$. This resolves the old puzzle of the missing electronic heat capacity, predicts the combined $C=\\gamma T+AT^3$ of a metal, and gives the temperature-independent Pauli paramagnetism of the electron gas.\n",{"path":19041,"title":19042,"module":19034,"summary":19043},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fwhite-dwarfs-and-the-chandrasekhar-limit","White Dwarfs and the Chandrasekhar Limit","A white dwarf is held up against its own gravity by the degeneracy pressure of its electrons. Balancing that pressure against gravity gives a mass-radius relation $R\\propto M^{-1\u002F3}$: heavier white dwarfs are smaller and denser. As the density rises the electrons turn relativistic, the pressure softens from $n^{5\u002F3}$ to $n^{4\u002F3}$, and the star can no longer support itself above a critical mass. This lesson derives that Chandrasekhar mass, about $1.4\\,M_\\odot$, and what lies beyond it.\n",{"path":19045,"title":19046,"module":19034,"summary":19047},"\u002Fstatistical-mechanics\u002Ffermi-gas\u002Fneutron-stars-and-nuclear-matter","Neutron Stars and Dense Matter","When a collapsing core passes nuclear density, electron capture converts the matter to neutrons and their degeneracy pressure takes over. The same balance that fixes a white dwarf, rescaled by the neutron mass, gives a neutron star of a few solar masses in a ten-kilometre radius. General relativity is no longer a correction: the Tolman-Oppenheimer-Volkoff equation replaces the Newtonian balance and sets a maximum mass around two solar masses. This lesson rescales the Fermi-gas argument, states where it breaks, and places the compact objects in one stability sequence.\n",{"path":19049,"title":19050,"module":19051,"summary":19052},"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-cluster-expansion-and-virial-coefficients","The Cluster Expansion and Virial Coefficients","Interacting Gases","A real gas departs from $PV=Nk_BT$ because its molecules interact. The configuration integral factors through the Mayer function $f_{ij}=e^{-\\beta u_{ij}}-1$, and expanding it in powers of density produces the virial expansion $PV\u002FNk_BT = 1 + B_2(T)n + B_3(T)n^2 + \\cdots$. The second virial coefficient $B_2(T)=-\\tfrac12\\int f\\,\\d^3r$ is a single integral over the pair potential; it is positive for a hard core, negative for an attractive well, and vanishes at the Boyle temperature where the two balance.\n",{"path":19054,"title":19055,"module":19051,"summary":19056},"\u002Fstatistical-mechanics\u002Finteractions\u002Fthe-van-der-waals-gas-and-liquid-gas-coexistence","The van der Waals Gas and Liquid-Gas Coexistence","Resumming the second virial coefficient $B_2=b-a\u002Fk_BT$ into an equation of state gives the van der Waals model $(P+a\u002Fv^2)(v-b)=k_BT$, the simplest theory of a fluid that condenses. Below the critical temperature its isotherms develop a mechanically unstable loop; the Maxwell equal-area construction replaces the loop with a coexistence tie line. The critical point sits at $v_c=3b$, $k_BT_c=8a\u002F27b$, $P_c=a\u002F27b^2$, and the model predicts universal but incorrect critical exponents because it ignores fluctuations.\n",{"path":19058,"title":19059,"module":19051,"summary":19060},"\u002Fstatistical-mechanics\u002Finteractions\u002Fquantum-gases-with-interactions-and-exchange","Quantum Gases with Interactions and Statistical Exchange","A quantum gas has a nonzero second virial coefficient even with no forces between the particles: symmetrization alone produces an effective statistical interaction, attractive for bosons and repulsive for fermions, with range the thermal wavelength $\\lambda$. This lesson derives that exchange contribution $B_2=\\mp\\lambda^3\u002F2^{5\u002F2}g$, writes it as a statistical potential $v_s(r)=-k_BT\\ln(1\\pm e^{-2\\pi r^2\u002F\\lambda^2})$, and shows how real interactions add on top through the Beth-Uhlenbeck phase-shift formula, reducing at low temperature to a single scattering length.\n",{"path":19062,"title":19063,"module":19064,"summary":19065},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fphases-coexistence-and-classification","Phases, Coexistence, and the Classification of Transitions","Phase Transitions","A phase transition is a point where the free energy of a substance loses analyticity, so a small change in temperature or pressure produces a qualitative change of state. This lesson maps the coexistence curves of a pure substance, derives the Clausius-Clapeyron relation between the slope of a coexistence line and its latent heat, and separates first-order transitions (discontinuous entropy and density) from continuous ones (a vanishing order parameter and divergent response). The Ehrenfest scheme, the order parameter, and the triple and critical points fix the vocabulary the rest of the module builds on.\n",{"path":19067,"title":19068,"module":19064,"summary":19069},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-ising-model-and-exact-solutions","The Ising Model and Exact Results","The Ising model reduces cooperative ordering to spins on a lattice coupled to their neighbors, and the same Hamiltonian describes uniaxial magnets, the liquid-gas critical point through the lattice gas, and binary alloys. This lesson solves the one-dimensional chain exactly with the transfer matrix, shows by a domain-wall argument why one dimension has no ordered phase at any positive temperature, contrasts the survival of order in two dimensions, and quotes Onsager's exact two-dimensional results: the critical temperature, the logarithmically divergent heat capacity, and the magnetization exponent one eighth.\n",{"path":19071,"title":19072,"module":19064,"summary":19073},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fmean-field-theory-and-the-weiss-model","Mean-Field Theory and Spontaneous Symmetry Breaking","Mean-field theory replaces the neighbors of each spin by their average, turning the interacting Ising model into a single spin in a self-consistent field. The resulting equation m = tanh(beta J z m + beta h) has only the zero solution above a critical temperature and gains a nonzero root below it, giving spontaneous magnetization and a mean-field critical temperature k T_c = J z. The Bragg-Williams free energy turns single-welled above T_c and double-welled below, the picture of spontaneous symmetry breaking. The approximation is exact in high dimension and fails below the upper critical dimension four, quantified by the Ginzburg criterion.\n",{"path":19075,"title":19076,"module":19064,"summary":19077},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fcritical-exponents-and-landau-theory","Critical Exponents, Scaling, and Landau Theory","Near a continuous transition every singular quantity follows a power law in the reduced temperature, and the exponents alpha, beta, gamma, delta, nu, and eta encode the transition more sharply than T_c itself. Landau theory expands the free energy in the order parameter and delivers the mean-field exponents in a few lines. They disagree with experiment and with the exact two-dimensional Ising values, but the exponents are not independent: the scaling relations of Rushbrooke, Widom, Fisher, and Josephson tie them together, and the correlation length sets the length scale that organizes universality classes.\n",{"path":19079,"title":19080,"module":19064,"summary":19081},"\u002Fstatistical-mechanics\u002Fphase-transitions\u002Fthe-renormalization-group-idea","Scaling and the Renormalization-Group Idea","At a critical point fluctuations exist on every length scale, so the system looks the same after coarse-graining. The renormalization group makes this self-similarity a computation: group spins into blocks, integrate out the short scales, and track how the couplings change. The transformation has fixed points, and the flow near a critical fixed point separates relevant couplings that grow from irrelevant ones that shrink, which is why only dimension and symmetry survive to set the exponents. The one-dimensional Ising decimation carries the whole scheme through in closed form and reproduces the absence of a finite-temperature transition.\n",{"path":19083,"title":19084,"module":19085,"summary":19086},"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fthermodynamic-fluctuations-and-response","Thermodynamic Fluctuations and Response Functions","Fluctuations and Response","Thermodynamic variables are sharp only on average; a macroscopic system in equilibrium fluctuates about its mean values. Einstein inverted Boltzmann's $S=k_B\\ln\\Omega$ into a Gaussian probability for a fluctuation, $w\\propto e^{\\Delta S\u002Fk_B}$, and the second moments it predicts reproduce the response functions: $\\langle\\Delta E^2\\rangle=k_BT^2C_V$, $\\langle\\Delta V^2\\rangle=k_BTV\\kappa_T$, $\\langle\\Delta M^2\\rangle=k_BT\\chi_T$. The variances diverge where the responses diverge, at a critical point, producing critical opalescence and the breakdown of the thermodynamic description.\n",{"path":19088,"title":19089,"module":19085,"summary":19090},"\u002Fstatistical-mechanics\u002Ffluctuations\u002Fbrownian-motion-and-the-langevin-equation","Brownian Motion and the Langevin Equation","A pollen grain in water executes a random walk driven by molecular collisions. Einstein tied its diffusion constant to its mobility, $D=\\mu_{\\mathrm{mob}}k_BT$, turning a visible motion into a measurement of Avogadro's number. The Langevin equation splits the collisions into a systematic drag and a random force whose strength is fixed by the drag through $\\langle\\xi(t)\\xi(t')\\rangle=2\\gamma k_BT\\,\\delta(t-t')$ — the first fluctuation–dissipation relation. The mean-square displacement grows ballistically at short times and linearly, $\\langle r^2\\rangle=2dDt$, at long times, and the Stokes–Einstein relation $D=k_BT\u002F6\\pi\\eta a$ closes the loop to Perrin's experiments.\n",{"path":19092,"title":19093,"module":19085,"summary":19094},"\u002Fstatistical-mechanics\u002Ffluctuations\u002Flinear-response-and-the-fluctuation-dissipation-theorem","Linear Response and the Fluctuation-Dissipation Theorem","A system driven by a weak external field responds through a generalized susceptibility $\\chi(\\omega)$ whose imaginary part measures dissipation. The Wiener–Khinchin theorem makes the power spectrum of equilibrium fluctuations the Fourier transform of their correlation function, and the fluctuation–dissipation theorem ties the two together: $S_x(\\omega)=(2k_BT\u002F\\omega)\\,\\chi''(\\omega)$, so the spectrum of spontaneous fluctuations is fixed by the dissipative response. The Johnson–Nyquist noise of a resistor, $\\langle V^2\\rangle=4k_BTR\\,\\Delta f$, is the canonical example, and Onsager reciprocity closes the subject.\n",{"path":19096,"title":19097,"module":6,"summary":6},"\u002Fstatistical-mechanics","Statistical Mechanics",{"path":19099,"title":19100,"module":19101,"summary":19102},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fbonding-mechanisms","Bonding Mechanisms","Molecules and Chemical Bonding","A molecule forms when the total energy of two atoms drops below the energy of the separated pair. This lesson works through the four mechanisms that produce that minimum: the ionic bond from charge transfer, the covalent bond from shared electron wave functions, the metallic bond, and the weak dipole-dipole and hydrogen bonds, computing bond lengths and dissociation energies for NaCl, H₂, and H₂⁺.\n",{"path":19104,"title":19105,"module":19101,"summary":19106},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fmolecular-orbitals-and-h2-plus","The Molecular-Orbital Method and H₂⁺","The hydrogen molecule ion is the two-center problem that fixes the language of chemical bonding. This lesson builds the molecular orbital as a linear combination of atomic orbitals, minimizes the energy through the variational secular equation, and reduces the result to three two-center integrals: the overlap, the Coulomb term, and the exchange (resonance) integral. The bonding and antibonding levels, their potential-energy curves, and the charge piled between the nuclei follow from those integrals.\n",{"path":19108,"title":19109,"module":19101,"summary":19110},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fhydrogen-molecule-and-exchange","The Hydrogen Molecule, Exchange, and Hybridization","Adding the second electron turns the one-electron ion into the two-electron hydrogen molecule, where electron-electron repulsion and the Pauli principle govern the bond. This lesson contrasts the Heitler-London valence-bond and molecular-orbital wave functions, derives the singlet-triplet splitting as an exchange energy, shows why naive molecular orbitals fail at dissociation, and builds the sp, sp², and sp³ hybrids that fix the directed geometry of covalent bonds.\n",{"path":19112,"title":19113,"module":19101,"summary":19114},"\u002Fcondensed-matter\u002Fmolecules-and-bonding\u002Fvan-der-waals-forces","Van der Waals Forces","The bond of last resort acts between all atoms, even closed-shell noble gases with no permanent moment. This lesson separates the three van der Waals contributions — Keesom orientation, Debye induction, and London dispersion — derives the London 1\u002Fr⁶ attraction from the coupled-oscillator and second-order perturbation pictures, and assembles the Lennard-Jones potential to compute the equilibrium spacing and cohesive energy of the noble-gas crystals, argon in particular.\n",{"path":19116,"title":19117,"module":19118,"summary":19119},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Frotational-vibrational-spectra","Rotational and Vibrational Spectra of Molecules","Molecular Spectra","A diatomic molecule stores energy in three well-separated ledgers: electronic, vibrational, and rotational. Quantizing the rigid rotor gives levels spaced as ℓ(ℓ+1); quantizing the bond as a harmonic oscillator gives equally spaced vibrational levels. Their combination produces the P and R branches of an infrared absorption band, from which the bond length and force constant are read directly.\n",{"path":19121,"title":19122,"module":19118,"summary":19123},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Fanharmonicity-and-rovibrational-structure","Anharmonicity and Rovibrational Structure","The rigid rotor and harmonic oscillator are first approximations. A real bond follows the Morse potential, whose levels converge toward dissociation; a real rotor stretches centrifugally; and vibration couples to rotation, so the rotational constant depends on the vibrational level. This lesson works out the anharmonic and centrifugal corrections, the Birge-Sponer route to the dissociation energy, the isotope shift, and the thermal band envelope.\n",{"path":19125,"title":19126,"module":19118,"summary":19127},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Framan-and-electronic-bands","Raman Scattering and Electronic Bands","Not every vibration absorbs in the infrared. Raman scattering reaches modes that modulate the polarizability, giving Stokes and anti-Stokes lines whose intensity ratio measures temperature, and the mutual-exclusion rule pairs it with infrared absorption. Electronic transitions add the vibronic structure of band spectra, governed by the Franck-Condon principle, and the radiative fates of an excited state are sorted by the Jablonski diagram into fluorescence and phosphorescence.\n",{"path":19129,"title":19130,"module":19118,"summary":19131},"\u002Fcondensed-matter\u002Fmolecular-spectra\u002Flasers-and-masers","Lasers, Masers, and Stimulated Emission","Einstein's three radiative processes — absorption, spontaneous emission, and stimulated emission — and the coefficients that relate them. Stimulated emission produces coherent photons, and inverting the level populations turns it into net amplification. We build the ruby three-level laser and the helium-neon four-level laser, and show why the fourth level makes inversion easy.\n",{"path":19133,"title":19134,"module":19135,"summary":19136},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fstructure-of-solids","The Structure of Solids","Crystal Structure","A crystal is a unit cell repeated in three dimensions. We classify the common cubic lattices, compute the Coulomb energy of an ionic crystal through the Madelung constant, and show how the divergent naive lattice sum is tamed by cubic shells. The cohesive energy that results predicts melting points and connects the diatomic bond of an earlier lesson to the bulk solid.\n",{"path":19138,"title":19139,"module":19135,"summary":19140},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fbravais-lattices-and-crystal-systems","Bravais Lattices, Bases, and Crystal Structures","A crystal is a Bravais lattice decorated by a basis. This lesson separates the two, builds primitive and Wigner-Seitz cells, enumerates the seven crystal systems and fourteen Bravais lattices, and fixes the language of point and space groups. Miller indices label planes and directions, and the packing fractions of the close-packed, cubic, and diamond structures follow from the geometry.\n",{"path":19142,"title":19143,"module":19135,"summary":19144},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Freciprocal-lattice-and-brillouin-zones","The Reciprocal Lattice and Brillouin Zones","Every periodic crystal has a dual lattice in wavevector space. This lesson defines the reciprocal lattice through the condition b_i dot a_j equals two pi delta, derives its properties, shows the reciprocal of fcc is bcc, links reciprocal vectors to families of lattice planes, and builds the first Brillouin zone as the Wigner-Seitz cell of the reciprocal lattice, including the higher zones.\n",{"path":19146,"title":19147,"module":19135,"summary":19148},"\u002Fcondensed-matter\u002Fcrystal-structure\u002Fdiffraction-and-structure-factors","X-ray and Neutron Diffraction","A crystal diffracts radiation whose wavelength matches its atomic spacing. This lesson derives the Bragg condition, the equivalent Laue condition 2k dot G equals G squared, and the Ewald-sphere construction, then computes the geometric structure factor that produces systematic absences for bcc and fcc, the atomic form factor, and the powder method. It closes on why neutrons and electrons complement X-rays.\n",{"path":19150,"title":19151,"module":19152,"summary":19153},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonon-dispersion","The Harmonic Crystal and Phonon Dispersion","Lattice Dynamics","Atoms in a crystal vibrate about their equilibrium sites, and expanding the potential to second order turns the whole lattice into a set of coupled harmonic oscillators. This lesson sets up the harmonic approximation and the dynamical matrix, solves the monatomic linear chain for its dispersion omega(k) = 2 sqrt(K\u002FM) times the absolute sine of ka over two, explains why wavevectors outside the first Brillouin zone are redundant, and extends the chain to two atoms per cell to produce acoustic and optical branches with a frequency gap.\n",{"path":19155,"title":19156,"module":19152,"summary":19157},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fphonons-quantization-and-dos","Phonons, Density of States, and Crystal Momentum","Quantizing the normal modes of a harmonic crystal turns each vibrational mode into a quantum oscillator whose excitations are phonons. This lesson counts phonons with Bose-Einstein statistics, defines crystal momentum and the normal versus Umklapp distinction in momentum conservation, builds the density of states with its van Hove singularities, and shows how inelastic neutron scattering measures a dispersion curve point by point.\n",{"path":19159,"title":19160,"module":19152,"summary":19161},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fdebye-einstein-heat-capacity","Thermal Properties — Einstein and Debye Models","The lattice heat capacity follows the classical Dulong-Petit value at high temperature but collapses toward zero as T approaches zero, a purely quantum effect. This lesson derives that behavior from the Einstein model of a single frequency, then the Debye model of a linear phonon spectrum with a cutoff, obtaining the Debye T-cubed law at low temperature and the Debye interpolation across all temperatures, and closes with thermal expansion and the Gruneisen parameter.\n",{"path":19163,"title":19164,"module":19152,"summary":19165},"\u002Fcondensed-matter\u002Flattice-dynamics\u002Fanharmonicity-and-thermal-transport","Anharmonicity, Thermal Expansion, and Heat Conduction","A perfectly harmonic crystal neither expands when heated nor resists heat flow. Both effects come from the cubic and higher terms the harmonic approximation discards. This lesson derives thermal expansion from an asymmetric interatomic potential, treats phonon-phonon scattering as the decay channel these terms open, shows why Umklapp processes are what make lattice thermal conductivity finite, and traces the temperature dependence of the conductivity and the phonon mean free path.\n",{"path":19167,"title":19168,"module":19169,"summary":19170},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ffree-electron-gas-and-conduction","Conduction and the Free-Electron Gas","Free-Electron Fermi Gas","Drude's classical free-electron model gets Ohm's law right but the resistivity, its temperature dependence, and the heat capacity wrong. Replacing the Maxwell-Boltzmann distribution with the Fermi-Dirac distribution and treating electron-lattice collisions as wave scattering repairs all three: the Fermi energy, Fermi speed, and a mean free path set by thermal lattice vibrations.\n",{"path":19172,"title":19173,"module":19169,"summary":19174},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fsommerfeld-model-and-heat-capacity","The Sommerfeld Model: Ground State and Heat Capacity","Quantizing the free-electron gas in a box fills a Fermi sphere in k-space. The density of states grows as the square root of energy in three dimensions, and the Fermi energy, temperature, and wavevector follow for real metals. The Sommerfeld expansion shows only a thermal shell of width k_BT near E_F is excited, giving an electronic heat capacity linear in T that sits beneath the phonon T-cubed term.\n",{"path":19176,"title":19177,"module":19169,"summary":19178},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Ftransport-and-the-hall-effect","Transport, Wiedemann–Franz, and the Hall Effect","The relaxation-time picture displaces the Fermi sphere under an applied field and gives the electrical conductivity ne-squared-tau over m. The same electrons carry heat, and their ratio yields the Wiedemann–Franz law with the universal Lorenz number. A magnetic field bends the carriers into cyclotron orbits and produces the Hall voltage, whose sign reveals the charge of the carriers.\n",{"path":19180,"title":19181,"module":19169,"summary":19182},"\u002Fcondensed-matter\u002Ffree-electron-fermi-gas\u002Fscreening-and-plasmons","Screening, Plasmons, and the Limits of Free Electrons","A mobile electron gas rearranges to screen any foreign charge, turning the bare Coulomb potential into a short-ranged Yukawa form over the Thomas–Fermi length. Displaced collectively, the gas rings at the plasma frequency, whose quantum is the plasmon and whose value sets the reflectivity edge of metals. A ledger of free-electron successes and failures then motivates band theory.\n",{"path":19184,"title":19185,"module":19186,"summary":19187},"\u002Fcondensed-matter\u002Fband-theory\u002Fblochs-theorem-and-energy-bands","Bloch's Theorem and Energy Bands","Band Theory","An electron in a periodic potential has stationary states that are plane waves modulated by a lattice-periodic envelope. This lesson proves Bloch's theorem two ways, defines crystal momentum and the band index, counts the allowed wavevectors from Born–von Kármán boundary conditions, and sets up the extended, reduced, and repeated-zone descriptions of a band.\n",{"path":19189,"title":19190,"module":19186,"summary":19191},"\u002Fcondensed-matter\u002Fband-theory\u002Fnearly-free-electron-model","The Nearly-Free-Electron Model","A weak periodic potential leaves the free-electron parabola almost intact except near Brillouin-zone boundaries, where two nearly degenerate plane waves mix. This lesson solves the resulting two-by-two secular problem, shows the gap of size twice the potential component opening at each boundary, identifies the two standing waves that pile charge on and between the ions, and works the exactly solvable Kronig–Penney model.\n",{"path":19193,"title":19194,"module":19186,"summary":19195},"\u002Fcondensed-matter\u002Fband-theory\u002Ftight-binding-method","The Tight-Binding Method","The opposite limit to nearly-free electrons builds bands from atomic orbitals. A Bloch sum of one orbital per site gives a dispersion set by the hopping integral between neighbours; the band widens from a sharp atomic level as the atoms approach. This lesson derives the s-band cosine dispersion, extends it to p-bands, and introduces Wannier functions as the localized dual of Bloch states.\n",{"path":19197,"title":19198,"module":19186,"summary":19199},"\u002Fcondensed-matter\u002Fband-theory\u002Ffermi-surfaces-and-semiclassical-dynamics","Fermi Surfaces, Effective Mass, and Metals vs Insulators","Filling the bands settles which crystals conduct. A filled band carries no current, so a crystal with filled bands and a gap is an insulator, while a partly filled band makes a metal. This lesson derives the no-current theorem for a filled band, defines the Fermi surface and Harrison's construction, introduces holes and the effective mass from band curvature, and states the semiclassical equations of motion that lead to Bloch oscillations.\n",{"path":19201,"title":19202,"module":19203,"summary":19204},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fsemiconductor-bands-and-junctions","Band Theory and Semiconductors","Semiconductors","The periodic lattice splits atomic levels into allowed energy bands separated by forbidden gaps. Whether the highest occupied band is full or partly full, and how wide the gap above it is, sorts every solid into conductor, insulator, or semiconductor. Doping adds donor or acceptor levels inside the gap, and a p-n junction built from doped regions gives the diode, the solar cell, the LED, and the transistor.\n",{"path":19206,"title":19207,"module":19203,"summary":19208},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fintrinsic-and-extrinsic-semiconductors","Carrier Statistics: Intrinsic and Extrinsic Semiconductors","The number of mobile electrons and holes in a semiconductor follows from the density of states near each band edge and the Fermi-Dirac tail that reaches into it. This lesson derives the effective densities of states, the intrinsic concentration and its exponential gap dependence, the law of mass action, the temperature march of the Fermi level, and the freeze-out, saturation, and intrinsic regimes of a doped crystal.\n",{"path":19210,"title":19211,"module":19203,"summary":19212},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fcarrier-transport-and-recombination","Carrier Transport and Recombination","Carriers move by drift in a field and by diffusion down a concentration gradient, the two tied together by the Einstein relation. This lesson derives mobility and its scattering-limited temperature dependence, the drift and diffusion currents, the continuity equations, band-to-band and trap-assisted recombination, and the minority-carrier lifetime and diffusion length that set the length scale of every junction device.\n",{"path":19214,"title":19215,"module":19203,"summary":19216},"\u002Fcondensed-matter\u002Fsemiconductors\u002Fthe-pn-junction","The p-n Junction in Depth","Joining p-type and n-type silicon aligns their Fermi levels and leaves a depletion region of fixed charge with a built-in potential. This lesson derives the space-charge field and potential from Poisson's equation in the depletion approximation, the built-in voltage from Fermi-level alignment, the Shockley diode equation from minority-carrier diffusion, junction and diffusion capacitance, and the avalanche and Zener breakdown mechanisms.\n",{"path":19218,"title":19219,"module":19203,"summary":19220},"\u002Fcondensed-matter\u002Fsemiconductors\u002Ftransistors-and-optoelectronics","Transistors and Optoelectronic Devices","Two junctions in series make a bipolar transistor whose thin base gives current gain; a gate over an oxide makes a MOSFET whose inversion channel switches digital logic. Run in reverse, a junction converts photons to current. This lesson derives the transistor current gain and the MOSFET channel current, then treats the LED, the diode laser, and the illuminated solar-cell characteristic.\n",{"path":19222,"title":19223,"module":19224,"summary":19225},"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fdielectrics-and-polarization","Dielectrics, Polarization, and the Local Field","Dielectrics and Ferroelectrics","An insulator responds to an electric field by polarizing. This lesson builds the macroscopic polarization and the dielectric constant, sorts the microscopic response into electronic, ionic, and orientational polarizability, and corrects the field an atom actually feels to the Lorentz local field E + P\u002F3 epsilon-0. The Clausius-Mossotti relation links the measured permittivity to the atomic polarizability, and the frequency dependence of each mechanism explains why the static and optical dielectric constants differ.\n",{"path":19227,"title":19228,"module":19224,"summary":19229},"\u002Fcondensed-matter\u002Fdielectrics-and-ferroelectrics\u002Fferroelectrics-and-piezoelectrics","Ferroelectrics, Piezoelectrics, and Structural Transitions","Some crystals carry a polarization with no applied field and switch it under a reversing field, tracing a hysteresis loop. This lesson develops the ferroelectric transition through the perovskite BaTiO3 displacive instability and its soft transverse-optical mode, builds the Landau free-energy theory of first- and second-order polar transitions, derives the Curie-Weiss divergence of the dielectric constant, and closes with piezoelectricity and pyroelectricity and their devices.\n",{"path":19231,"title":19232,"module":19233,"summary":19234},"\u002Fcondensed-matter\u002Fmagnetism\u002Fdiamagnetism-and-paramagnetism","Diamagnetism and Paramagnetism","Magnetism in Solids","Every solid responds to a magnetic field. Filled shells give a small negative diamagnetic susceptibility from induced Larmor currents; localized moments give a positive Curie paramagnetism described by the Brillouin function, with the ground-state moment fixed by Hund's rules. The conduction electrons add a temperature-independent Pauli paramagnetism from the thermal shell near the Fermi surface, partly cancelled by Landau diamagnetism of their orbital motion.\n",{"path":19236,"title":19237,"module":19233,"summary":19238},"\u002Fcondensed-matter\u002Fmagnetism\u002Fexchange-and-ferromagnetism","Exchange and Ferromagnetism","Magnetic ordering at hundreds of kelvin cannot be dipolar; it is an exchange effect, the Coulomb repulsion sorted by the Pauli principle into a spin-dependent energy captured by the Heisenberg Hamiltonian. Weiss molecular-field theory replaces the exchange field by an average proportional to the magnetization, giving a self-consistent equation whose solution is spontaneous magnetization below a Curie temperature and a Curie–Weiss susceptibility above it. Itinerant ferromagnetism follows from the Stoner criterion on the band density of states.\n",{"path":19240,"title":19241,"module":19233,"summary":19242},"\u002Fcondensed-matter\u002Fmagnetism\u002Fantiferromagnetism-and-domains","Antiferromagnetism, Ferrimagnetism, and Domains","A negative exchange coupling orders neighboring spins antiparallel. Two-sublattice molecular-field theory gives a Néel temperature marked by a cusp in the susceptibility, and unequal sublattices leave a net moment — ferrimagnetism, the magnetism of the ferrites. A ferromagnet breaks into domains to reduce its magnetostatic energy, separated by Bloch walls whose width is set by the competition between exchange and magnetocrystalline anisotropy, and the irreversible motion of those walls produces the hysteresis loop.\n",{"path":19244,"title":19245,"module":19233,"summary":19246},"\u002Fcondensed-matter\u002Fmagnetism\u002Fspin-waves-and-magnons","Spin Waves and Magnons","The lowest excitations of a ferromagnet are not single flipped spins but collective precessions in which every moment tips slightly and its phase advances along the crystal. These spin waves have a quadratic dispersion at long wavelength, quantize into magnons obeying Bose statistics, and their thermal population removes magnetization as the Bloch T-to-the-three-halves law. Antiferromagnetic magnons disperse linearly, and inelastic neutron scattering measures both.\n",{"path":19248,"title":19249,"module":19250,"summary":19251},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fsuperconductivity-phenomenology","Superconductivity: Phenomenology and BCS","Superconductivity","Below a critical temperature some materials lose all resistance and expel magnetic flux — the Meissner effect that defines the state. The isotope effect points to lattice vibrations, and BCS theory binds electrons into Cooper pairs through phonon exchange. The paired condensate opens an energy gap, quantizes magnetic flux, and drives the Josephson effects.\n",{"path":19253,"title":19254,"module":19250,"summary":19255},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Flondon-theory-and-the-meissner-effect","London Theory and the Meissner Effect","A perfect conductor freezes the field it was cooled in; a superconductor expels it. The distinction needs a constitutive law beyond zero resistance — the two London equations — whose solution is exponential flux decay over the penetration depth. The same rigidity follows from a macroscopic condensate wave function, and the thermodynamics of the critical field fixes the condensation energy, the latent heat, and the specific-heat jump.\n",{"path":19257,"title":19258,"module":19250,"summary":19259},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fginzburg-landau-theory","Ginzburg–Landau Theory, Vortices, and Type-II","A complex order parameter and a free-energy expansion turn the superconducting transition into a Landau theory. Two lengths emerge — the coherence length and the penetration depth — whose ratio kappa sorts superconductors into type I and type II. Type-II materials admit flux as an Abrikosov lattice of vortices, each threading exactly one quantum h\u002F2e, between a lower and an upper critical field.\n",{"path":19261,"title":19262,"module":19250,"summary":19263},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fbcs-theory","Microscopic BCS Theory","A phonon-mediated attraction, however weak, binds two electrons above the Fermi sea — the Cooper problem shows the sea is unstable. The BCS variational ground state pairs all electrons near the Fermi surface and, through a self-consistent gap equation, opens an energy gap. Weak-coupling solution gives the exponential T_c and the universal ratios 2 Delta(0) = 3.53 k_B T_c and Delta C \u002F C_n = 1.43.\n",{"path":19265,"title":19266,"module":19250,"summary":19267},"\u002Fcondensed-matter\u002Fsuperconductivity\u002Fjosephson-and-high-tc","Josephson Effects and Unconventional Superconductors","Two superconductors joined by a thin barrier carry a supercurrent set by their phase difference — the dc Josephson effect — and oscillate at 2eV\u002Fh under a voltage. A two-junction loop turns flux quantization into a magnetometer of single-quantum sensitivity. The cuprates superconduct in CuO2 planes with a doping-dependent dome, d-wave pairing, and a pseudogap that lie outside the phonon picture.\n",{"path":19269,"title":19270,"module":19271,"summary":19272},"\u002Fcondensed-matter\u002Fnanostructures\u002Fquantum-wells-wires-and-dots","Quantum Wells, Wires, and Dots","Nanostructures","When a crystal is shrunk until one or more of its dimensions approaches the electron wavelength, the continuous bands of the bulk break into discrete subbands. Confining in one direction gives a quantum well with a step-like density of states, in two directions a quantum wire with inverse-square-root singularities, and in all three a quantum dot whose levels are sharp like an atom's. This lesson derives the density of states in each case and applies it to size-tunable dot emission and the Coulomb blockade of a single-electron transistor.\n",{"path":19274,"title":19275,"module":19271,"summary":19276},"\u002Fcondensed-matter\u002Fnanostructures\u002Finteger-quantum-hall-effect","The 2D Electron Gas and the Integer Quantum Hall Effect","A two-dimensional electron gas in a strong perpendicular magnetic field has its continuous density of states collapse into macroscopically degenerate Landau levels. As the field is swept, the Hall resistance locks onto exact plateaus at h over an integer times e squared, while the longitudinal resistance drops to zero. This lesson derives the Landau levels and their degeneracy, explains the plateaus through disorder-localized states and current-carrying edge channels, and states why the von Klitzing constant is now a resistance standard.\n",{"path":19278,"title":19279,"module":19271,"summary":19280},"\u002Fcondensed-matter\u002Fnanostructures\u002Ffractional-quantum-hall-and-topology","The Fractional Quantum Hall Effect and Topological Order","When the lowest Landau level is only partly filled, the non-interacting theory predicts no gap, yet a plateau appears at filling one-third. It is a many-body effect: Coulomb repulsion selects a correlated ground state, the Laughlin wavefunction, whose excitations carry a fraction of the electron charge. This lesson builds the Laughlin state, introduces composite fermions that map the fractional effect onto an integer one, and explains how the quantum Hall effect brought the Chern number and topology into condensed-matter physics.\n",{"path":19282,"title":19283,"module":19271,"summary":19284},"\u002Fcondensed-matter\u002Fnanostructures\u002Fgraphene-and-dirac-materials","Graphene and Dirac Materials","Graphene is one atomic layer of carbon on a honeycomb lattice. A tight-binding calculation on its two-atom basis gives valence and conduction bands that touch at the corners of the Brillouin zone, where the dispersion is linear and the electrons behave as massless two-dimensional Dirac particles with a fixed speed. This lesson derives the Dirac cones, the Berry phase of pi and the sublattice chirality, the anomalous half-integer quantum Hall effect that follows, and how opening a gap in a Dirac cone points toward topological insulators.\n",{"path":19286,"title":19287,"module":6,"summary":6},"\u002Fcondensed-matter","Condensed Matter Physics",{"path":19289,"title":19290,"module":16062,"summary":19291},"\u002Flogic\u002Ffoundations\u002Flogic-as-a-mathematical-model","Logic as a Mathematical Model of Deduction","Symbolic logic models deductive reasoning the way probability theory models chance: it keeps the form of a correct deduction and discards its content. A deduction is valid when its conclusion follows from the form of the premises alone, independent of what the non-logical words mean. Two models carry the subject — coarse sentential logic and fine first-order logic — and four questions organize it: logical consequence, methods of proof, the gap between provable and true, and the link between logic and computability. Tuples, relations, functions, equivalence classes, and cardinality supply the set-theoretic vocabulary every later chapter uses.\n",{"path":19293,"title":19294,"module":19295,"summary":19296},"\u002Flogic\u002Fsentential-logic\u002Fformal-languages-and-well-formed-formulas","Formal Languages and Well-Formed Formulas","Sentential Logic","The language of sentential logic has an alphabet of sentence symbols, five connectives, and two parentheses, with formation rules that pick out the well-formed formulas. The wffs are the least set of expressions closed under the five formula-building operations, and every such generated set carries an induction principle.\n",{"path":19298,"title":19299,"module":19295,"summary":19300},"\u002Flogic\u002Fsentential-logic\u002Ftruth-assignments-and-tautologies","Truth Assignments, Tautologies, and Consequence","A truth assignment fixes the sentence symbols true or false, and a recursion extends it uniquely to every formula. Satisfaction, tautologies, and tautological implication — one formula following semantically from others — rest on that extension, and the truth-table procedure decides implication for finite premise sets.\n",{"path":19302,"title":19303,"module":19295,"summary":19304},"\u002Flogic\u002Fsentential-logic\u002Funique-readability-and-parsing","Unique Readability and a Parsing Algorithm","Parentheses keep a formula from being read two ways. The parenthesis lemmas and a top-down parsing algorithm recover a formula's structure and yield unique readability: every wff has exactly one formation tree, which is what makes the truth recursion well defined.\n",{"path":19306,"title":19307,"module":19295,"summary":19308},"\u002Flogic\u002Fsentential-logic\u002Finduction-and-recursion","Induction and Recursion on Formulas","Two principles govern any set generated from initial elements by operations: prove a property of all its members by covering the initial elements and the closure steps, and define a function on it by recursion on structure. The recursion theorem needs the set to be freely generated, and unique readability supplies that condition for the well-formed formulas.\n",{"path":19310,"title":19311,"module":19295,"summary":19312},"\u002Flogic\u002Fsentential-logic\u002Fexpressive-completeness-and-normal-forms","Sentential Connectives and Normal Forms","Every formula computes a Boolean function of its atoms, and Post's theorem gives the converse: every Boolean function is realized by a wff in disjunctive normal form, so the five connectives are more than enough. Minimal complete sets follow, down to the single connectives NAND and NOR, together with a method for proving a set of connectives incomplete.\n",{"path":19314,"title":19315,"module":19295,"summary":19316},"\u002Flogic\u002Fsentential-logic\u002Fboolean-circuits","Switching Circuits","A memoryless two-valued circuit computes a Boolean function, so every formula names a gate network and every network a formula. Cost and delay are read off the formula by recursion, and tautological equivalence and normal forms design and simplify circuits realizing a given specification.\n",{"path":19318,"title":19319,"module":19295,"summary":19320},"\u002Flogic\u002Fsentential-logic\u002Fcompactness-and-effectiveness","Compactness and Effectiveness","The compactness theorem reduces satisfiability of an infinite set of formulas to its finite subsets, proved by extension to a maximal finitely satisfiable set and applied to color infinite graphs. Effectiveness fixes what \"decidable\" and \"effectively enumerable\" mean and settles the decidability of tautologyhood.\n",{"path":19322,"title":19323,"module":19324,"summary":19325},"\u002Flogic\u002Ffirst-order-languages\u002Ffirst-order-languages","First-Order Languages","First-Order Languages and Structures","Sentential logic cannot see inside a simple statement, so it misses valid arguments that turn on quantifiers and predicates. A first-order language adds a quantifier, variables, and a chosen vocabulary of predicate, function, and constant symbols. Terms and well-formed formulas are built by recursion over this alphabet, and a variable occurs free or bound according to the quantifiers that reach it.\n",{"path":19327,"title":19328,"module":19324,"summary":19329},"\u002Flogic\u002Ffirst-order-languages\u002Fstructures-truth-and-satisfaction","Structures, Truth, and Satisfaction","A structure interprets a language: a nonempty universe plus a meaning for every predicate, function, and constant symbol. Tarski's recursion defines when a structure satisfies a formula under a variable assignment, and hence when a sentence is true. From satisfaction we recover logical implication, validity, and logical equivalence for first-order logic.\n",{"path":19331,"title":19332,"module":19324,"summary":19333},"\u002Flogic\u002Ffirst-order-languages\u002Fdefinability-and-elementary-equivalence","Definability and Elementary Equivalence","Fix a structure and ask which relations a formula can pick out: the definable ones. A set of sentences picks out a class of structures, the elementary classes. Homomorphisms and isomorphisms compare structures, and the homomorphism theorem shows isomorphic structures satisfy the same sentences. Automorphisms bound what first-order logic can distinguish, giving a tool for proving relations undefinable.\n",{"path":19335,"title":19336,"module":19324,"summary":19337},"\u002Flogic\u002Ffirst-order-languages\u002Fterms-substitution-and-parsing","Parsing, Substitution, and Substitutability","Every recursion on first-order syntax rests on unique readability. A parenthesis-counting function proves that terms and formulas decompose in exactly one way, and a parsing algorithm recovers the decomposition. Substituting a term for a free variable can capture it under a quantifier; the substitutability condition rules that out, and the substitution lemma trades syntactic substitution for a change of assignment.\n",{"path":19339,"title":19340,"module":19341,"summary":19342},"\u002Flogic\u002Fdeductive-calculus\u002Fa-deductive-calculus","A Deductive Calculus for First-Order Logic","The Deductive Calculus and Its Metatheorems","A proof must be finite and mechanically checkable. A Hilbert-style calculus meets both demands: six schemas of logical axioms, a single rule of inference (modus ponens), and the syntactic consequence relation they generate. Substitution and substitutability are defined by recursion, and the bridge theorem reduces deducibility to tautological implication from the axioms.\n",{"path":19344,"title":19345,"module":19341,"summary":19346},"\u002Flogic\u002Fdeductive-calculus\u002Fdeduction-theorem-and-derived-rules","The Deduction Theorem and Derived Rules","Raw deductions from axioms are unusable by hand. The generalization theorem, the deduction theorem, contraposition, reductio ad absurdum, and rule T reduce the calculus to the moves of ordinary mathematics, each proved once to license a block of axiom-level steps. Generalization on constants and alphabetic variants handle the quantifier and substitution bookkeeping.\n",{"path":19348,"title":19349,"module":19341,"summary":19350},"\u002Flogic\u002Fdeductive-calculus\u002Fsoundness","The Soundness Theorem","Soundness is the easy half of the match between proof and truth. Whatever the calculus deduces is logically implied, by an induction on deduction length that rests on one lemma: every logical axiom is valid. The only hard case, quantifier instantiation, needs the substitution lemma. The contrapositive corollary states that every satisfiable set is consistent.\n",{"path":19352,"title":19353,"module":19341,"summary":19354},"\u002Flogic\u002Fdeductive-calculus\u002Fcompleteness-and-consistency","The Completeness Theorem","Gödel's completeness theorem is the deep converse of soundness: whatever is logically implied can be deduced. Equivalently, every consistent set has a model. The Henkin proof manufactures that model out of syntax alone: add witnessing constants, extend to a maximal consistent set, and read a term model off the formulas it contains. Compactness and the enumerability theorem drop out.\n",{"path":19356,"title":19357,"module":19358,"summary":19359},"\u002Flogic\u002Fmodels-and-theories\u002Fcompactness-and-lowenheim-skolem","Compactness and the Löwenheim–Skolem Theorems","Models, Compactness, and Theories","A set of first-order sentences has a model whenever each of its finite subsets does. This compactness theorem follows from completeness and yields the finiteness limitation, the downward and upward Löwenheim–Skolem theorems, models of every infinite cardinality, and nonstandard models of arithmetic.\n",{"path":19361,"title":19362,"module":19358,"summary":19363},"\u002Flogic\u002Fmodels-and-theories\u002Ftheories-elementary-classes-and-categoricity","Theories, Elementary Classes, and Categoricity","A theory is a set of sentences closed under logical consequence. Theories correspond to classes of models; a theory may be complete, axiomatizable, or finitely axiomatizable, and completeness together with axiomatizability yields decidability. The Łoś–Vaught test derives completeness from categoricity in a cardinal, applied to dense linear orders and to algebraically closed fields.\n",{"path":19365,"title":19366,"module":19358,"summary":19367},"\u002Flogic\u002Fmodels-and-theories\u002Finterpretations-between-theories","Interpretations Between Theories","An interpretation translates the vocabulary of one theory into formulas of another, relativizing quantifiers to a definable domain and mapping symbols to defining formulas. Defined function symbols meet a noncreativity criterion; the syntactic translation of formulas carries theoremhood forward, and a faithful interpretation transfers decidability and undecidability between theories.\n",{"path":19369,"title":19370,"module":19358,"summary":19371},"\u002Flogic\u002Fmodels-and-theories\u002Fnonstandard-analysis","Nonstandard Analysis","Compactness builds a model of the real ordered field containing infinite elements and nonzero infinitesimals. The transfer principle carries every first-order truth from the reals to this extension, the standard-part map collapses finite hyperreals back onto the reals, and continuity and the derivative are rederived by working with infinitely small quantities directly.\n",{"path":19373,"title":19374,"module":19375,"summary":19376},"\u002Flogic\u002Farithmetic-and-definability\u002Fdefinability-in-arithmetic","The Structure of Arithmetic and Definability","Number Theory and Definability","Number theory is the theory of one fixed structure, the natural numbers under successor, order, addition, multiplication, and exponentiation. Every number is named by a numeral, and a relation is definable when a single formula picks out exactly its tuples. The central gap separates the sentences true in that structure from those any reasonable set of axioms can prove.\n",{"path":19378,"title":19379,"module":19375,"summary":19380},"\u002Flogic\u002Farithmetic-and-definability\u002Fnatural-numbers-with-successor","Natural Numbers with Successor","The weakest reduct keeps only zero and successor. Its models are a standard chain together with disjoint copies of the integers, which makes the theory categorical in every uncountable power, hence complete and decidable. A quantifier-elimination procedure gives a practical decision method and shows a subset is definable if and only if it is finite or cofinite.\n",{"path":19382,"title":19383,"module":19375,"summary":19384},"\u002Flogic\u002Farithmetic-and-definability\u002Fpresburger-and-reducts","Reducts: Order, Addition, and Multiplication","Adding order to the successor reduct keeps decidability and makes the theory finitely axiomatizable; adding addition gives Presburger arithmetic, still decidable by quantifier elimination once congruence predicates are included, with definable sets exactly the eventually periodic ones. Multiplication is the break point: neither addition nor order can define it, and once it joins addition the theory stops being decidable.\n",{"path":19386,"title":19387,"module":19375,"summary":19388},"\u002Flogic\u002Farithmetic-and-definability\u002Fa-subtheory-and-representability","A Subtheory of Number Theory and Representability","A finite set of eleven axioms, the recursion equations for successor, order, addition, multiplication, and exponentiation, already proves every true quantifier-free and existential sentence. Representability asks a theory to prove the right instances of a formula rather than merely make them true, and a relation is defined to be recursive exactly when some consistent finite theory represents it. Church's thesis identifies that with decidability, and closure under composition, minimization, and primitive recursion builds the catalog the incompleteness proofs need.\n",{"path":19390,"title":19391,"module":19392,"summary":19393},"\u002Flogic\u002Fincompleteness\u002Farithmetization-of-syntax","Arithmetization of Syntax","Arithmetization and the Incompleteness Theorems","Gödel numbering assigns a natural number to every symbol, expression, formula, and deduction, turning statements about syntax into statements about numbers. The syntactic operations — substitution, \"is a wff\", \"is an axiom\", \"d codes a deduction of a\" — come out primitive recursive and hence representable in the subtheory, which lets a formula of arithmetic talk about formulas, including itself.\n",{"path":19395,"title":19396,"module":19392,"summary":19397},"\u002Flogic\u002Fincompleteness\u002Fincompleteness-and-undecidability","Incompleteness, Undecidability, and Church's Theorem","The fixed-point lemma manufactures a sentence that talks about its own Gödel number. Pointed at truth it gives Tarski's theorem — arithmetic truth is not arithmetically definable; pointed at provability it gives Gödel's first incompleteness theorem and the undecidability of the theory of the natural numbers, and, applied to validity, Church's theorem that first-order logic is undecidable. The set of theorems of a recursive theory is only recursively enumerable — the gap between provable and true.\n",{"path":19399,"title":19400,"module":19392,"summary":19401},"\u002Flogic\u002Fincompleteness\u002Fsecond-incompleteness-theorem","The Second Incompleteness Theorem","Consistency of a recursively axiomatized theory is itself an arithmetic sentence, built from a provability predicate. When the theory is strong enough to formalize its own reflection and modus ponens — the Hilbert–Bernays–Löb derivability conditions — it cannot prove that sentence unless it is inconsistent. Löb's theorem is the companion result, and set theory is the case that closes Hilbert's program.\n",{"path":19403,"title":19404,"module":19405,"summary":19406},"\u002Flogic\u002Fcomputability-and-representability\u002Frecursive-functions","Recursive Functions and Church's Thesis","Recursive Functions and Representability","The recursive functions are the formal counterpart of the effectively computable ones: built from three initial functions by composition, primitive recursion, and minimization, and equivalently the functions representable in a finitely axiomatized arithmetic. Church's thesis identifies the class with effective calculability; Kleene's normal form theorem and the unsolvable halting problem place the recursive sets strictly inside the recursively enumerable ones.\n",{"path":19408,"title":19409,"module":19405,"summary":19410},"\u002Flogic\u002Fcomputability-and-representability\u002Frepresenting-exponentiation","Representing Exponentiation and the β-Function","Coding finite sequences by prime-power exponents already assumes exponentiation, so representing exponentiation from addition and multiplication alone needs a different encoder. Gödel's β-function, built from a pairing function and the Chinese remainder theorem, reads back arbitrary finite sequences using only plus and times. This represents exponentiation in the addition-multiplication arithmetic and closes the last gap in the representability of every recursive syntactic operation.\n",{"path":19412,"title":19413,"module":19414,"summary":19415},"\u002Flogic\u002Fsecond-order-logic\u002Fsecond-order-languages","Second-Order Languages","Second-Order Logic and Beyond","Second-order logic quantifies over relations and functions, not just individuals. Second-order Peano arithmetic and the second-order theory of the reals become categorical, and finiteness is definable by a single sentence. Compactness, completeness, and the Löwenheim–Skolem theorems all fail for the standard semantics.\n",{"path":19417,"title":19418,"module":19414,"summary":19419},"\u002Flogic\u002Fsecond-order-logic\u002Fskolem-functions-and-many-sorted-logic","Skolem Functions and Many-Sorted Logic","Skolem functions replace existential quantifiers with named witnesses, putting any first-order formula into a prenex form with all existentials — now over functions — pulled to the front. The Skolemized formula is equisatisfiable with the original, which reduces satisfiability to universal sentences and, through Herbrand expansions, to sentential logic. Many-sorted logic then adds several universes at once and reduces cleanly to ordinary one-sorted logic.\n",{"path":19421,"title":19422,"module":19414,"summary":19423},"\u002Flogic\u002Fsecond-order-logic\u002Fgeneral-structures","General (Henkin) Structures","General semantics reinterprets second-order logic by letting the predicate and function quantifiers range over a designated collection of relations and functions rather than all of them. Recast as many-sorted first-order logic with comprehension axioms, general second-order logic recovers a sound and complete calculus together with compactness and Löwenheim–Skolem, giving up the categoricity of the standard semantics. The ω-models of analysis show the trade.\n",{"path":19425,"title":19426,"module":6,"summary":6},"\u002Flogic","Logic",{"path":19428,"title":19429,"module":16062,"summary":19430},"\u002Freinforcement-learning\u002Ffoundations\u002Fwhat-is-reinforcement-learning","What Is Reinforcement Learning?","Reinforcement learning is learning what to do — how to map situations to actions — so as to maximize a numerical reward signal, discovered by trial and error rather than told. We set up the agent–environment loop, separate it from supervised and unsupervised learning, name the four elements (policy, reward, value, and an optional model), and train a tic-tac-toe player with a temporal-difference value update.\n",{"path":19432,"title":19433,"module":16062,"summary":19434},"\u002Freinforcement-learning\u002Ffoundations\u002Fa-brief-history-of-rl","A Brief History of Reinforcement Learning","The origins of reinforcement learning. Three threads — trial-and-error learning from animal psychology, optimal control and dynamic programming, and temporal-difference learning — ran independently for decades and merged around 1989 into the modern field. Replacing the lookup table with a neural network then produced deep reinforcement learning: DQN, AlphaGo, AlphaZero, MuZero, and RLHF.\n",{"path":19436,"title":19437,"module":16062,"summary":19438},"\u002Freinforcement-learning\u002Ffoundations\u002Fmulti-armed-bandits","Multi-Armed Bandits","A bandit is reinforcement learning stripped to a single decision, repeated: no state, no consequences, only the tension between exploiting the arm that looks best and exploring the ones that might be better. We build up the whole toolkit — sample-average value estimates, the incremental update rule, ε-greedy, optimistic initialization, UCB, and gradient bandits — and use it to study exploration in isolation, the one problem that carries over to the full setting.\n",{"path":19440,"title":19441,"module":16062,"summary":19442},"\u002Freinforcement-learning\u002Ffoundations\u002Fbandit-exploration-algorithms","Bandit Exploration Algorithms","Better ways to explore than picking at random. Upper-confidence-bound selection explores by optimism about what it hasn't measured; gradient bandits learn action preferences by stochastic gradient ascent on reward. We then add context to get the contextual bandit, the bridge to full RL, and measure everything by regret — where UCB1 and Thompson sampling reach the logarithmic optimum that fixed-ε greedy cannot.\n",{"path":19444,"title":19445,"module":16062,"summary":19446},"\u002Freinforcement-learning\u002Ffoundations\u002Fmarkov-decision-processes","Markov Decision Processes","A Markov decision process is the formal interface between an agent and its environment: at each step the agent reads a state, chooses an action, and receives a reward and a next state. We fix that loop, the dynamics function that governs it, and the Markov property that makes the state sufficient; then turn goals into a scalar reward and rewards into a discounted return, with one notation that covers both episodic and continuing tasks.\n",{"path":19448,"title":19449,"module":16062,"summary":19450},"\u002Freinforcement-learning\u002Ffoundations\u002Fvalue-functions-and-optimality","Value Functions and Optimality","A value function scores how good a state (or state–action pair) is under a policy: the expected return from there onward. Its defining property is the Bellman equation, a self-consistency condition linking a state's value to its successors' values, which we derive from the return and the dynamics. Pushing the same idea to the best-achievable value gives the Bellman optimality equations, whose solution yields an optimal policy — and whose intractability is what the rest of the course is about.\n",{"path":19452,"title":16281,"module":19453,"summary":19454},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdynamic-programming","Tabular Solution Methods","Dynamic programming computes optimal policies when a perfect model of the MDP is given, by turning the Bellman equations into assignment statements. We build up iterative policy evaluation (the expected update), the policy improvement theorem, and the two classic algorithms that alternate them — policy iteration and value iteration — worked on the gridworld, a two-state MDP, Jack's car rental, and the gambler's problem.\n",{"path":19456,"title":19457,"module":19453,"summary":19458},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdp-async-and-gpi","Dynamic Programming: Asynchronous DP and Generalized Policy Iteration","Policy and value iteration both sweep the entire state set on every pass, which is impossible once the state space is huge. This lesson loosens the schedule: asynchronous DP updates states in any order, generalized policy iteration names the alternation of evaluation and improvement that underlies nearly every RL method, and a look at efficiency and the curse of dimensionality places DP among the alternatives. We close past Sutton & Barto with prioritized sweeping, neuro-dynamic programming, value-iteration networks, and MuZero.\n",{"path":19460,"title":19461,"module":19453,"summary":19462},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-methods","Monte Carlo Methods","Monte Carlo methods learn value functions and optimal policies from complete sampled episodes, with no model of the environment: they simply average the returns that actually followed each state. We build prediction (first-visit and every-visit averaging), see why estimating action values forces the exploration question, and answer it two ways on-policy — exploring starts and epsilon-soft control. Throughout, Monte Carlo samples one whole trajectory to termination and never bootstraps.\n",{"path":19464,"title":19465,"module":19453,"summary":19466},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-off-policy","Monte Carlo Methods: Off-Policy Learning","On-policy Monte Carlo can only reach the best exploring policy, not the true optimum. Off-policy methods remove that ceiling by learning about a greedy target policy from data generated by a soft behavior policy, corrected with importance sampling. We derive the importance-sampling ratio, weigh ordinary against weighted estimators on real numbers, give the incremental off-policy algorithm, sharpen it with discounting-aware sampling, and close by placing Monte Carlo on the model\u002Fbootstrap map beside DP and temporal-difference learning.\n",{"path":19468,"title":19469,"module":19453,"summary":19470},"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftemporal-difference-learning","Temporal-Difference Learning","Temporal-difference learning is the one idea most central to reinforcement learning: learn a value directly from experience, like Monte Carlo, but update each guess toward the next guess before the episode ends, like dynamic programming. We derive the TD(0) prediction rule and its reward-prediction error, contrast its one-step backup with MC and DP, work the driving-home and random-walk examples, and show the batch-updating optimality that makes TD approximate the certainty-equivalence estimate.\n",{"path":19472,"title":19473,"module":19453,"summary":19474},"\u002Freinforcement-learning\u002Ftabular-methods\u002Ftd-control-sarsa-and-q-learning","TD Control: Sarsa, Q-learning, and Double Learning","With TD prediction in hand, control follows the generalized-policy-iteration pattern with TD as the evaluation step. We build Sarsa (on-policy), Q-learning (off-policy, targeting the optimal policy), and Expected Sarsa that spans the two, then confront the maximization bias every max-based method inherits and fix it with Double Q-learning. We close past Sutton & Barto, following each one-step tabular update into its deep-RL descendant — DQN, Double DQN, and Rainbow.\n",{"path":19476,"title":19477,"module":19453,"summary":19478},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-bootstrapping","n-Step Bootstrapping","Monte Carlo waits for the full return; one-step TD bootstraps after a single reward. Between them lies a whole spectrum, indexed by one integer n: look ahead n real rewards, then bootstrap from the value n steps out. The n-step return unifies the previous two lessons, and — on the random walk — an intermediate n beats both extremes. We build the n-step return, the n-step TD update, the backup-diagram spectrum, and n-step Sarsa for control.\n",{"path":19480,"title":19481,"module":19453,"summary":19482},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fn-step-off-policy-methods","n-Step Bootstrapping: Off-Policy Methods","Taking the n-step family off-policy raises the same importance-sampling questions Monte Carlo did, now over a window of exactly n actions. We reweight n-step returns by the policy ratio, watch the ratio product inflate variance on real numbers, then build the tree-backup algorithm that learns off-policy with no ratios at all — and finally n-step Q(sigma), one algorithm whose per-step switch recovers Sarsa, tree backup, and Expected Sarsa as special cases.\n",{"path":19484,"title":19485,"module":19453,"summary":19486},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-and-learning","Planning and Learning","Planning and learning are the same operation run on two kinds of experience. A model turns states and actions into simulated transitions; planning backs up values over that simulated experience exactly as learning backs them up over real experience. We build the Dyna architecture that interleaves acting, model-learning, direct RL, and planning in one loop, trace a single Dyna-Q step by hand, and patch the architecture for when the model goes stale.\n",{"path":19488,"title":19489,"module":19453,"summary":19490},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fplanning-focusing-and-decision-time","Planning: Focusing Updates and Decision-Time Search","Dyna plans by replaying remembered transitions, but sampling them uniformly wastes most of the effort. This lesson sharpens planning: prioritized sweeping works backward from states whose value just changed, expected versus sample updates weigh thoroughness against cost, and trajectory sampling and real-time DP focus updates on the states the policy actually visits. We trace Dyna forward to model-based deep RL, then turn to decision-time planning — heuristic search, rollouts, and Monte Carlo Tree Search.\n",{"path":19492,"title":19493,"module":19453,"summary":19494},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fdecision-time-planning","Decision-Time Planning","Planning need not build a global policy. Decision-time planning runs a fresh lookahead every time a state arrives and returns just one action, then throws the work away. We start from real-time dynamic programming — asynchronous value iteration on the states the agent actually visits — then move through heuristic search and rollout algorithms, each a one-step policy improvement applied on the fly to the current state.\n",{"path":19496,"title":19497,"module":19453,"summary":19498},"\u002Freinforcement-learning\u002Ftabular-methods\u002Fmonte-carlo-tree-search","Monte Carlo Tree Search","Monte Carlo Tree Search is a rollout algorithm with memory: it accumulates value estimates across simulations and steers later ones toward promising branches. We work through the four steps — selection, expansion, simulation, backup — the UCT selection rule computed on real numbers, the asymmetric growing tree, and the full pseudocode. We close past Sutton & Barto with the lineage from UCT to AlphaGo, AlphaZero, and MuZero, where a learned network stands in for the leaf value and the rollout.\n",{"path":19500,"title":19501,"module":19502,"summary":19503},"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-prediction","On-Policy Prediction with Approximation","Approximate Solution Methods","Every tabular method so far stored one number per state, which fails once the state space is large or continuous. We replace the table with a parameterized value function $\\hat v(s,\\mathbf{w})$, define the mean squared value error it should minimize under the on-policy distribution, and derive stochastic- and semi-gradient learning rules — the semi-gradient TD(0) update that bootstraps and so is not a true gradient. Linear methods make the analysis clean and give the TD fixed point; feature construction (polynomials, Fourier basis, coarse and tile coding, RBFs) supplies the vectors $\\mathbf{x}(s)$, and neural networks are the nonlinear bridge to deep RL.\n",{"path":19505,"title":19506,"module":19502,"summary":19507},"\u002Freinforcement-learning\u002Fapproximation\u002Ffeature-construction-and-nonlinear","Feature Construction and Nonlinear Approximation","Linear methods are only as good as the feature vectors $\\mathbf{x}(s)$ fed to them, and this lesson builds those vectors. Polynomials and the Fourier basis turn a state's coordinates into smooth global features; coarse coding, tile coding, and radial basis functions cover a continuous space with overlapping local receptive fields whose size sets the reach of generalization. Then we stop designing features by hand: a neural network learns the representation itself by gradient descent, trading the convergence guarantees of the linear case for expressiveness — the bridge to deep reinforcement learning.\n",{"path":19509,"title":19510,"module":19502,"summary":19511},"\u002Freinforcement-learning\u002Fapproximation\u002Fon-policy-control","On-Policy Control with Approximation","Prediction learned a value function from features; control learns to act. We carry semi-gradient methods over to action values $\\hat q(s,a,\\mathbf{w})$, giving episodic semi-gradient Sarsa and its n-step form, and solve Mountain Car by descending a cost-to-go surface. In the continuing case, function approximation makes discounting unable to affect which policy is best, so we replace it with the average-reward setting — the differential return, differential value functions, and differential semi-gradient Sarsa.\n",{"path":19513,"title":19514,"module":19502,"summary":19515},"\u002Freinforcement-learning\u002Fapproximation\u002Faverage-reward-control","Average-Reward Control for Continuing Tasks","With function approximation, discounting has no effect on a continuing task: averaged over the on-policy distribution, the discounted objective equals the average reward times a policy-independent constant, so $\\gamma$ cannot change which policy is best. This lesson replaces discounting with the average-reward setting — the long-run reward rate $r(\\pi)$, the differential return that measures each state's transient advantage over that rate, differential value functions and TD error, and differential semi-gradient Sarsa, the control method for continuing tasks that never invokes a discount factor.\n",{"path":19517,"title":19518,"module":19502,"summary":19519},"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-and-the-deadly-triad","Off-Policy Methods and the Deadly Triad","Off-policy learning with function approximation is where the convergence guarantees of reinforcement learning fail. We extend the tabular off-policy updates to semi-gradient form with per-step importance sampling, show Baird's counterexample driving the weights to infinity, and identify the cause: the deadly triad of function approximation, bootstrapping, and off-policy training — any two are safe, all three can diverge. The divergence is not caused by sampling noise: a fully synchronous dynamic-programming update blows up just the same, which is what makes the triad a structural hazard rather than a fluke.\n",{"path":19521,"title":19522,"module":19502,"summary":19523},"\u002Freinforcement-learning\u002Fapproximation\u002Fbellman-error-and-gradient-td","Value-Function Geometry and Gradient-TD Methods","Why does the deadly triad diverge, and how do you stop it? This lesson develops the geometry that explains the failure: value functions as vectors, the projection operator onto the representable subspace, and the split between the Bellman error, the value error, and the projected Bellman error: the three objectives have different minimizers. The projected Bellman error is the learnable one, and Gradient-TD methods (GTD2, TDC) do true stochastic gradient descent on it, staying stable even off-policy at $O(d)$ cost. Emphatic TD reweights states instead, and a survey of variance-reduction techniques closes the gap between stability and usable learning.\n",{"path":19525,"title":19526,"module":19502,"summary":19527},"\u002Freinforcement-learning\u002Fapproximation\u002Feligibility-traces","Eligibility Traces","n-step methods unify TD and Monte Carlo by storing the last n feature vectors; eligibility traces do the same job with a single short-term memory vector. The λ-return averages every n-step return under a geometric weighting; the forward view looks ahead to that average, and the backward view produces nearly the same updates online through a decaying trace vector. We build the λ-return, TD(λ) with its trace, the two ways λ recovers TD(0) and Monte Carlo, a note on the exact equivalence of true online TD(λ), and Sarsa(λ) for control.\n",{"path":19529,"title":19530,"module":19502,"summary":19531},"\u002Freinforcement-learning\u002Fapproximation\u002Ftrue-online-and-sarsa-lambda","True Online TD(λ) and Sarsa(λ)","Plain TD(λ) makes the forward and backward views nearly agree; this lesson closes the gap. True online TD(λ) uses a dutch trace and a small correction term to produce exactly the same weight sequence as the online λ-return algorithm, at the same memory and only a constant factor more compute — the sharpest statement of the forward\u002Fbackward duality. The whole apparatus then lifts to control unchanged: Sarsa(λ) threads a single delayed reward back along an entire trajectory in one sweep, and the λ-weighting reappears in modern deep RL as generalized advantage estimation.\n",{"path":19533,"title":19534,"module":19502,"summary":19535},"\u002Freinforcement-learning\u002Fapproximation\u002Fpolicy-gradient-methods","Policy Gradient Methods","Every method so far learned values and read a policy off them. Policy gradient methods drop the intermediary: parameterize the policy directly and climb the performance gradient. We build the softmax-in-preferences parameterization, prove the policy gradient theorem that makes the gradient computable without the unknown state distribution, and derive REINFORCE and its variance-cutting state-value baseline — the launch point for the bootstrapping actor-critic that follows.\n",{"path":19537,"title":19538,"module":19502,"summary":19539},"\u002Freinforcement-learning\u002Fapproximation\u002Factor-critic-and-continuous-actions","Actor-Critic Methods and Continuous Actions","REINFORCE with a baseline learns a value function but never bootstraps; this lesson adds the bootstrapping critic that completes the actor-critic architecture. The critic scores each transition into a single TD error that steers both the actor's policy step and its own value step, trading a little bias for much lower variance and fully online, continuing-task learning. The policy gradient theorem carries over unchanged to the average-reward setting, a Gaussian policy handles real-valued actions with self-tuning exploration, and the natural policy gradient leads straight to TRPO, PPO, and the deep actor-critic methods that train today's agents.\n",{"path":19541,"title":19542,"module":19502,"summary":19543},"\u002Freinforcement-learning\u002Fapproximation\u002Fleast-squares-and-memory-based-methods","Least-Squares TD","Semi-gradient TD spends one cheap step per example and needs many examples; this lesson makes the opposite tradeoff. Least-Squares TD (LSTD) accumulates the matrices $\\mathbf{A}$ and $\\mathbf{b}$ and solves the TD fixed point $\\mathbf{w} = \\mathbf{A}^{-1}\\mathbf{b}$ directly, using the Sherman-Morrison identity to maintain the inverse in $O(d^2)$ — the most data-efficient linear TD method, at a quadratic cost. We work a solve by hand, weigh the quadratic cost against semi-gradient TD's cheap steps, and note that LSTD never forgets — a problem in control, where least-squares policy iteration is the natural extension.\n",{"path":19545,"title":19546,"module":19502,"summary":19547},"\u002Freinforcement-learning\u002Fapproximation\u002Fmemory-and-kernel-methods","Memory-Based and Kernel Methods","Least-squares TD spent more compute to extract more from each example; this lesson drops the parametric form entirely. Memory-based methods store training examples untouched and answer a query locally at retrieval time — nearest neighbor, weighted average, locally weighted regression — so accuracy grows with the data and effort concentrates where the agent actually goes. Kernel-based methods weight stored examples by a similarity kernel $k(s,s')$, and every linear method turns out to be a kernel method. Interest and emphasis, finally, make the on-policy weighting itself a design choice, aiming scarce approximation capacity at the states that matter.\n",{"path":19549,"title":19550,"module":19502,"summary":19551},"\u002Freinforcement-learning\u002Fapproximation\u002Foff-policy-eligibility-traces","Off-Policy Eligibility Traces","Eligibility traces meet off-policy learning and function approximation — the corner where stability gets hard. We first let the bootstrapping and discounting parameters vary with state, so a single generalized return covers episodic and continuing tasks and folds termination into the discount. Then we fold the per-decision importance ratio into the trace with a control-variate correction, and build Watkins's Q(λ) and its importance-sampling-free successor Tree-Backup(λ) — all correct in expectation, but still semi-gradient, so the deadly triad and its fixes wait for the next lesson.\n",{"path":19553,"title":19554,"module":19502,"summary":19555},"\u002Freinforcement-learning\u002Fapproximation\u002Fstable-off-policy-traces","Stable Off-Policy Methods with Traces","Off-policy traces get the expected target right, but with $\\lambda \u003C 1$ they bootstrap, so off-policy plus bootstrapping plus function approximation is the deadly triad and the weights can diverge. This lesson carries the two one-step fixes to traces: GTD(λ) and GQ(λ) add a second weight vector and a gradient correction for true gradient descent on the projected Bellman error, while Emphatic TD(λ) reweights updates through a followon trace and interest to recover the on-policy stability. It closes with the implementation reality that traces are cheap because they are sparse, and with Retrace and V-trace — the clipped-ratio descendants that make off-policy traces work at deep-RL scale.\n",{"path":19557,"title":18876,"module":19558,"summary":19559},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdeep-q-networks","Deep Reinforcement Learning","Deep Q-networks replace the linear value function with a neural network $Q(s,a;\\mathbf{w})$ and confront the fact that a nonlinear approximator, off-policy bootstrapping, and correlated online data — the deadly triad — make naive Q-learning diverge. DQN counters this empirically with two stabilizers: an experience replay buffer that decorrelates and reuses samples, and a periodically-frozen target network that fixes the bootstrap target. We derive the DQN loss and gradient, walk through the Atari convolutional architecture and its results, and then add the three refinements that define modern value-based deep RL — Double DQN, dueling networks, and prioritized experience replay.\n",{"path":19561,"title":19562,"module":19558,"summary":19563},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fdqn-improvements","DQN Improvements: Double, Dueling, and Prioritized Replay","Three refinements that turn plain DQN into the standard modern value-based agent, each touching a different part of the system. Double DQN fixes the maximization bias in the target by splitting action selection from evaluation; dueling networks restructure the network around a state value and per-action advantages; prioritized replay changes which transitions are learned from. We close with Rainbow, which combines them, and the distributional view that predicts the whole return distribution rather than its mean.\n",{"path":19565,"title":19566,"module":19558,"summary":19567},"\u002Freinforcement-learning\u002Fdeep-rl\u002Factor-critic-and-ppo","Actor–Critic and GAE","Make the actor and the critic deep networks and the policy-gradient architecture becomes modern deep RL. We build the neural actor-critic, the advantage estimate that replaces the raw return, and Generalized Advantage Estimation as a λ-blend of n-step advantages, then the parallel-worker methods A3C and A2C that decorrelate on-policy data. The step-size constraints — trust regions, PPO, and the continuous-control family — follow in the next lesson.\n",{"path":19569,"title":19570,"module":19558,"summary":19571},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fppo-and-continuous-control","PPO and Continuous Control","Keeping the policy-gradient step from destroying the policy, and the algorithms that result. Trust-region optimization bounds each update by a KL constraint; PPO keeps that goal but replaces the second-order machinery with a first-order clip on the probability ratio, which is why it is the modern default and the optimizer inside RLHF. We then tour the off-policy continuous-control family — DDPG, TD3, and SAC — and where actor-critic went at scale, from OpenAI Five to language-model alignment.\n",{"path":19573,"title":19574,"module":19558,"summary":19575},"\u002Freinforcement-learning\u002Fdeep-rl\u002Fcase-studies","Case Studies: Learning to Play","The game-playing systems that turned reinforcement learning from a theory into a track record: Samuel's checkers player, TD-Gammon, Watson's Daily-Double wagering, a reinforcement-learning memory controller, DQN, and AlphaGo through AlphaGo Zero. Read as a set they draw one line — a value function, learned by self-play or interaction, refined by search, carried by a deep network — that runs from a 1959 checkers program to superhuman Go.\n",{"path":19577,"title":19578,"module":19558,"summary":19579},"\u002Freinforcement-learning\u002Fdeep-rl\u002Frl-beyond-games","Reinforcement Learning Beyond Games","The same value-and-reward machinery, pointed at problems with no opponent. Web personalization as a contextual bandit and then a full MDP for life-time value; thermal soaring, where a glider learns to climb on turbulent air and reward design does most of the work; and the industrial-scale systems that carried the same design past Sutton & Barto — AlphaStar, OpenAI Five, GT Sophy, and RLHF, where the reward itself is learned from human preference.\n",{"path":19581,"title":19582,"module":19558,"summary":19583},"\u002Freinforcement-learning\u002Fdeep-rl\u002Ffrontiers","Frontiers: Beyond the Standard MDP","The standard MDP fixes three things — state, reward, and single-step actions — and this lesson loosens two of them. We generalize the value function into a general value function that predicts any signal, and use those predictions as auxiliary tasks that shape representations; we extend actions in time with the options framework; and we treat state as a construction the agent builds from a stream of observations. Reward design and the open problems follow in the next lesson.\n",{"path":19585,"title":19586,"module":19558,"summary":19587},"\u002Freinforcement-learning\u002Fdeep-rl\u002Freward-design-and-open-problems","Reward Design and Open Problems","How to design a reward signal that encodes the intended goal — sparse reward, shaping, and reward hacking — and the problems the whole tabular, approximate, and deep arc leaves unsolved. We close with how the frontiers were pushed after Sutton & Barto: auxiliary tasks, learned options, intrinsic-motivation bonuses, learned world models, and offline RL, then the two concerns of reward hacking and safety that any real-world agent must address.\n",{"path":19589,"title":19590,"module":19591,"summary":19592},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow","Sharpening DQN: Improvements and the Distributional Idea","Modern Deep Reinforcement Learning","In the years after the 2015 DQN paper, a stream of focused improvements each fixed one weakness of the baseline without disturbing its frame. This lesson recaps five that keep the scalar $Q$-value — Double DQN, multi-step returns, dueling networks, prioritized replay, and NoisyNets, each changing a different slot of the same Q-learning loop — then develops the sixth, distributional RL, which changes the objective itself: learn the whole return distribution $Z(s,a)$. We build the distributional Bellman equation and the C51 categorical algorithm, projection step and all, worked end to end on real numbers. A companion lesson takes up QR-DQN, Rainbow, and the modern distributional line.\n",{"path":19594,"title":19595,"module":19591,"summary":19596},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fdistributional-and-rainbow-part-2","Distributional RL and Rainbow","A companion to the DQN improvements lesson. C51 fixed the return atoms and learned their probabilities; QR-DQN does the reverse — fix the probabilities, learn the values — which removes the projection and trains with a quantile loss. We cover why the distribution helps even when you act on the mean, then assemble Rainbow: all six improvements in one Q-learning loop, with the component ablation that shows each one's real weight. The distributional line then runs on through IQN, FQF, and Agent57, the first agent to beat the human baseline on all 57 Atari games.\n",{"path":19598,"title":19599,"module":19591,"summary":19600},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control","Continuous Control: DDPG and TD3","When actions are real-valued, the $\\arg\\max_a Q(s,a)$ in Q-learning becomes an optimization problem on every step. This lesson builds the off-policy actor-critic family that sidesteps it: the deterministic policy gradient and DDPG, which replaces the max with a learned actor, and the three fixes of TD3 that counter the value overestimation DDPG inherits. A companion lesson takes up SAC's maximum-entropy objective and the methods built on this template.\n",{"path":19602,"title":19603,"module":19591,"summary":19604},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fcontinuous-control-part-2","Continuous Control: SAC and Beyond","A companion to the DDPG and TD3 lesson. Where those actors are deterministic and explore with bolted-on noise, soft actor-critic (SAC) changes the objective itself: maximize return plus the entropy of the policy, so exploration becomes intrinsic and the agent stays robust. We develop the maximum-entropy objective, the reparameterized squashed-Gaussian actor, and automatic temperature tuning, then survey the methods built on this off-policy template — distributional critics (D4PG), critic ensembles (REDQ), and control from pixels (DrQ, RAD).\n",{"path":19606,"title":19607,"module":19591,"summary":19608},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl","Model-Based Deep RL: Sample Efficiency and PETS","A model turns experience into imagined planning. This lesson makes the sample-efficiency case for learning a dynamics model, works through why a learned model's errors compound over the planning horizon, and builds the most direct model-based method: PETS plans online with a probabilistic ensemble under model-predictive control, distrusting the model exactly where its members disagree. A companion lesson takes up latent world models (Dreamer) and MuZero.\n",{"path":19610,"title":19611,"module":19591,"summary":19612},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmodel-based-rl-part-2","Model-Based Deep RL: World Models, Dreamer, and MuZero","A companion to the PETS lesson. PETS plans in the environment's native state space; these methods change what the model represents. World Models and Dreamer learn a compact latent state and do almost all their learning by imagining inside it, with value gradients flowing through the differentiable dynamics. MuZero predicts neither states nor pixels — only the reward, value, and policy that MCTS reads — and plans with search against that learned model, AlphaZero without the rules. We close with MBPO, TD-MPC, and EfficientZero.\n",{"path":19614,"title":19615,"module":19591,"summary":19616},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration","Exploration in Deep RL: Novelty as Reward","When the state space is enormous and reward is rare, ε-greedy amounts to a random walk that almost never reaches the first reward. This lesson scales the bandit's exploration ideas up to deep RL through the dominant approach — manufacture a reward for novelty and let the agent chase it: optimism and pseudo-counts from density models, and intrinsic motivation and curiosity (the Intrinsic Curiosity Module and Random Network Distillation). A companion lesson takes up posterior sampling, Go-Explore, and the modern methods.\n",{"path":19618,"title":19619,"module":19591,"summary":19620},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fexploration-part-2","Exploration in Deep RL: Posterior Sampling and Go-Explore","A companion to the novelty-as-reward lesson. Pseudo-counts and curiosity reward the unfamiliar after the agent stumbles into it; this lesson covers two ideas that go further. Bootstrapped DQN keeps an ensemble that approximates a posterior over value functions and explores by committing to one sampled hypothesis per episode — the deep, directed exploration ε-greedy cannot manage. Go-Explore remembers and returns to the frontier, defeating detachment and derailment to solve Montezuma's Revenge. We close with episodic memory (Never Give Up), Agent57, and model-based exploration.\n",{"path":19622,"title":19623,"module":19591,"summary":19624},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl","Offline RL: The Problem and Value-Based Fixes","Offline reinforcement learning learns a policy from a fixed logged dataset with no further environment interaction — off-policy learning pushed to the extreme, and it breaks for the extreme version of the same reason. Bootstrapping queries the value function at out-of-distribution actions the data never covers, those errors are optimistic, and with no online feedback to correct them they compound through the Bellman backup. This lesson sets up the failure and off-policy evaluation, then builds the first two families of pessimistic fixes: policy constraint (BCQ) and conservative value estimation (CQL). A companion lesson takes up implicit methods, model-based offline RL, and Decision Transformer.\n",{"path":19626,"title":19627,"module":19591,"summary":19628},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Foffline-rl-part-2","Offline RL: Implicit Methods, Sequence Models, and Beyond","A companion to the offline-RL problem lesson. Policy constraint and conservative value estimation both still query a learned value function; implicit methods (IQL) avoid querying it off the data at all, using an in-sample expectile backup. We then build pessimism into a learned model (MOPO, COMBO) and drop bootstrapping entirely with Decision Transformer's return-conditioned sequence modeling, closing with offline-to-online fine-tuning, diffusion planners, and the offline view of RLHF. The one rule throughout: without online correction, be pessimistic about what you cannot verify.\n",{"path":19630,"title":19631,"module":19591,"summary":19632},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl","Imitation Learning: Cloning, DAgger, and Inverse RL","When a reward is hard to specify but an expert is easy to watch, learn from demonstrations instead. Behavioral cloning treats control as supervised learning of the expert's state-to-action map, and fails through compounding error: small mistakes carry the agent off the expert's distribution, where it was never trained. DAgger fixes the mismatch by querying the expert on the learner's own states. Inverse RL instead recovers the reward the expert seems to optimize — an ill-posed problem that maximum-entropy IRL disambiguates. A companion lesson casts imitation as adversarial occupancy matching (GAIL, AIRL).\n",{"path":19634,"title":19635,"module":19591,"summary":19636},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fimitation-and-inverse-rl-part-2","Imitation as Adversarial Matching: GAIL and AIRL","A companion to the imitation-learning lesson. If the point of recovering a reward is only to re-run RL and match the expert, you can skip the reward and match the behavior directly. GAIL casts imitation as a GAN — a discriminator separating expert from learner state-action pairs supplies the reward a policy-gradient method optimizes — matching occupancy measures without ever naming a reward. AIRL reads a transferable reward back out of the discriminator. We compare all four methods and close with reward models in RLHF, scaled cloning, and diffusion policies.\n",{"path":19638,"title":19639,"module":19591,"summary":19640},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl","Multi-Agent RL: Markov Games and Centralized Training","With more than one learning agent in an environment, each agent's world becomes non-stationary because the others are changing too. This lesson builds the Markov-game generalization of the MDP, diagnoses non-stationarity as the central obstacle, shows why the naive baselines fail, and develops the dominant fix — centralized training with decentralized execution (MADDPG, VDN, QMIX). A companion lesson takes up self-play, the landmark game-playing systems, and the equilibrium concepts that define what \"solved\" means.\n",{"path":19642,"title":19643,"module":19591,"summary":19644},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmulti-agent-rl-part-2","Multi-Agent RL: Self-Play and Solution Concepts","A companion to the Markov-games lesson. In the purely competitive setting, an agent can generate its own training curriculum by playing against copies of itself — self-play, the method behind AlphaGo, OpenAI Five, and AlphaStar. We develop why self-play produces an ever-improving opponent, the systems it built, and then the equilibrium solution concepts (Nash, correlated, coarse-correlated) that define what \"solved\" means once there is an opponent, closing with PSRO, MAPPO, and the language-model-agent frontier.\n",{"path":19646,"title":19647,"module":19591,"summary":19648},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl","Hierarchical RL: Options and the Option-Critic","Flat RL cannot explore a long horizon: reaching reward through hundreds of primitive actions is exponentially unlikely, and every credit-assignment update crawls one step at a time. Hierarchy breaks one hard long-horizon problem into many short ones. This lesson develops temporal abstraction — the options framework and its semi-Markov view, and learning options end to end with the option-critic. A companion lesson takes up goal-conditioned manager\u002Fworker hierarchies (FeUdal Networks and HIRO), hindsight relabeling, and unsupervised skill discovery.\n",{"path":19650,"title":19651,"module":19591,"summary":19652},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fhierarchical-rl-part-2","Hierarchical RL: Goal-Conditioned Hierarchies and Skills","A companion to the options lesson. Options package a behavior; goal-conditioned hierarchies instead give the top level an explicit language of goals — a manager proposes a target state or a latent direction, and a worker is rewarded for reaching it (FeUdal Networks, HIRO). We develop that architecture, the hindsight relabeling that lets it learn from sparse reward, and unsupervised skill discovery (DIAYN) that learns a repertoire of behaviors with no reward at all. The shared idea throughout: shorten the horizon by inserting a level that decides less often.\n",{"path":19654,"title":19655,"module":19591,"summary":19656},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Frlhf-and-language-models","RLHF and Language Models","A language model trained to predict the next token is fluent but not helpful, honest, or harmless — the objective it was optimized for is not the objective we want. RLHF closes that gap by turning the one thing humans do reliably, comparing two outputs, into a reward. We build the three-stage pipeline: supervised fine-tuning, a Bradley-Terry reward model fit to preference pairs, then PPO against that reward with a KL penalty keeping it near the reference policy. We then cover reward hacking and why the KL penalty matters, Direct Preference Optimization, which folds the reward model into a single classification loss, and the RLAIF and verifiable-reward variants. This pipeline is what makes the largest models usable as assistants.\n",{"path":19658,"title":19659,"module":19591,"summary":19660},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps","Partial Observability: POMDPs and the Belief State","Drop the assumption that the agent sees the state. It sees an observation, a partial and noisy function of a hidden state, and one observation is no longer a Markov signal. This lesson builds the POMDP tuple, shows that the belief state — the posterior over hidden states — is a sufficient statistic that turns a POMDP back into an MDP over beliefs, and works the Bayes-filter belief update step by step. A companion lesson explains why exact planning is intractable and develops the deep-RL answer of recurrent, history-based policies.\n",{"path":19662,"title":19663,"module":19591,"summary":19664},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fpartial-observability-pomdps-part-2","Partial Observability: Planning and Recurrent Policies","A companion to the belief-state lesson. In principle a POMDP reduces to an MDP over beliefs; in practice two obstacles block that. Exact planning over the belief simplex is intractable — the value function is piecewise-linear-and-convex with a number of pieces that can explode — and computing the belief needs a model the agent rarely has. This lesson develops the intractability, the point-based approximations that address it, and the deep-RL answer: make the policy a function of history with a recurrent network (DRQN, R2D2), with frame-stacking, attention, and world-model latents as learned beliefs.\n",{"path":19666,"title":19667,"module":19591,"summary":19668},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl","Safe and Constrained RL: The CMDP and Policy Methods","Maximizing a scalar reward is not the same as behaving well: a capable optimizer will find and exploit any gap between the reward and what its designer actually meant, a failure called specification gaming or reward hacking. The remedy is to add explicit cost constraints — the constrained MDP — maximizing return subject to an expected-cost budget. This lesson builds the core toolkit: the CMDP itself, Lagrangian primal-dual methods that learn a multiplier on the constraint (RCPO), and constrained policy optimization (CPO) with its trust-region cost bound. A companion lesson covers risk-sensitivity, safe exploration, and the alignment framing.\n",{"path":19670,"title":19671,"module":19591,"summary":19672},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fsafe-and-constrained-rl-part-2","Safe RL: Risk, Safe Exploration, and Alignment","A companion to the constrained-MDP lesson. Constraining the mean cost is not enough: a policy safe on average can be catastrophic in the tail, and a policy safe at convergence can violate its limits wildly while learning. This lesson optimizes the tail with risk-sensitive objectives (CVaR), then makes exploration itself safe with shields, Lyapunov methods, and safety layers that project unsafe actions onto the feasible set — closing with benchmarks, safe RLHF, robustness, and the alignment framing that ties safety back to the problem of incompletely specified reward.\n",{"path":19674,"title":19675,"module":19591,"summary":19676},"\u002Freinforcement-learning\u002Fmodern-deep-rl\u002Fmeta-rl-and-generalization","Meta-RL and Generalization","An agent that masters one task often fails on the next; it has overfit to a single environment. This lesson treats fast adaptation as a meta-problem over a distribution of tasks: meta-train so that a few episodes at meta-test time suffice. We cover the two families — optimization-based (MAML learns an initialization) and context-based (RL-squared and PEARL infer a latent task) — the exploration cost of adaptation, and the parallel problem of generalization: why deep RL memorizes environments and what fixes it (domain randomization, procedural generation, augmentation, regularization). It closes on foundation models and sequence-model agents as the generalist endpoint.\n",{"path":19678,"title":19679,"module":19680,"summary":19681},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fpsychology-of-reinforcement","The Psychology of Reinforcement","Reinforcement Learning in Minds and Brains","Reinforcement learning is both an engineering method and a theory of how animals learn. The prediction\u002Fcontrol split of the algorithms mirrors the psychologist's split between classical and instrumental conditioning. We trace the correspondence: the Rescorla–Wagner model as a prediction-error rule that explains blocking, its real-time TD extension, Thorndike's Law of Effect behind trial-and-error control, and the habitual\u002Fgoal-directed distinction that maps onto model-free versus model-based learning.\n",{"path":19683,"title":19684,"module":19680,"summary":19685},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Finstrumental-conditioning-and-control","The Psychology of Reinforcement: Instrumental Control","Classical conditioning was prediction; instrumental conditioning is control. Thorndike's Law of Effect is trial-and-error control — selection plus association, search plus memory — and Skinner's shaping and schedules are reward engineering. The habitual\u002Fgoal-directed distinction maps onto model-free versus model-based control, dissociated by outcome devaluation and arbitrated by uncertainty. Delayed reinforcement is the credit-assignment problem, and the stimulus traces and secondary reinforcers of animal-learning theory are eligibility traces and value functions.\n",{"path":19687,"title":19688,"module":19680,"summary":19689},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-and-td-error","Dopamine and the TD Error","The TD error was invented as an algorithm; a decade later it turned out to closely describe the firing of the brain's dopamine neurons. We follow Schultz's experiments — dopamine fires at an unpredicted reward, shifts to the earliest predictive cue, and dips below baseline when a predicted reward is withheld — and match each result to the TD error term by term. We then read the basal ganglia as a neural actor–critic with dopamine as its shared training signal, and close on addiction as a hijacking of that signal.\n",{"path":19691,"title":19692,"module":19680,"summary":19693},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fdopamine-in-the-brain","Dopamine in the Brain: The Neural Actor–Critic","If phasic dopamine is a TD error, where does it go and what does it change? We follow the axons into the basal ganglia, read the corticostriatal synapse as the place where state, action, and error meet, and map the ventral and dorsal striatum onto the critic and the actor of an actor–critic. Addiction becomes a broken cancellation in the same learning signal, and distributional dopamine extends the scalar RPE into a population code.\n",{"path":19695,"title":19696,"module":19680,"summary":19697},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fanimal-learning-and-cognition","Animal Learning and Cognition","Three classic associative phenomena turn out to be reinforcement-learning mechanisms seen in behavior. Blocking says learning is driven by prediction error, not co-occurrence, and reduces to least-squares regression fitting a collinear feature. Higher-order conditioning and conditioned reinforcement make a value estimate a secondary reinforcer — bootstrapping in an animal. Delayed reinforcement is the credit-assignment problem, and the stimulus traces and goal gradients of Pavlov and Hull are eligibility traces and TD-learned value functions.\n",{"path":19699,"title":19700,"module":19680,"summary":19701},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fcognitive-maps-and-planning","Cognitive Maps and Model-Based Learning","Tolman's rats learned the layout of a maze with no reward, then used it the moment food appeared — latent learning, a cognitive map, and the behavioral face of model-based reinforcement learning. The map is learned by system identification (stimulus–stimulus associations), which fills in whether or not reward is present, and queried by planning, which re-solves a route from a single changed reward. The successor representation sits between cache and model, and hippocampal predictive maps and scaled-up world models carry the same idea into brain and machine.\n",{"path":19703,"title":19704,"module":19680,"summary":19705},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fneuroscience-of-reinforcement","The Neuroscience of Reinforcement","The dopamine story is one contact point between reinforcement learning and the brain; this lesson fills in the surrounding neuroscience so the mapping stands on its own. We build a working primer of neurons, synapses, and neuromodulation; separate four signals that casual usage conflates — reward, reinforcement, value, and prediction error; and read the actor and critic as corticostriatal synapses updated by two- and three-factor rules, grounded in spike-timing-dependent and reward-modulated plasticity.\n",{"path":19707,"title":19708,"module":19680,"summary":19709},"\u002Freinforcement-learning\u002Fminds-and-brains\u002Fseveral-learning-systems","The Brain's Several Learning Systems","The actor's three-factor rule has an ancestor in Klopf's hedonistic neuron — a single cell as a reinforcement-seeking agent — and a bacterium's run-and-twiddle shows the Law of Effect with no synapses at all. Teams of such neurons implement policy gradient collectively, the broadcast reward replacing backpropagation. And the brain is not only model-free: outcome devaluation, prefrontal value coding, and hippocampal forward sweeps localize a model-based system. The recurring conclusion is that the brain is several interacting learning systems, not one algorithm.\n",{"path":19711,"title":18868,"module":6,"summary":6},"\u002Freinforcement-learning",{"path":19713,"title":19714,"module":16062,"summary":19715},"\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai","What Is Artificial Intelligence?","Eight definitions of AI fall into a two-by-two grid: think versus act, and measure success against human performance versus an ideal standard of rationality. We work through all four schools — the Turing test, cognitive modelling, the laws of thought, and the rational agent — and adopt the last as the frame for the whole course: AI is the study and design of rational agents.\n",{"path":19717,"title":19718,"module":16062,"summary":19719},"\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai","The Foundations of AI","Where the rational-agent idea came from and what surrounds it. AI inherited its core tools from eight older disciplines — philosophy, mathematics, economics, neuroscience, psychology, computer engineering, control theory, and linguistics. Its history runs in cycles of boom and winter, from the 1956 Dartmouth workshop through expert systems to the statistical turn. And the deep-learning era — AlexNet, the Transformer, GPT-3, AlphaGo — is a new way of computing the agent function at scale, not a new definition of AI.\n",{"path":19721,"title":19722,"module":16062,"summary":19723},"\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents","Intelligent Agents","An agent perceives an environment through sensors and acts on it through actuators; its behavior is an agent function mapping percept sequences to actions. A rational agent chooses, for each percept sequence, the action that maximizes its expected performance measure given its knowledge. We build the first half of the vocabulary the whole course rests on — the agent function, rationality, PEAS task specifications, and the six axes along which task environments vary.\n",{"path":19725,"title":19726,"module":16062,"summary":19727},"\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures","Agent Architectures","How to build a program that computes a good agent function without storing an astronomically large lookup table. Four skeleton architectures in order of increasing power — simple reflex, model-based, goal-based, and utility-based — plus the learning agent that improves any of them, the scale of world representations (atomic, factored, structured) they rest on, and how a modern language-model agent fits the same frame.\n",{"path":19729,"title":19730,"module":19731,"summary":19732},"\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search","Uninformed Search","Search","A goal-based agent that cannot see which action is best turns the problem into a state space — an initial state, a set of actions, a transition model, a goal test, and a path cost — and searches for a sequence of actions reaching the goal. We build the state-space formulation on the 8-puzzle and route-finding, give the one TREE-SEARCH \u002F GRAPH-SEARCH skeleton every algorithm specializes, and measure strategies by completeness, optimality, and complexity. This lesson develops the first two frontier disciplines — breadth-first and uniform-cost search; the rest follow in the next lesson.\n",{"path":19734,"title":19735,"module":19731,"summary":19736},"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared","Search Strategies Compared","Breadth-first and uniform-cost search pay for optimality in memory. This lesson develops the strategies that trade memory for depth: depth-first search, which keeps only the current path; depth-limited and iterative-deepening search, which fix DFS's failure on infinite paths; and bidirectional search, which meets in the middle for a square-root saving. It closes by lining up all six uninformed strategies against completeness, optimality, and complexity, and tracing where the algorithms came from and where they went.\n",{"path":19738,"title":19739,"module":19731,"summary":19740},"\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search","Informed Search and A*","An informed search uses a heuristic $h(n)$, an estimate of the cost from a node to the goal, to decide what to expand next. Greedy best-first search follows the heuristic blindly and gives up optimality; A* corrects it by ranking nodes on $f(n) = g(n) + h(n)$, and is optimal when the heuristic is admissible (tree search) or consistent (graph search). This lesson defines the heuristic, builds best-first search, and proves why A* is optimal, with the contour picture that explains its pruning. Where good heuristics come from is the next lesson.\n",{"path":19742,"title":19743,"module":19731,"summary":19744},"\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions","Heuristic Functions and Memory-Bounded Search","A* is only as good as its heuristic, so this lesson answers where good heuristics come from: relaxed problems, whose exact solution cost is an admissible heuristic, and pattern databases, which precompute subproblem costs. It measures heuristic quality with dominance and the effective branching factor, then tackles A*'s memory problem with IDA*, RBFS, and SMA*. It closes with modern heuristic search — weighted A*, learned and disjoint pattern-database heuristics, and bidirectional A*.\n",{"path":19746,"title":19747,"module":19731,"summary":19748},"\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search","Local Search and Optimization","When the path to a goal is irrelevant and only the final state matters, we can discard the search tree entirely and keep just the current state, moving to a better neighbor at each step. This lesson builds the state-space landscape metaphor, works through hill climbing and the three obstacles that defeat it (local maxima, ridges, plateaus), then develops the first escapes: random restarts and simulated annealing with its temperature schedule. The population-based methods and continuous-space calculus follow in the next lesson.\n",{"path":19750,"title":19751,"module":19731,"summary":19752},"\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search","Population and Continuous Search","Single-state local search escapes a trap by restarting or tolerating downhill moves. This lesson develops the alternatives that keep several states at once — local beam search, which shares successors across parallel threads, and genetic algorithms, which recombine two parents through crossover and mutation — then crosses into continuous spaces, where calculus replaces the finite neighbor set: gradient ascent, line search, and Newton's method. It closes with the industrial descendants of these methods and the loop they all share.\n",{"path":19754,"title":19755,"module":19731,"summary":19756},"\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search","Adversarial Search and Games","When another agent plans against you, search becomes a game. We formalize two-player, zero-sum, perfect-information games as search problems, define the minimax value that optimal play backs up through the game tree, and give the MINIMAX algorithm that computes it. Alpha–beta pruning then cuts the cost of that search roughly in half in the exponent without changing the answer, and a heuristic evaluation function plus a cutoff test turns the exact algorithm into a real-time player that copes with the horizon effect.\n",{"path":19758,"title":19759,"module":19731,"summary":19760},"\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information","Games of Chance and Imperfect Information","Minimax and alpha–beta assume a deterministic game both players can see in full. Drop either assumption and search must change. This lesson adds chance nodes and the expectiminimax value for games with dice, then belief-state reasoning for partially observable games — Kriegspiel and card games — where averaging over clairvoyance both helps and misleads. It closes with the line from Deep Blue's alpha–beta to AlphaGo's learned evaluation and Monte Carlo tree search, and the provable-pruning and self-play research around each end of that story.\n",{"path":19762,"title":19763,"module":19731,"summary":19764},"\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction","Constraint Satisfaction Problems","A constraint satisfaction problem replaces the black-box state with a factored one: variables, domains, and constraints. That structure supports inference before any search runs. This lesson defines the CSP on map coloring, Sudoku, and scheduling, then develops constraint propagation: node and arc consistency, the AC-3 algorithm that makes a whole network arc-consistent, and the way one deleted value cascades across the graph to prune impossible options ahead of search.\n",{"path":19766,"title":19767,"module":19731,"summary":19768},"\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure","CSP Search and Structure","Propagation prunes a CSP but rarely finishes it, so we search. This lesson builds backtracking search over partial assignments and the general-purpose heuristics that make it fast — MRV, degree, least-constraining-value, forward checking, MAC, and intelligent backtracking. It then shows how the shape of the constraint graph controls difficulty: tree-structured problems fall in linear time, cutset conditioning handles the rest, and min-conflicts local search solves a million queens in a constant number of steps.\n",{"path":19770,"title":19771,"module":19731,"summary":19772},"\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty","Search Under Uncertainty","Classical search assumes the agent knows the state it is in and exactly what each action does. Drop the second assumption and a plan can no longer be a fixed sequence of actions. This lesson develops the first response: AND-OR search over nondeterministic actions, which returns a branching contingency plan rather than a straight line. We build it on the erratic vacuum world, show how OR nodes (the agent's choices) alternate with AND nodes (nature's outcomes), trace the recursion that finds a plan, and handle the case where the only solution is a cyclic \"try, try again.\"\n",{"path":19774,"title":19775,"module":19731,"summary":19776},"\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search","Belief-State and Online Search","When the agent cannot see the full state, a plan can no longer test where it actually is — it must reason over the set of states it might be in. This lesson develops belief-state search, from sensorless (conformant) planning that coerces an unknown world into a goal, through the predict-observe-update cycle of contingent planning with percepts, to online search in unknown environments, where the agent must act in order to learn. It closes with LRTA*, which refines its own heuristic as it explores, one step from reinforcement learning.\n",{"path":19778,"title":19779,"module":19780,"summary":19781},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic","Logical Agents and Propositional Logic","Logic and Planning","A knowledge-based agent keeps a store of sentences and acts by asking it what to do. To make \"asking\" mean something we need entailment — the relation $KB \\models \\alpha$ that holds when every model of the knowledge base is a model of the query. Propositional logic gives a syntax and a truth-table semantics for which entailment is decidable. This first part builds the foundations: the agent loop, the Wumpus World, models and entailment, the connectives and truth tables, theorem proving by refutation, and the resolution rule with its CNF conversion — a single complete inference procedure for all of propositional logic.\n",{"path":19783,"title":19784,"module":19780,"summary":19785},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference","Propositional Inference and Logical Agents","Model checking and resolution decide entailment, but both can blow up. This part turns propositional logic into a practical engine and a working agent. Horn clauses give linear-time forward and backward chaining — the basis of logic programming. DPLL and WalkSAT make satisfiability testing fast in the common case. Then we make the agent situated: time-indexed fluents, the frame problem and its solution by successor-state axioms, a hybrid agent that deduces a safe map and plans a route through it, and SATPlan, which finds a plan by asking a SAT solver for a satisfying model.\n",{"path":19787,"title":19788,"module":19780,"summary":19789},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic","First-Order Logic","Propositional logic can only say that facts hold; it cannot talk about the objects a fact is about, or state a rule once and have it cover every object. First-order logic fixes this by committing to a world of objects, relations, and functions. This first part builds the language from the ground up: the ontology it commits to, the model that gives a sentence a truth value, the syntax of terms and sentences, the two quantifiers with their standard mistakes, and equality.\n",{"path":19791,"title":19792,"module":19780,"summary":19793},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use","First-Order Logic in Use","With the language of first-order logic in hand, this part is about using it well. Database semantics trades expressive power for the convenience of a single intended model; higher-order logic shows what first-order logic gives up for decidability. Then we put the language to work: the Tell\u002FAsk interface, the kinship domain axiomatized from scratch, and the seven-step knowledge-engineering process applied to a digital circuit.\n",{"path":19795,"title":19796,"module":19780,"summary":19797},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution","Inference in First-Order Logic","Propositional inference lifts to first-order logic once we can make terms match. Unification is that machinery: the algorithm that finds the substitution making two expressions identical, and the basis of generalized modus ponens. This first part builds the lifted inference rules and the two chaining algorithms they drive — forward chaining, the data-driven procedure behind production systems and Datalog, and backward chaining, the goal-driven procedure behind Prolog.\n",{"path":19799,"title":19800,"module":19780,"summary":19801},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution","First-Order Resolution","Chaining is complete only for Horn knowledge bases. General first-order sentences — with disjunctive conclusions and negations — need a single sound and complete rule: resolution. This part converts arbitrary sentences to CNF by skolemizing away the existentials, lifts the resolution rule with unification, and proves entailment by refuting the negated goal. The result is the proof procedure Gödel's completeness theorem guarantees will find any entailment, together with the search strategies that make it usable.\n",{"path":19803,"title":19804,"module":19780,"summary":19805},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning","Classical Planning","Classical planning represents a problem in a factored language, PDDL: states are sets of ground fluents, and actions are lifted schemas with a precondition and an effect. That structure turns planning into search — forward through states or backward through goals — and lets a program read heuristics straight off the schemas by relaxing the problem. This first part develops the representation, the two search directions, and the domain-independent heuristics that come from ignoring preconditions or delete lists.\n",{"path":19807,"title":19808,"module":19780,"summary":19809},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan","Planning Heuristics and GraphPlan","Every relaxation heuristic can be inaccurate, and none can tell how far apart subgoals sit. The planning graph is a polynomial-size structure that does better: leveled off the problem, it yields admissible distance estimates and a record of which actions and fluents cannot coexist. This part builds the graph, reads heuristics from it, extracts plans with GraphPlan, and closes with the other classical approaches — SATPlan and partial-order planning — and the representational trade that makes all of it work.\n",{"path":19811,"title":19812,"module":19780,"summary":19813},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world","Planning and Acting in the Real World","Classical planning's clean theory rests on four assumptions: time is ignored, actions are atomic, the world is deterministic and fully observable, and the agent is alone. This first part drops the first two. We add durations and resource constraints — turning a plan into a schedule, solved by the critical-path method and, once resources contend, by NP-hard job-shop scheduling — and let a planner reason at multiple levels of abstraction through high-level actions and their angelic reachable sets.\n",{"path":19815,"title":19816,"module":19780,"summary":19817},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty","Planning Under Uncertainty","Classical planning assumed the world was deterministic, fully observable, and the agent alone. This part drops the last two assumptions. When the agent cannot see or predict the world, planning moves into belief-state space: sensorless plans that coerce the world into the goal without sensing, contingent plans that branch on what is sensed, and online agents that monitor and replan when execution diverges. Then we add other agents — joint plans, the coordination problem, and the conventions that let a team act without constant negotiation.\n",{"path":19819,"title":19820,"module":19780,"summary":19821},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation","Knowledge Representation","First-order logic gives you the language; this lesson is about what to say in it. This first part builds the content: a general upper ontology from the top down, categories as first-class objects with taxonomies and inheritance, physical composition and the count-noun\u002Fmass-noun split, events and time reified through the event calculus, and belief modeled with modal logic — the machinery for representing the world an agent reasons about.\n",{"path":19823,"title":19824,"module":19780,"summary":19825},"\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults","Reasoning Systems and Default Logic","Having represented the world, this part is about reasoning with it at scale. Semantic networks give a graphical notation with fast inheritance; description logics keep subsumption and classification tractable by design. Then we confront the fact that most useful rules hold only by default: circumscription and default logic give a logical account of nonmonotonic reasoning, and truth maintenance systems retract conclusions cleanly when the beliefs beneath them change.\n",{"path":19827,"title":19828,"module":19829,"summary":19830},"\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes","Quantifying Uncertainty","Uncertainty","Logic breaks down in any domain where the rules have exceptions you cannot enumerate — the qualification problem. Probability replaces truth values with degrees of belief that obey Kolmogorov's axioms, and the full joint distribution becomes a knowledge base from which any query is answered by summing entries: marginalization, conditioning, and normalization. Independence factors that joint into smaller pieces — the first step toward a calculus of rational belief that an agent can actually compute with.\n",{"path":19832,"title":19833,"module":19829,"summary":19834},"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes","Bayes' Rule and Naive Bayes","Bayes' rule inverts a causal model into a diagnostic one, turning \"how a cause produces its symptoms\" into \"which cause explains what I observed.\" Ignoring the prior is the base-rate fallacy behind overconfident test results. Conditional independence then lets several pieces of evidence combine by multiplying likelihood ratios instead of building an exponential joint, giving the naive Bayes model and pointing directly at Bayesian networks.\n",{"path":19836,"title":19837,"module":19829,"summary":19838},"\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks","Bayesian Networks","A Bayesian network is a directed acyclic graph of random variables in which each node carries a conditional probability table for itself given its parents. That structure factors the full joint distribution into a product of local terms, turning an exponential table into a linear one, and it makes the conditional independences of the domain explicit. We build the canonical burglary–alarm network, read compactness and d-separation off the graph, run exact inference by variable elimination, and, where that is intractable, estimate answers by sampling.\n",{"path":19840,"title":19841,"module":19829,"summary":19842},"\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks","Bayesian Networks: Inference and Relational Models","When exact inference is intractable, sampling estimates the posterior instead: prior and rejection sampling, likelihood weighting, and Gibbs\u002FMCMC, whose error shrinks as one over the square root of the sample count. The same graphical idea then lifts from a fixed set of variables to whole populations — relational and open-universe probability models write dependencies once and unroll them over objects — and we close by placing probability against the rule-based, Dempster–Shafer, and fuzzy alternatives it displaced.\n",{"path":19844,"title":19845,"module":19829,"summary":19846},"\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time","Probabilistic Reasoning over Time","A world that changes needs a state variable at every point in time. The Markov assumption cuts the dependence on history down to the previous slice, leaving a transition model and a sensor model that define a temporal Bayesian network. Four recursive tasks fall out — filtering, prediction, smoothing, and the most likely explanation — each a message passed along the sequence. We ground them in hidden Markov models and their matrix form, sketch the Kalman filter for continuous state, and reach dynamic Bayesian networks with particle filtering as the general approximate method.\n",{"path":19848,"title":19849,"module":19829,"summary":19850},"\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association","Reasoning over Time: Tracking and Data Association","Dynamic Bayesian networks generalize HMMs and Kalman filters to arbitrarily many state variables per slice, and when exact inference blows up, particle filtering approximates the belief state with a population of weighted samples that propagate, reweight, and resample. Tracking several objects at once adds the data-association problem — which observation came from which object — whose combinatorics defeat any exact filter, so particle filters and MCMC keep many hypotheses alive. We close with SLAM and learned state-space models.\n",{"path":19852,"title":19853,"module":19829,"summary":19854},"\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions","Making Decisions: Utility Theory","A rational agent chooses the action that maximizes expected utility — the probability of each outcome weighted by how much the agent wants it. We derive the utility function from six axioms on preferences, so maximizing expected utility is forced by consistency rather than assumed; look at risk aversion in the utility-of-money curve; package one-shot choices into decision networks; and quantify what an observation is worth with the value of information.\n",{"path":19856,"title":19445,"module":19829,"summary":19857},"\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes","When an agent must act repeatedly in a stochastic world, a fixed plan is useless — it needs a policy, an action for every state. The Markov decision process makes this precise with a transition model, a reward, and a discount factor; the Bellman equation characterizes the optimal state utilities, and value iteration and policy iteration solve it. Partial observability lifts the problem to belief states, and bandits, Monte-Carlo tree search, and scalable POMDP solvers extend it — this is the model-known half of reinforcement learning.\n",{"path":19859,"title":19860,"module":19829,"summary":19861},"\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory","Decision Analysis: Multi-Attribute Utility and Decision Networks","Decision analysis takes the single-agent utility framework and makes it practical: utility over several attributes, dominance and additive value functions, influence diagrams that fold Bayesian networks together with decision and utility nodes, and the value of information that tells an agent which questions are worth asking. Structure in an agent's preferences — dominance, preferential and utility independence — collapses an exponential utility table into a few one-dimensional functions, the same move that made Bayesian networks compact.\n",{"path":19863,"title":19864,"module":19829,"summary":19865},"\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design","Game Theory and Mechanism Design","When outcomes depend on other rational agents, single-agent utility maximization no longer suffices. Game theory studies decisions among agents — normal-form games, dominant strategies, Nash and maximin equilibria, and repeated games — and mechanism design runs the logic backwards, engineering rules (auctions, VCG) so that self-interested play produces a good collective outcome. Algorithmic game theory then asks whether equilibria can be computed, what selfishness costs society, and how the mechanisms deployed at internet scale actually behave.\n",{"path":19867,"title":19868,"module":19869,"summary":19870},"\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples","Learning from Examples","Learning","An agent that improves with experience does not need its designer to anticipate every situation. Inductive learning takes that ambition and narrows it to one tractable problem: from labelled input-output pairs, recover a function that predicts the output for inputs never seen. This first part builds the foundation around a single organizing question — generalization — through decision trees and information gain, and the training\u002Fvalidation\u002Ftest discipline for evaluating and choosing hypotheses. A second part takes up the theory of learning and the main model families.\n",{"path":19872,"title":19873,"module":19869,"summary":19874},"\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families","The Theory of Learning and Model Families","Cross-validation measures generalization but does not explain it. This part supplies the theory — PAC learning, sample complexity, and the VC dimension — that says when a hypothesis consistent with enough data is probably approximately correct, and why an unrestricted hypothesis space can never generalize. It then surveys the model families a practitioner reaches for: linear regression and gradient descent, the perceptron and logistic regression, support vector machines and the kernel trick, and ensembles by bagging and boosting — closing with what deep learning changed about the classical picture.\n",{"path":19876,"title":19877,"module":19869,"summary":19878},"\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning","Learning Probabilistic Models","A [Bayesian network](\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks) is useless until its numbers are filled in, and those numbers come from data. This first part casts learning itself as probabilistic inference: hypotheses carry a prior, data update it to a posterior, and predictions average over what remains. From that frame fall the standard estimators — maximum likelihood by counting, MAP with a conjugate prior, full Bayesian updating — for the case where every variable is observed. A second part takes up the harder case of hidden variables and the EM algorithm.\n",{"path":19880,"title":19881,"module":19869,"summary":19882},"\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization","Learning with Hidden Variables: The EM Algorithm","Complete data can be learned by counting; real data usually hide some variables — the disease behind the symptoms, the cluster behind the points. This part develops the expectation-maximization algorithm, which learns those models by alternating an expected completion of the missing data with a re-estimation of the parameters. It works the idea through mixtures of Gaussians, Bayesian networks, and hidden Markov models, proves the monotone-likelihood guarantee from the evidence lower bound, and traces the line from EM to variational inference and the variational autoencoder.\n",{"path":19884,"title":18868,"module":19869,"summary":19885},"\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning","Reinforcement learning is an MDP with the model unknown: the agent knows neither how its actions move the world nor which states are rewarded, and must recover good behaviour from experienced transitions and rewards alone. This first part builds the classical tabular theory — passive learning (fix a policy, learn its value, by direct estimation, adaptive dynamic programming, and temporal differences) and active learning (choose actions, trade exploration against exploitation, and learn control with Q-learning and SARSA). A second part lifts it off the lookup table with function approximation and policy search.\n",{"path":19887,"title":19888,"module":19869,"summary":19889},"\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search","Reinforcement Learning: Generalization and Policy Search","Tabular reinforcement learning stores one number per state, which is hopeless for backgammon or chess. This part lifts RL off the lookup table with function approximation, so that updating one state generalizes to related ones, then turns to policy search — representing and optimizing the policy directly, up to the REINFORCE policy gradient and correlated sampling. It closes with the bridge to deep reinforcement learning (deep Q-networks, actor-critic, PPO), the classic applications, and the hand-off to the dedicated RL subject.\n",{"path":19891,"title":19892,"module":19869,"summary":19893},"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning","Knowledge in Learning","Pure induction learns a function from labelled examples while knowing almost nothing to begin with. This first part brings prior knowledge into the loop by recasting learning as logical inference — hypotheses, examples, and classifications as sentences. It develops current-best-hypothesis search, the version space and its general\u002Fspecific boundary maintained by candidate elimination, and states the three entailment constraints that fix how background knowledge enters. A second part builds the three knowledge-based methods those constraints define.\n",{"path":19895,"title":19896,"module":19869,"summary":19897},"\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods","Knowledge-Based Learning: EBL, Relevance, and ILP","Once learning is cast as logical inference, three methods follow from the three ways prior knowledge can enter. Explanation-based learning generalizes a single example by explaining it with the domain theory, gaining speed but nothing new. Relevance-based learning uses determinations to shrink the hypothesis space and converge from fewer examples. Inductive logic programming learns genuinely new first-order rules — top-down with FOIL, bottom-up by inverting resolution, even inventing new predicates — and connects to modern statistical relational and neuro-symbolic learning.\n",{"path":19899,"title":19900,"module":19901,"summary":19902},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception","Vision and Perception","Frontiers","Perception connects an agent to the physical world. We follow one modality — vision — from the physics of image formation (the pinhole camera, perspective projection, lenses, shading, color) through the early operations that turn a pixel array into edges, texture, and motion, and into recognition by appearance. The recurring problem is inversion: a camera collapses a 3-D world onto a 2-D grid, and an agent that wants to act must build the scene back up. Rebuilding the scene is the subject of the companion lesson.\n",{"path":19904,"title":19905,"module":19901,"summary":19906},"\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world","Vision: Reconstructing the 3D World","A camera collapses a three-dimensional world onto a flat grid; this lesson inverts that collapse. We build the camera projection matrix (intrinsics and extrinsics), triangulate a point from two views, then work through the toolbox of depth cues — motion parallax, binocular stereopsis, multiple views, texture, shading, and contour — that turn an ambiguous image back into a scene. We add structural recognition (pictorial-structure \"cardboard people\"), the task-driven use of vision in cars and robots, and the shift from hand-built pipelines to learned deep-vision networks.\n",{"path":19908,"title":19909,"module":19901,"summary":19910},"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics","Robotics","A robot is an agent with a body: sensors that read the physical world and effectors that push back on it. This lesson grounds the abstract AI machinery in that body. We build up the hardware (range finders, proprioception, degrees of freedom), then cast perception as probabilistic filtering — the kinematic motion and sensor models, Monte Carlo localization, the extended Kalman filter, and simultaneous localization and mapping (SLAM). The companion lesson takes the estimated pose forward into planning and control.\n",{"path":19912,"title":19913,"module":19901,"summary":19914},"\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control","Robotics: Planning and Control","A robot that knows where it is still has to decide how to move, and then make a slipping, sensing-imperfect body actually go there. This lesson takes the pose estimate forward: planning motion in configuration space with cell decomposition and sampling-based roadmaps (PRMs and RRTs), planning under uncertainty with most-likely-state and online replanning, closing the loop with P\u002FPD\u002FPID control and potential fields, and finally the software architectures — subsumption, three-layer, and pipeline — that assemble it all, plus the learning-based turn in modern robotics.\n",{"path":19916,"title":19917,"module":19901,"summary":19918},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai","Natural Language for AI Agents","Language is how agents acquire the knowledge already written down and how they communicate with the humans they serve. This lesson gives the classical AI account of language as a source of information: n-gram language models and the information-seeking tasks built on them — text classification, information retrieval (BM25, the inverted index, PageRank), and information extraction with finite-state templates and hidden Markov models. Throughout, we point to the dedicated NLP subject for the modern deep-learning treatment; the companion lesson takes up grammar, translation, and speech.\n",{"path":19920,"title":19921,"module":19901,"summary":19922},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech","Language for AI Agents: Grammar, Translation, and Speech","N-gram models see only a local window; they cannot say why \"black dog\" is well-formed English and \"dog black\" is not, because that is a fact about structure. This lesson takes up structure: phrase-structure and probabilistic context-free grammars, syntactic analysis by chart parsing and CYK, augmented grammars and compositional semantics, then the two major statistical successes — machine translation and speech recognition — cast as noisy-channel problems. It closes with the bridge from n-grams to transformers and where the classical account sits relative to modern NLP.\n",{"path":19924,"title":19925,"module":19901,"summary":19926},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future","Philosophy, Ethics, and the Future of AI","Two questions have shadowed the field since its founding: can machines act intelligently (weak AI), and can they really think (strong AI)? We work through Turing's objections and their rebuttals — the arguments from disability, mathematics, and informality — then the strong-AI debate: the mind-body problem, functionalism and the brain prosthesis, Searle's Chinese Room and the systems reply, and consciousness and qualia. The companion lesson turns from what AI can do to what it should, and closes the course.\n",{"path":19928,"title":19929,"module":19901,"summary":19930},"\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future","The Ethics and Future of AI","Having asked whether machines can act intelligently and really think, we turn to whether we should build them at all. This lesson works through the six ethical risks — lost jobs, autonomous weapons, surveillance and privacy, biased decisions, the safety of superintelligence, and the erosion of accountability — then the value-alignment problem in the LLM era, and where the classical agent components could go next. It closes the course by tying search, logic, probability, and learning into a single picture of intelligence as rational agency.\n",{"path":19932,"title":19933,"module":6,"summary":6},"\u002Fartificial-intelligence","Artificial Intelligence",{"path":19935,"title":19936,"module":19937,"summary":19938},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart","Nuclear Composition and Ground-State Properties","Nuclear Properties","The nucleus is a bound assembly of Z protons and N neutrons packed to a radius R = R0 A^(1\u002F3) at a nearly constant density of about 10^17 kg\u002Fm^3. We fix the vocabulary of nuclides, derive nuclear size from mirror-nuclide and electron-scattering data, read the binding-energy-per-nucleon curve, and model it with the liquid-drop semiempirical mass formula.\n",{"path":19940,"title":19941,"module":19937,"summary":19942},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions","Nuclear Size, Shape, and Charge Distributions","Elastic electron scattering resolves the nucleus by its de Broglie wavelength. The measured cross section is the Mott point-charge cross section modulated by a form factor, and that form factor is the Fourier transform of the charge density. Diffraction minima fix the radius, the small-angle slope fixes the mean-square radius, and the fitted Woods-Saxon profile gives a central density and a skin thickness. Mirror-nucleus Coulomb energies, muonic-atom X-rays, and optical isotope shifts give independent radii that all track R = R0 A^(1\u002F3).\n",{"path":19944,"title":19945,"module":19937,"summary":19946},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy","Nuclear Masses, Mass Excess, and Separation Energies","The atomic mass unit fixes the scale, and the mass excess collects the small binding-driven deviation from the integer mass number. Penning-trap cyclotron frequencies now measure masses to parts in a billion, and every decay and reaction Q-value is a difference of these masses. One- and two-nucleon separation energies read the binding difference between neighbouring nuclides directly, showing the even-odd pairing stagger and the sharp drops at magic numbers, and their vanishing marks the neutron and proton drip lines that bound the chart of the nuclides.\n",{"path":19948,"title":19949,"module":19937,"summary":19950},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula","The Semi-Empirical Mass Formula and the Valley of Stability","Five physical terms reproduce nuclear binding across the chart: a volume term from saturation, a surface term from the deficit of edge neighbours, a Coulomb term from the electrostatic self-energy of a charged sphere, an asymmetry term from the Pauli cost of unequal proton and neutron filling, and a pairing term. The formula is quadratic in Z at fixed A, so isobars lie on a mass parabola whose minimum sets the most stable charge and whose slope dictates the direction of beta decay. The same competition between surface and Coulomb energy defines the fissility parameter and the onset of fission.\n",{"path":19952,"title":19953,"module":19937,"summary":19954},"\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles","Nuclear Spin, Magnetic Dipole, and Electric Quadrupole Moments","The ground state of a nucleus carries a definite spin and parity, a magnetic dipole moment of order the nuclear magneton, and, when its spin exceeds one-half, an electric quadrupole moment that measures its shape. The single-particle Schmidt lines predict the magnetic moment of an odd-A nucleus from the last unpaired nucleon, and the measured moments fall between them. The quadrupole moment distinguishes prolate from oblate deformation, and hyperfine structure is the experimental handle that fixes the spin and the moments from an atomic spectrum.\n",{"path":19956,"title":19957,"module":19958,"summary":19959},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview","The Nuclear Force and the Shell Model","The Nuclear Force","The strong force between nucleons is short-range, charge-independent, saturated, and repulsive at its core, about a hundred times stronger than Coulomb. Yukawa explained it as an exchange of massive mesons, tying the force's range to the meson mass through the uncertainty principle. Layered on top, an independent-particle shell model with strong spin-orbit coupling reproduces the magic numbers 2, 8, 20, 28, 50, 82, 126.\n",{"path":19961,"title":19962,"module":19958,"summary":19963},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron","The Deuteron and the Tensor Force","The deuteron is the only bound two-nucleon state: one shallow level at 2.22 MeV, no excited states. A square-well fit fixes a depth near 35 MeV over a 2 fm range, yet the wavefunction leaks so far past the edge that most of the probability lies outside the force. Its spin-1 ground state, magnetic moment close to the sum of the free-nucleon moments, and small but nonzero electric quadrupole moment together force a D-state admixture and a non-central tensor force.\n",{"path":19965,"title":19966,"module":19958,"summary":19967},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering","Nucleon-Nucleon Scattering and the Interaction's Structure","Scattering probes the nuclear force above threshold. Partial-wave analysis reduces low-energy data to a single s-wave phase shift, and the effective-range expansion packages that into a scattering length and an effective range. The triplet channel binds (the deuteron) while the singlet is only virtual, which together explain the anomalously large free neutron-proton cross section. Comparing pp, nn, and np results establishes charge symmetry and charge independence, and polarization experiments expose the spin-orbit and tensor pieces.\n",{"path":19969,"title":19970,"module":19958,"summary":19971},"\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin","Meson Exchange, the Yukawa Potential, and Isospin","Yukawa's massive-field propagator turns the range of the nuclear force into a meson mass: the exchanged quantum's Compton wavelength is the range. One-pion exchange fixes the long-range tail, complete with the tensor structure the deuteron demanded, while heavier mesons build the intermediate attraction and the repulsive core. Charge independence becomes an isospin symmetry, the force is diagonalized by the total isospin through a tau-dot-tau interaction, and the whole picture sits inside QCD as a residual color force between color-neutral nucleons.\n",{"path":19973,"title":19974,"module":19975,"summary":19976},"\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model","The Fermi Gas Model","Nuclear Models","Treating the nucleus as two degenerate Fermi gases of protons and neutrons confined in a common well fixes the Fermi momentum near 250 MeV\u002Fc and the Fermi energy near 33 MeV from the nuclear density alone. The average kinetic energy per nucleon is about 20 MeV, the well depth is the Fermi energy plus the separation energy, and unequal proton and neutron Fermi levels reproduce the asymmetry term of the mass formula.\n",{"path":19978,"title":19979,"module":19975,"summary":19980},"\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates","The Liquid-Drop Model and Collective Deformation","Deforming a charged liquid drop into a spheroid raises its surface energy and lowers its Coulomb energy; the two effects compete through the deformation parameter to set a stability minimum and a fission barrier. The ratio of Coulomb to twice the surface energy is the fissility Z-squared over A, which crosses one near 49 and marks the point where the sphere is unstable. The same surface tension that restores small deformations quantizes into collective vibrations, carrying the static mass formula into dynamic collective motion.\n",{"path":19982,"title":19983,"module":19975,"summary":19984},"\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle","The Shell Model: Single-Particle States and Spin-Orbit Coupling","A harmonic-oscillator well reproduces the first three magic numbers but fails above twenty; adding a strong inverted spin-orbit term that drives the stretched j equals l plus one-half level down closes the gaps at 28, 50, 82, and 126. The filled shells couple to zero, so the last unpaired nucleon fixes the ground-state spin and parity, and its single-particle magnetic moment falls on the Schmidt lines. Configuration mixing sets the limits of the extreme single-particle model.\n",{"path":19986,"title":19987,"module":19975,"summary":19988},"\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations","The Collective Model: Rotations, Vibrations, and Deformed Nuclei","Deformed nuclei rotate with energies proportional to I times I plus one, giving the ground-state band its characteristic level ratios, while near-spherical nuclei vibrate in quantized surface phonons that build one- and two-phonon multiplets. The Nilsson model tracks single-particle levels as the well deforms, moments of inertia fall between the rigid and irrotational limits, backbending marks the sudden alignment of a broken pair, and giant resonances are the bulk dipole and quadrupole modes of the whole nucleus.\n",{"path":19990,"title":19991,"module":19992,"summary":19993},"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes","Radioactivity and Decay Modes","Radioactive Decay","Unstable nuclei decay at a rate proportional to how many remain, giving the exponential law N(t) = N0 e^(-lambda t) with half-life t = 0.693\u002Flambda. We work through the three common modes: alpha decay as Coulomb-barrier tunneling with the Geiger-Nuttall rule, beta decay whose continuous spectrum demands the neutrino, and gamma de-excitation, and follow a decay chain across the chart of nuclides.\n",{"path":19995,"title":19996,"module":19992,"summary":19997},"\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium","Serial Decay, the Bateman Equations, and Radioactive Equilibrium","A radioactive parent that decays into a radioactive daughter obeys a coupled pair of rate equations whose solution is the Bateman formula. Depending on the half-life ordering the chain settles into secular equilibrium (equal activities), transient equilibrium (a fixed activity ratio), or no equilibrium. Constant production under irradiation drives the activity toward a saturation value equal to the production rate, competing decay modes split the total decay constant into partial constants, and the natural decay series in secular equilibrium underpin radiometric dating.\n",{"path":19999,"title":20000,"module":20001,"summary":20002},"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory","Alpha Decay and the Gamow Theory of Tunneling","Alpha Decay","The alpha Q-value turns positive above mass number 150 because the emitted helium-4 is exceptionally tightly bound. Emission proceeds by quantum tunneling through the Coulomb barrier: a WKB integral from the nuclear surface to the outer turning point gives the Gamow factor, and multiplying its penetrability by the assault frequency yields half-lives spanning more than twenty orders of magnitude. The leading term reproduces the Geiger-Nuttall relation, log t½ proportional to the daughter charge over the square root of Q.\n",{"path":20004,"title":20005,"module":20001,"summary":20006},"\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance","Fine Structure, Angular Momentum, and Hindrance Factors","A single parent emits several alpha groups of slightly different energy, each feeding a distinct level of the daughter, so the alpha spectrum maps the daughter's low-lying states. Emission with orbital angular momentum L raises the barrier by a centrifugal term and is allowed only when angular-momentum and parity selection rules permit. Comparing the measured partial half-life to the Gamow estimate defines a hindrance factor near unity for even-even ground-state transitions and large for odd-A decays that must rearrange the unpaired nucleon.\n",{"path":20008,"title":20009,"module":20010,"summary":20011},"\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino","Beta Decay Energetics and the Neutrino","Beta Decay and the Weak Interaction","Beta decay converts a neutron into a proton or the reverse, adjusting Z at fixed A along an isobaric mass parabola. We write the three processes (beta-minus, beta-plus, electron capture), reduce every Q-value to a difference of neutral atomic masses, and read the continuous electron spectrum as the fingerprint of a third, nearly massless particle. Pauli's neutrino, its detection by Reines and Cowan, and the endpoint bound on its mass close the lesson.\n",{"path":20013,"title":20014,"module":20010,"summary":20015},"\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay","Fermi's Theory: Kurie Plots and ft Values","Fermi treated beta decay as a point-contact weak transition and read its rate from the golden rule. The electron spectrum then follows from phase space and the Coulomb Fermi function; the Kurie plot straightens it to a line whose intercept is the endpoint. Integrating the spectrum gives the comparative half-life ft, whose logarithm sorts transitions into superallowed, allowed, and forbidden classes governed by the Fermi and Gamow-Teller selection rules.\n",{"path":20017,"title":20018,"module":20010,"summary":20019},"\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation","The Weak Interaction and Parity Violation","Beta decay violates mirror symmetry. The Wu experiment on polarized cobalt-60 showed electrons emitted preferentially against the nuclear spin, a pseudoscalar correlation forbidden if parity were conserved. The result fixes the weak charged current as left-handed V minus A, forces neutrinos to be left-handed and antineutrinos right-handed (measured by Goldhaber), and places beta decay within the electroweak theory as W-boson exchange turning a down quark into an up quark.\n",{"path":20021,"title":20022,"module":20010,"summary":20023},"\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass","Double Beta Decay and Neutrino Mass","For even-A isobars the pairing term splits the mass parabola into two curves, and a handful of even-even nuclides sit below their odd-odd neighbor yet above the next even-even one: single beta decay is forbidden but second-order double beta decay is allowed. The two-neutrino mode is a standard-model process with the longest measured lifetimes in nature; the neutrinoless mode would require the neutrino to be its own antiparticle and its rate measures the effective Majorana mass, the sharpest probe of the absolute neutrino mass scale.\n",{"path":20025,"title":20026,"module":20027,"summary":20028},"\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation","Multipole Radiation and Selection Rules","Gamma Decay","Gamma decay carries a nucleus from an excited state to a lower one by emitting a photon of definite angular momentum and parity. We correct the photon energy for nuclear recoil, expand the radiation field into electric and magnetic multipoles, and read off how the transition rate collapses with each increase in multipole order. The Weisskopf single-particle estimates set the scale, and angular-momentum and parity conservation fix which multipole dominates.\n",{"path":20030,"title":20031,"module":20027,"summary":20032},"\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers","Internal Conversion and Isomers","A nucleus can shed excitation energy without emitting a photon by handing it directly to an atomic electron. We define the internal-conversion coefficient, trace its growth with atomic number, multipole order, and decreasing energy, and treat the electron-only E0 transitions and internal pair formation. When the lowest allowed multipole is high and the energy low, the gamma rate falls so far that the excited state survives as a metastable isomer.\n",{"path":20034,"title":20035,"module":20027,"summary":20036},"\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer","Angular Correlations and the Mössbauer Effect","Two gammas emitted in cascade are not independent in direction: detecting the first selects magnetic substates of the intermediate level and makes the second anisotropic, so the correlation function fixes the intermediate spin. The same nuclear resonance that recoil normally destroys is recovered when the emitter is locked in a lattice, giving the Mössbauer effect and its part-in-a-trillion resolution of isomer shifts and hyperfine fields.\n",{"path":20038,"title":20039,"module":20040,"summary":20041},"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections","Nuclear Reactions, Fission, and Fusion","Nuclear Reactions","A nuclear reaction X(x, y)Y is governed by its Q value and its cross section, the effective target area for a given process. Splitting the curve of binding energy near iron in either direction releases energy: fission of heavy nuclei by neutron capture and a chain reaction, and fusion of light nuclei that powers the Sun and needs Lawson's density-confinement criterion to be practical.\n",{"path":20043,"title":20044,"module":20040,"summary":20045},"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances","The Compound Nucleus and Resonance Reactions","Low-energy reactions proceed through a long-lived intermediate state whose decay forgets how it formed. Bohr's independence hypothesis factorizes the cross section into a formation step and a branching ratio, an isolated level gives the single-level Breit-Wigner line shape with total width Γ tied to the lifetime by Γτ = ħ, and at high excitation overlapping levels merge into a statistical continuum described by evaporation spectra and the Hauser-Feshbach average.\n",{"path":20047,"title":20048,"module":20040,"summary":20049},"\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model","Direct Reactions and the Optical Model","A complex optical potential replaces the many-body target by a single particle moving in an average field whose imaginary part removes flux into non-elastic channels, reproducing the diffraction pattern of elastic scattering. Direct reactions bypass the compound nucleus, transferring a nucleon in one step: stripping and pickup deposit or remove a single nucleon, the angle of the first peak in the distorted-wave angular distribution fixes the transferred orbital angular momentum, and its magnitude gives the spectroscopic factor.\n",{"path":20051,"title":20052,"module":20053,"summary":20054},"\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics","The Fission Barrier and Fragment Energetics","Nuclear Fission","Fission is the large-amplitude collective deformation of a heavy nucleus into two fragments. The liquid-drop model sets a barrier from the competition between rising surface energy and falling Coulomb energy under quadrupole deformation, with the fissility parameter Z²\u002FA measuring how close a nucleus is to instability. Bohr-Wheeler theory separates spontaneous from neutron-induced fission, the fragment mass yield is double-humped and asymmetric, about 200 MeV is released per event, and shell corrections add a second minimum that produces fission isomers.\n",{"path":20056,"title":20057,"module":20053,"summary":20058},"\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics","Chain Reactions and Reactor Physics","A self-sustaining chain reaction is a fixed point of neutron bookkeeping: the multiplication factor k counts the neutrons in one generation per neutron in the last, and criticality is k = 1. The four-factor formula tracks a neutron through fast fission, resonance escape, thermal utilization, and reproduction; moderation slows fission neutrons to the thermal energies where the fission cross section is largest; and the small delayed-neutron fraction sets the timescale that makes a reactor controllable. Breeding converts fertile U-238 and Th-232 into new fissile fuel.\n",{"path":20060,"title":20061,"module":20062,"summary":20063},"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement","Fusion Reactions and Confinement","Fusion and Nucleosynthesis","Light nuclei release energy when they fuse because binding per nucleon rises steeply toward the iron peak, but the Coulomb barrier suppresses the rate at reactor temperatures. The thermonuclear rate is a convolution of the Maxwell distribution with the tunneling probability, sharply peaked at the Gamow energy. The deuterium-tritium reaction has the lowest barrier and largest cross section; sustained energy gain requires the Lawson triple product of density, temperature, and confinement time, reached by magnetic or inertial confinement.\n",{"path":20065,"title":20066,"module":20062,"summary":20067},"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis","Stellar Nucleosynthesis","Main-sequence stars burn hydrogen to helium through the proton-proton chain and the CNO cycle, both releasing 26.7 MeV per helium nucleus. Helium burning bridges the mass-5 and mass-8 gaps by the triple-alpha process through the Beryllium-8 and Hoyle resonances, and successive carbon-to-silicon burning stages climb to the iron peak, where fusion stops. The elements beyond iron are built by slow and rapid neutron capture, and the solar neutrino flux confirms the reactions directly.\n",{"path":20069,"title":20070,"module":20062,"summary":20071},"\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis","Big-Bang Nucleosynthesis","In the first three minutes the expanding universe forged the light elements. The weak interaction froze the neutron-to-proton ratio near one in six when the reaction rate fell below the expansion rate, and free-neutron decay lowered it to about one in seven before the deuterium bottleneck broke. Almost every surviving neutron ended in helium-4, fixing the primordial helium mass fraction near 0.25, with trace deuterium, helium-3, and lithium-7. The deuterium abundance measures the cosmic baryon density.\n",{"path":20073,"title":20074,"module":20075,"summary":20076},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power","Stopping Power and the Range of Charged Particles","Radiation and Applications","A heavy charged particle loses energy in a dense sequence of small Coulomb collisions with atomic electrons, at a rate the Bethe-Bloch formula fixes from the particle's charge and speed and the medium's electron density and mean excitation energy. The rate scales as the inverse square of the speed, so most energy is deposited at the end of the track in the Bragg peak, and integrating the reciprocal rate gives a sharp range. Electrons differ: they also radiate, and above a critical energy bremsstrahlung dominates. Fast particles above the phase velocity of light in the medium emit Cherenkov radiation.\n",{"path":20078,"title":20079,"module":20075,"summary":20080},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions","Interactions of Photons and Neutrons","Photons are removed from a beam in single events, so their intensity falls exponentially with a linear attenuation coefficient built from three processes: the photoelectric effect at low energy, Compton scattering at intermediate energy, and pair production above twice the electron rest energy, each with its own atomic-number and energy dependence. Neutrons carry no charge and interact only with nuclei, moderating by elastic scattering and being captured with a cross section that rises as one over speed away from resonances.\n",{"path":20082,"title":20083,"module":20075,"summary":20084},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors","Radiation Detectors and Nuclear Spectroscopy","Every detector converts the energy a radiation deposits into a measurable electrical signal. Gas counters read the ionization directly, in three operating regions set by the applied voltage; scintillators convert the energy to light read out by a photomultiplier; semiconductor detectors collect electron-hole pairs and give the best energy resolution because so many carriers are made per event. The resolution is governed by the number of independent charge carriers, and the pulse-height spectrum of a gamma line shows a full-energy photopeak, a Compton continuum with its edge, and escape peaks.\n",{"path":20086,"title":20087,"module":20075,"summary":20088},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology","Dosimetry, Radiation Biology, and Protection","Absorbed dose is the energy deposited per unit mass, measured in gray. Equal absorbed doses do unequal biological damage because densely ionizing radiation deposits its energy along short tracks: weighting the dose by a radiation factor gives the equivalent dose, and weighting by tissue sensitivity gives the effective dose, both in sieverts. Deterministic effects have a threshold and a severity that grows with dose; stochastic effects are assumed to follow a linear-no-threshold probability. Natural background dominates the dose to the population, and protection rests on time, distance, and shielding.\n",{"path":20090,"title":20091,"module":20075,"summary":20092},"\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine","Applications — Dating, Analysis, and Nuclear Medicine","Charged particles lose energy continuously and stop at a well-defined range with a Bragg peak, while gamma rays are attenuated exponentially. These interactions define radiation detectors and dosimetry (gray and sievert) and drive the applications: neutron activation analysis, magnetic resonance imaging, PET, and radiometric dating with carbon-14 and long-lived rock clocks.\n",{"path":20094,"title":20095,"module":6,"summary":6},"\u002Fnuclear-physics","Nuclear Physics",{"path":20097,"title":20098,"module":16062,"summary":20099},"\u002Fnatural-language-processing\u002Ffoundations\u002Fwhat-is-nlp","What Is Natural Language Processing?","Natural language processing is the computational treatment of human language: reading it, representing it, and generating it. We set up why the problem is hard — ambiguity at every level, from sound to intent — trace the field from ELIZA's pattern-matching through statistical methods to today's neural models, lay out the linguistic levels and task families the course covers, and fix the vocabulary of tokens, types, and corpora the rest of the notes rely on.\n",{"path":20101,"title":20102,"module":16062,"summary":20103},"\u002Fnatural-language-processing\u002Ffoundations\u002Fregex-and-text-normalization","Regular Expressions and Text Normalization","Before any model touches text, the text has to be found and cleaned. Regular expressions give an algebra for describing string patterns; tokenization, case folding, and stemming turn raw characters into the units a model counts; and byte-pair encoding builds a subword vocabulary that spells out any word. Measuring how far apart two strings are — minimum edit distance — is the next lesson.\n",{"path":20105,"title":20106,"module":16062,"summary":20107},"\u002Fnatural-language-processing\u002Ffoundations\u002Fminimum-edit-distance","Minimum Edit Distance","Much of language processing needs to measure how similar two strings are — a speller ranking corrections, a diff tool, a coreference resolver. Minimum edit distance counts the insertions, deletions, and substitutions that turn one string into another, computed by a dynamic-programming table. We fill the table for intention to execution, backtrace to recover the alignment, and see how the same machinery generalizes to weighted edits, Viterbi, and biological sequence alignment.\n",{"path":20109,"title":20110,"module":16062,"summary":20111},"\u002Fnatural-language-processing\u002Ffoundations\u002Fn-gram-language-models","N-Gram Language Models","A language model assigns a probability to a sequence of words and, equivalently, predicts the next word from its history. The n-gram model makes this tractable by truncating the history to the last few words, estimates the resulting conditional probabilities by counting, and is scored by perplexity. We build the model from the chain rule, work a bigram example on a small corpus, and read perplexity as a branching factor. The next lesson covers the zero counts that break this model and the smoothing that repairs them.\n",{"path":20113,"title":20114,"module":16062,"summary":20115},"\u002Fnatural-language-processing\u002Ffoundations\u002Fsmoothing-and-backoff","Smoothing and Backoff","Every finite corpus is missing good word sequences it simply never saw, so a raw n-gram model assigns them probability zero and breaks. Smoothing repairs the zeros: add-one and add-k shave mass off seen events, backoff and interpolation fall back on shorter contexts, and Kneser-Ney — worked here by hand — replaces raw frequency with how many contexts a word completes. We close on web-scale stupid backoff and the neural models that dissolve the zero problem rather than patch it.\n",{"path":20117,"title":20118,"module":20119,"summary":20120},"\u002Fnatural-language-processing\u002Fclassification\u002Fnaive-bayes-and-sentiment","Naive Bayes and Sentiment Classification","Text Classification","Text classification assigns a category to a document — positive or negative, spam or not, one topic among many. Naive Bayes is a generative solution: apply Bayes' rule, assume the words are conditionally independent given the class, and the winning class is the one maximizing the product of a prior and per-word likelihoods. We train it by counting with add-one smoothing, work a full sentiment example by hand, sharpen it for sentiment (binary counts, negation, lexicons), and place it among the transformer classifiers that came after.\n",{"path":20122,"title":20123,"module":20119,"summary":20124},"\u002Fnatural-language-processing\u002Fclassification\u002Fevaluating-classifiers","Evaluating Classifiers","A trained classifier is only useful once we can measure how good it is. We build the confusion matrix, see why accuracy misleads on unbalanced data, and define precision, recall, and the F-measure that balances them. Multi-class tasks need macro- versus micro-averaging; reliable estimates need cross-validation. We close on statistical significance — the paired bootstrap test for whether one system's lead over another is significant.\n",{"path":20126,"title":20127,"module":20119,"summary":20128},"\u002Fnatural-language-processing\u002Fclassification\u002Flogistic-regression","Logistic Regression","Logistic regression is the discriminative counterpart to naive Bayes: instead of modelling how a document is generated, it learns weights that directly separate the classes. We build it from the sigmoid, derive the cross-entropy loss from maximum likelihood, learn the weights by stochastic gradient descent, regularize to curb overfitting, and generalize to many classes with the softmax. The two-class model is already a one-neuron network, so this is the bridge to neural language models.\n",{"path":20130,"title":20131,"module":20119,"summary":20132},"\u002Fnatural-language-processing\u002Fclassification\u002Fsentiment-and-affect-lexicons","Sentiment and Affect Lexicons","A sentiment lexicon is a list of words annotated with the affective meaning they carry — positive or negative, or scores along valence, arousal, and dominance. We fix what \"emotion\" means (basic-emotion versus dimensional models), survey the standard lexicons, and then build lexicons three ways: by human labeling with best-worst scaling, by semi-supervised induction from seed words over an embedding space, and by supervised learning from starred reviews. We close on connotation frames, which record the sentiment a verb implies about each of its arguments.\n",{"path":20134,"title":20135,"module":20136,"summary":20137},"\u002Fnatural-language-processing\u002Fsemantics\u002Fvector-semantics-and-embeddings","Vector Semantics and Embeddings","Semantics","Vector semantics represents a word's meaning as a point in space, derived from the company the word keeps. This first part builds the count-based side: the distributional hypothesis, co-occurrence matrices in their term-document and word-word forms, cosine as the similarity measure, and the two weightings — tf-idf and PPMI — that fix what raw counts get wrong. The result is a sparse, interpretable vector for every word, and the setup for the dense embeddings of the next lesson.\n",{"path":20139,"title":20140,"module":20136,"summary":20141},"\u002Fnatural-language-processing\u002Fsemantics\u002Fstatic-word-embeddings","Static Word Embeddings: word2vec and After","Count-based vectors are long and sparse; embeddings are the short, dense alternative. This lesson builds them with word2vec's skip-gram and negative sampling — a classifier whose learned weights are the vectors — derives its gradient, and works one update by hand. It then reads relations off the analogy parallelogram, surveys the papers that framed the static-embedding era (word2vec, GloVe, the SGNS-as-PPMI equivalence, fastText, ELMo), and closes on the biases embeddings inherit and the single-vector-per-word ceiling that contextual models break.\n",{"path":20143,"title":20144,"module":20136,"summary":20145},"\u002Fnatural-language-processing\u002Fsemantics\u002Fneural-language-models","Neural Networks and Neural Language Models","A neural network is a stack of units, each a weighted sum passed through a non-linearity — a single unit on its own is logistic regression. We build the network up from that unit: the activation functions that give it power, the XOR problem that forces a hidden layer, the feedforward forward pass in matrix form, and the Bengio-style feedforward neural language model that concatenates word embeddings and predicts the next word with a softmax. Training is cross-entropy minimized by gradient descent, with backpropagation supplying the gradient. Embeddings let the model share statistical strength across similar words, avoiding the sparsity that limits n-gram models.\n",{"path":20147,"title":20148,"module":16528,"summary":20149},"\u002Fnatural-language-processing\u002Fsequences\u002Fsequence-labeling","Sequence Labeling: POS and NER","Sequence labeling assigns one tag to every token in a sentence. This first part sets up the task through its two canonical cases — part-of-speech tagging over the Penn Treebank tagset, and named-entity recognition reframed as token labeling with the BIO scheme — then builds the hidden Markov model, the classic probabilistic tagger. The HMM tags by Bayesian inference: transition and emission probabilities under two Markov assumptions, reducing tagging to an argmax over tag sequences. That argmax is exponential to enumerate, which sets up the Viterbi decoder, the CRF, and neural taggers of the next lesson.\n",{"path":20151,"title":20152,"module":16528,"summary":20153},"\u002Fnatural-language-processing\u002Fsequences\u002Fcrfs-and-neural-taggers","Viterbi Decoding, CRFs, and Neural Taggers","The HMM reduced tagging to an argmax over exponentially many tag sequences. This lesson builds the decoder that makes it tractable — the Viterbi dynamic program, worked through a full numeric trace on real WSJ probabilities — then keeps that same decoder while replacing the HMM's rigid tables. The linear-chain conditional random field is a discriminative log-linear model whose global feature functions can inspect any part of the input, which is why CRFs win for NER. Finally it traces the shift to neural taggers (biLSTM-CRF, character-aware NER, ELMo), where hand-built features become learned representations while the Viterbi decoder carries over unchanged.\n",{"path":20155,"title":20156,"module":16528,"summary":20157},"\u002Fnatural-language-processing\u002Fsequences\u002Frnns-and-lstms","RNNs and LSTMs","A feedforward neural language model sees a fixed window of words and can look no further back. The recurrent neural network removes that limit: it carries a hidden state across time, so each word is read in the context of everything before it. We build the RNN from its one recurrent equation, use it as a language model, train it by backpropagation through time, and diagnose the vanishing-gradient problem that makes plain RNNs forget. The LSTM fixes the forgetting with a cell state and three gates, and the encoder-decoder stacks two RNNs into a sequence-to-sequence model — and its single-vector bottleneck is the problem attention was invented to remove.\n",{"path":20159,"title":20160,"module":17010,"summary":20161},"\u002Fnatural-language-processing\u002Ftransformers\u002Ftransformers-and-attention","Transformers and Self-Attention","Recurrence forced language models to read one word at a time and to squeeze every dependency through a chain of hidden states. Self-attention removes the recurrence: at every layer each position compares itself to every other and reads a weighted mixture of them, in a single parallel step. This first part builds the attention operation from the ground up — the soft lookup, queries and keys and values, the scaled dot-product, the numeric trace, the matrix form, and the causal mask — and sets up the full transformer architecture that follows.\n",{"path":20163,"title":5,"module":17010,"summary":20164},"\u002Fnatural-language-processing\u002Ftransformers\u002Fthe-transformer-architecture","This part takes the scaled dot-product attention of the previous lesson and assembles the full transformer architecture around it: multi-head attention so several relations can be read at once, the transformer block of residual connections and layer norm that makes deep stacks trainable, positional embeddings that restore word order, the decoder-only language model, and the encoder, decoder, and encoder-decoder shapes — closing with the 2017 paper and the pre-norm, FlashAttention, and RoPE refinements that scaled it up.\n",{"path":20166,"title":18822,"module":17010,"summary":20167},"\u002Fnatural-language-processing\u002Ftransformers\u002Flarge-language-models","A large language model is a decoder-only transformer trained on one objective — predict the next token. This first part assembles the inference side: the language-modeling head that turns a hidden state into a distribution over the vocabulary, autoregressive generation, and the decoding strategies — greedy, beam, and sampling with temperature, top-k, and nucleus — that read text back out of that distribution. Training the distribution at web scale comes next.\n",{"path":20169,"title":20170,"module":17010,"summary":20171},"\u002Fnatural-language-processing\u002Ftransformers\u002Fllm-pretraining-and-scaling","Large Language Models: Pretraining and Scaling","A language model's next-token distribution is only as good as the parameters behind it. This part is where those parameters come from: self-supervised pretraining on web-scale text with teacher forcing and cross-entropy, the scaling laws that make test loss a predictable power law in parameters, data, and compute, the KV cache that keeps long-context inference affordable, and how a finished model is evaluated by perplexity and benchmarks — closing with the Kaplan, Chinchilla, GPT-3, and emergence papers behind the scaling story.\n",{"path":20173,"title":20174,"module":17010,"summary":20175},"\u002Fnatural-language-processing\u002Ftransformers\u002Ffine-tuning-and-prompting","Fine-Tuning and Prompting","A pretrained transformer is a general-purpose knowledge source; a task is what you do with it. There are two ways to adapt one, and this first part covers the one that updates the weights: fine-tuning. A bidirectional encoder like BERT is pretrained by masked language modeling, then a small task head is bolted on and the whole thing is trained on labelled data for classification, sequence labeling, or span-based question answering — with parameter-efficient variants (adapters, LoRA) that touch only a sliver of the weights. Prompting, the family that leaves the weights frozen, comes next.\n",{"path":20177,"title":20178,"module":17010,"summary":20179},"\u002Fnatural-language-processing\u002Ftransformers\u002Fprompting-and-alignment","Prompting and Alignment","Fine-tuning adapts a model by changing its weights. The second family of adaptation changes nothing: a large frozen model performs a task from an instruction and a few examples placed in its context. This part covers prompting and in-context learning, chain-of-thought that elicits reasoning, and the two training stages — instruction tuning and RLHF — that turn a fluent base predictor into an aligned assistant, closing with the BERT, LoRA, chain-of-thought, InstructGPT, and retrieval-augmentation papers behind the modern adaptation pipeline.\n",{"path":20181,"title":20182,"module":20183,"summary":20184},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-parsing","Constituency Parsing","Linguistic Structure","A constituency parse groups a sentence into nested phrases described by a context-free grammar. We build the CFG formalism, read the phrase structure of English off a treebank, confront the structural ambiguity that makes parsing hard, convert to Chomsky normal form, and then solve it with CKY — the dynamic-programming chart that fills a triangular table bottom-up. Probabilistic and neural span parsers, evaluation, and shallow parsing follow in the companion lesson.\n",{"path":20186,"title":20187,"module":20183,"summary":20188},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcky-scoring-and-evaluation","CKY Scoring, Evaluation, and Shallow Parsing","The CKY chart returns every parse but does not say which is correct. Disambiguation needs a score on trees. This lesson attaches probabilities to a grammar (the PCFG and lexicalization), replaces the grammar with a neural span scorer over a pretrained encoder, states the self-attentive results that made it the state of the art, evaluates parsers against a treebank with PARSEVAL, and closes with chunking and shallow parsing for tasks that need only the flat phrases.\n",{"path":20190,"title":20191,"module":20183,"summary":20192},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdependency-parsing","Dependency Parsing","A dependency parse throws away phrases and keeps only directed, labeled arcs from heads to their dependents, so the subject and object of a verb hang off the verb directly. We fix the formalism (rooted trees, typed Universal-Dependency relations, projectivity), then build the first parser family: transition-based arc-standard and arc-eager parsing, a greedy stack-and-buffer machine trained from an oracle. Graph-based and neural dependency parsing follow in the companion lesson.\n",{"path":20194,"title":20195,"module":20183,"summary":20196},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fgraph-based-and-neural-dependency-parsing","Graph-Based and Neural Dependency Parsing","Greedy transition parsing commits locally; the graph-based family scores whole trees instead. This lesson scores every candidate head-dependent edge and extracts the maximum spanning tree with Chu-Liu\u002FEdmonds, develops the biaffine neural scorer that made graph-based parsing the accuracy leader, evaluates parsers with the unlabeled and labeled attachment scores (UAS and LAS), and closes on where the two parser families sit and what they feed downstream.\n",{"path":20198,"title":20199,"module":20183,"summary":20200},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fword-senses-and-wsd","Word Senses and Disambiguation","A word is not an atom of meaning: \"bass\" names a fish, a voice, and an instrument, and one static embedding blurs them into a single point. This lesson pulls those senses apart. We define polysemy and the relations that organize senses — synonymy, antonymy, hyponymy, meronymy — build them into WordNet's synset graph, measure similarity along that graph, and then solve the core of word sense disambiguation: the most-frequent-sense baseline, the Lesk gloss-overlap algorithm, feature-based classifiers, and the nearest-neighbor method over BERT embeddings. WSD variants, embeddings, and evaluation follow in the companion lesson.\n",{"path":20202,"title":20203,"module":20183,"summary":20204},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fwsd-in-practice-and-induction","WSD in Practice and Word Sense Induction","Beyond core word sense disambiguation lie the variants and loose ends: the sense-inventory-free Word-in-Context task, retrofitting static embeddings to a thesaurus, discovering senses without a fixed inventory (word sense induction), the gloss-aware and bi-encoder neural systems that hold the state of the art, and how WSD and its cousins are evaluated. Together they connect one-vector-per-word embeddings to sense-aware contextual representations.\n",{"path":20206,"title":20207,"module":20183,"summary":20208},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-roles-and-information-extraction","Semantic Roles and Information Extraction","Semantic roles answer \"who did what to whom\" for a single event, abstracting away the syntax that expresses it. We show why syntax alone is not enough, generalize over diathesis alternations with thematic roles, number a predicate's arguments with PropBank and group predicates into frames with FrameNet, tag each argument automatically with semantic role labeling, and factor predicates into primitives. Information extraction scales the idea to a corpus in the companion lesson.\n",{"path":20210,"title":20211,"module":20183,"summary":20212},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Frelations-events-and-templates","Relations, Events, and Templates","Semantic roles answer \"who did what\" for one predicate; information extraction scales the idea to a whole corpus. This lesson turns unstructured text into structured data: relation extraction pulls entity-relation-entity triples out of sentences by patterns, supervision, and distant supervision; event and temporal extraction place those facts on a timeline; and template filling and knowledge-base population assemble them into a database a downstream system can query.\n",{"path":20214,"title":20215,"module":20183,"summary":20216},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoreference-and-discourse","Coreference and Discourse","A text is more than a bag of sentences: entities recur under different names. Coreference resolution links every mention to the discourse entity it evokes — the linguistic background of pronouns, definite NPs, and names; mention detection; the mention-pair, mention-ranking, and entity-based architectures; a neural end-to-end span model that scores candidate antecedents; features, evaluation by the CoNLL F1, gender bias, and the neural coreference lineage. Discourse coherence follows in the companion lesson.\n",{"path":20218,"title":20219,"module":20183,"summary":20220},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcoherence-and-discourse-structure","Coherence and Discourse Structure","Coherence is what makes a run of sentences a discourse rather than an arbitrary collection. This lesson develops coherence relations and Rhetorical Structure Theory trees, discourse-structure parsing, Centering and the entity grid for entity-based coherence, and representation-learning models of local coherence, measured in part over the coreference chains recovered in the companion lesson.\n",{"path":20222,"title":20223,"module":20183,"summary":20224},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Flogical-semantics","Logical Representations of Meaning","A meaning representation turns a sentence into a formal structure a machine can check against a world and reason over. We set the desiderata a good representation must meet, ground truth in a model, build up first-order logic for sentences with its connectives, quantifiers, and inference, and reify events with the neo-Davidsonian event variable to escape fixed predicate arity. The compositional lambda calculus, quantifier scope, and description logics follow in the companion lesson.\n",{"path":20226,"title":20227,"module":20183,"summary":20228},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fcompositional-semantics-and-description-logics","Compositional Semantics and Description Logics","How do you compute a logical form from a sentence automatically? This lesson builds the compositional machinery: the lambda calculus that assembles a formula from a parse tree one beta-reduction at a time, the quantifier-scope ambiguity a single syntax tree leaves open, and the decidable description logics — TBox, ABox, subsumption, role restrictions — behind the Web Ontology Language, closing with how the map from string to logical form can be learned.\n",{"path":20230,"title":20231,"module":20183,"summary":20232},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fsemantic-parsing","Semantic Parsing","Turning a sentence into a structured, executable meaning, the grammar-based way. We take the logical forms defined earlier and build them compositionally: a rule-based parser that walks a syntax tree applying lambda terms, then Combinatory Categorial Grammar (CCG), which fuses syntax and semantics so one lexicalized derivation produces both — including supertagging and A* parsing. Learned and neural semantic parsers follow in the companion lesson.\n",{"path":20234,"title":20235,"module":20183,"summary":20236},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fneural-semantic-parsing","Learned and Neural Semantic Parsing","Hand-writing a lexicon of lambda terms does not scale, so this lesson learns the parser instead. We cover the two supervision regimes (from logical forms and from denotations), Abstract Meaning Representation as a rooted concept graph, neural sequence-to-sequence parsing with constrained decoding and copy mechanisms, executable text-to-SQL and knowledge-based question answering, the practical systems that made learned parsers accurate, and how the task is evaluated.\n",{"path":20238,"title":20239,"module":20183,"summary":20240},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Finformation-extraction","Information Extraction","Information extraction turns free text into a database, and the first step is relation extraction: pulling entity-relation-entity triples out of sentences. We cover all five families — hand-built patterns, supervised classifiers, semi-supervised bootstrapping, distant supervision, and unsupervised Open IE — with worked bootstrapping and distant-supervision traces, then the neural and LLM systems that extended them. Times, events, and templates follow in the companion lesson.\n",{"path":20242,"title":20243,"module":20183,"summary":20244},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftimes-events-and-templates","Extracting Times, Events, and Templates","Once relation extraction has produced typed triples, the information-extraction pipeline still has to place facts in time and assemble them into records. This lesson detects and normalizes temporal expressions to ISO 8601 values, detects events and orders them on a timeline with the 13 Allen relations, and fills slot-and-filler templates — flat and hierarchical — for stereotyped situations, closing the loop from text to a queryable database.\n",{"path":20246,"title":20247,"module":20183,"summary":20248},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fdiscourse-coherence","Discourse Coherence","A text is more than a set of sentences. What binds a run of sentences into a discourse is coherence, and one of its sources is structured relations between clauses. This lesson develops relational coherence — RST and the PDTB models of coherence relations — and discourse-structure parsing: EDU segmentation and shift-reduce RST parsing, then PDTB relation classification. Entity-based and global coherence follow in the companion lesson.\n",{"path":20250,"title":20251,"module":20183,"summary":20252},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fentity-based-and-global-coherence","Entity-Based and Global Coherence","A text coheres not only through relations between clauses but by staying about the same entities and the same topic, and by obeying the macro-structure of its genre. This lesson develops Centering Theory and the entity grid for entity-based coherence, representation-learning models of local coherence, and global coherence — topic segmentation, narrative and argumentation structure, and scientific discourse — then the neural models that learn each.\n",{"path":20254,"title":20255,"module":20183,"summary":20256},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Fconstituency-grammars","Constituency Grammars","A constituency grammar is the declarative theory of sentence structure that a parser operates on. We build the context-free grammar formalism from its four parts, show how derivations become parse trees, and work through the phrase structure of English — noun phrases, verb phrases and their subcategorization frames, agreement, coordination, and long-distance dependencies. The treebank, normal-form, and lexicalized views follow in the companion lesson.\n",{"path":20258,"title":20259,"module":20183,"summary":20260},"\u002Fnatural-language-processing\u002Flinguistic-structure\u002Ftreebanks-and-lexicalized-grammars","Treebanks and Lexicalized Grammars","Where does a grammar come from, and how is it prepared for a parser? We read a context-free grammar off the Penn Treebank, normalize it to Chomsky Normal Form for the CKY chart, then invert the phrase-structure emphasis with lexicalized grammars — Combinatory Categorial Grammar and its slash categories — and close with the grammar's fate in the neural era: span scoring, self-attention, and grammar induction.\n",{"path":20262,"title":20263,"module":18810,"summary":20264},"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation","Machine Translation","Machine translation is the task that built the modern toolkit: the encoder-decoder was invented for it, attention was invented to fix its fixed-context bottleneck, and both were later folded into the general transformer. We work through why translation is hard (word order, morphology, lexical and structural divergences), the sequence-to-sequence model and its attention mechanism, transformer-based NMT with cross-attention, subword tokenization with a shared vocabulary, beam-search decoding, and evaluation by BLEU and its successors chrF, BERTScore, and COMET — closing on multilingual and low-resource translation and backtranslation.\n",{"path":20266,"title":20267,"module":18810,"summary":20268},"\u002Fnatural-language-processing\u002Fapplications\u002Fmachine-translation-decoding-and-evaluation","Machine Translation: Decoding, Evaluation, and Scale","Having built the transformer translation model, we now decode from it and measure the output. Beam search turns the decoder's per-step distributions into a single output string; length normalization keeps it from favoring short translations. We then score translations automatically — BLEU with its n-gram precision, clipping, and brevity penalty, worked through by hand, then its successors chrF, BERTScore, and COMET — and close on the parts of MT that scale beyond one language pair: multilingual and low-resource translation, backtranslation, gender bias, and the lineage from the Transformer to massively multilingual models like NLLB-200.\n",{"path":20270,"title":20271,"module":18810,"summary":20272},"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering","Question Answering","A question-answering system takes a natural-language question and returns an answer, not a ranked list of documents. Almost every modern system is built on one pattern: retrieve then read. We start with the information-retrieval machinery that finds candidate text — tf-idf and BM25 term weighting, a worked ranking example, the inverted index, and dense embedding retrieval — then build the retriever-reader pipeline that extracts an answer span with BERT and trace a full retrieve-and-read example end to end.\n",{"path":20274,"title":20275,"module":18810,"summary":20276},"\u002Fnatural-language-processing\u002Fapplications\u002Fquestion-answering-knowledge-and-llms","Question Answering: Knowledge Bases and Language Models","The retrieve-and-read pipeline extracts an answer span from prose, but not all knowledge lives in prose. This part covers the rest of the QA stack: entity linking (Wikification) that grounds a question's entities to a knowledge base, knowledge-based QA by semantic parsing a question into an executable query, and the modern default — closed-book QA and retrieval-augmented generation with a large language model — closing on the DPR\u002FRAG\u002Ffusion-in-decoder lineage and how factoid answers are scored by exact match and F1.\n",{"path":20278,"title":20279,"module":18810,"summary":20280},"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-and-chatbots","Dialogue and Chatbots","Conversation is the most natural interface to a machine and one of the hardest to build. We set up what makes human dialogue work — turns, speech acts, grounding, and the local structure of adjacency pairs — then trace the two traditions that answer it: chatbots built to chat (ELIZA's pattern-matching, corpus retrieval, and seq2seq generation with its blandness problem) and task-oriented systems built to get something done (the GUS frame-and-slot architecture and the modern NLU \u002F state-tracker \u002F policy \u002F NLG pipeline that accumulates a frame across turns).\n",{"path":20282,"title":20283,"module":18810,"summary":20284},"\u002Fnatural-language-processing\u002Fapplications\u002Fdialogue-systems-and-assistants","Dialogue Systems: LLM Assistants, Evaluation, and Design","Two dialogue traditions — chatbots built to chat and task-oriented frame systems built to get something done — met in the aligned LLM assistant. Instruction tuning plus RLHF fold chit-chat and task dialogue into one model; the LaMDA \u002F InstructGPT \u002F ChatGPT lineage fills in how. The lesson then turns to evaluation (human ratings and acute-eval for chatbots, task success and slot error rate for task systems), user-centered design with Wizard-of-Oz prototyping, and the ethical stakes of building agents people talk to.\n",{"path":20286,"title":20287,"module":18810,"summary":20288},"\u002Fnatural-language-processing\u002Fapplications\u002Ftext-summarization","Text Summarization","Summarization compresses a document to its essential meaning, by either selecting sentences to keep (extractive) or writing new ones (abstractive). This part fixes the task and its flavors — single vs. multi-document, generic vs. query-focused, extractive vs. abstractive — then works through extractive summarization in full: scoring by position and centrality, the TextRank\u002FLexRank graph algorithm run as PageRank over a sentence-similarity graph with a worked iteration, and supervised sentence selection.\n",{"path":20290,"title":20291,"module":18810,"summary":20292},"\u002Fnatural-language-processing\u002Fapplications\u002Fabstractive-summarization-and-evaluation","Abstractive Summarization and Evaluation","Extractive methods can only reuse the source's own sentences; to compress within a sentence or paraphrase, a summarizer has to generate. This part covers abstractive summarization: the sequence-to-sequence approach, the pointer-generator's copy switch and coverage mechanism, pretrained summarizers (BART, PEGASUS) and zero-shot LLM prompting, the long-document and factuality problems, and ROUGE evaluation with a worked example and its limits — closing on the abstractive lineage from See 2017 through faithfulness metrics.\n",{"path":20294,"title":20295,"module":20296,"summary":20297},"\u002Fnatural-language-processing\u002Fspeech\u002Fphonetics","Phonetics","Speech","Before a recognizer can read speech it has to know what speech is. This first part covers the linguistic substrate: phones and their transcription in the IPA and ARPAbet; articulatory phonetics — how the vocal tract shapes airflow into consonants and vowels; and prosody — stress, tune, and the F0 contour. The acoustic side — the waveform, its spectrum, formants, and the spectrogram — is the second part.\n",{"path":20299,"title":20300,"module":20296,"summary":20301},"\u002Fnatural-language-processing\u002Fspeech\u002Facoustic-phonetics","Acoustic Phonetics","Articulation is the cause; the acoustic signal is the effect, and the effect is all a microphone ever gets. This part follows the sound out of the mouth: waves, sampling and the Nyquist limit, F0 and the pitch track, the mel scale, the spectrum and Fourier analysis, the source-filter model that explains why each vowel carries its own formants, and the spectrogram the log-mel front end of every ASR system sits directly on top of — closing with neural TTS, wav2vec, HuBERT, and Whisper, where phonetics went in neural speech.\n",{"path":20303,"title":20304,"module":20296,"summary":20305},"\u002Fnatural-language-processing\u002Fspeech\u002Fautomatic-speech-recognition","Automatic Speech Recognition","Speech recognition maps an acoustic waveform to a string of words, and once the waveform is turned into a sequence of log-mel spectrogram frames the problem is the same sequence-to-sequence transduction the rest of the course already solved. This first part builds the feature front end (framing, the DFT, the mel filterbank, the log), then the modern architectures: the attention-based encoder-decoder, the CTC alignment trick that collapses repeated and blank frames, and RNN-T for streaming. Training-data advances, evaluation, TTS, and the other speech tasks come next.\n",{"path":20307,"title":20308,"module":20296,"summary":20309},"\u002Fnatural-language-processing\u002Fspeech\u002Fasr-evaluation-and-applications","ASR Evaluation and Speech Applications","A recognizer turns a waveform into text; this part scores that text and puts the same machinery to other uses. It opens with the self-supervised and weakly- supervised systems (wav2vec 2.0, HuBERT, Whisper) that made ASR error rates fall. Word error rate reuses the edit distance from the first module, run over words. Text-to-speech runs the whole pipeline in reverse — text to mel spectrogram to waveform. And a family of smaller tasks — wake-word detection, speaker recognition and diarization, language identification — reuse the same log-mel front end without the decoder.\n",{"path":20311,"title":20312,"module":6,"summary":6},"\u002Fnatural-language-processing","Natural Language Processing",{"path":20314,"title":20315,"module":16062,"summary":20316},"\u002Fparticle-physics\u002Ffoundations\u002Fhistorical-overview-particle-zoo","From the Electron to the Particle Zoo","A timeline of the subject, from J. J. Thomson's electron in 1897 to the Higgs boson in 2012. The electron, photon, nucleus, proton, and neutron gave a tidy picture that Yukawa's meson prediction and the muon–pion confusion complicated; strange particles in cosmic rays and the accelerator-era flood of hadrons then produced a \"particle zoo\" that only the quark model organized.\n",{"path":20318,"title":20319,"module":16062,"summary":20320},"\u002Fparticle-physics\u002Ffoundations\u002Fparticle-physics-basic-concepts","Basic Concepts and Particle Classification","Every particle has an antiparticle of equal mass and opposite charge, a consequence of the Dirac equation confirmed by the positron. Feynman diagrams track interactions in spacetime; the material particles sort into leptons and the composite hadrons built from quarks, with baryons carrying three quarks and mesons a quark-antiquark pair.\n",{"path":20322,"title":20323,"module":16062,"summary":20324},"\u002Fparticle-physics\u002Ffoundations\u002Ffundamental-interactions-force-carriers","Fundamental Interactions and Force Carriers","Four interactions account for every force in nature: strong, electromagnetic, weak, and gravitational, in decreasing strength. Each is carried by a boson — the gluon, photon, W and Z, and the graviton — with a range fixed by the carrier's mass through the Yukawa relation, and a coupling constant that itself varies with distance.\n",{"path":20326,"title":20327,"module":20328,"summary":20329},"\u002Fparticle-physics\u002Funits-kinematics\u002Fnatural-units-and-scales","Natural Units and Scales","Units and Kinematics","Setting $\\hbar = c = 1$ collapses mass, momentum, and energy into a single unit, the GeV, and turns lengths and times into inverse energies through the conversion $\\hbar c = 197.3$ MeV·fm. This lesson fixes the natural-unit conventions used for the rest of the course, converts cross sections between barns and GeV$^{-2}$, and shows how to restore factors of $\\hbar$ and $c$ by dimensional analysis.\n",{"path":20331,"title":20332,"module":20328,"summary":20333},"\u002Fparticle-physics\u002Funits-kinematics\u002Ffour-vectors-invariant-mass","Four-Vectors and Invariant Mass","The energy and momentum of a particle form a four-vector whose square is the frame-independent quantity $p^2 = m^2$. This lesson develops the metric and four-vector products, the invariant mass of a multiparticle system, the center-of-momentum and laboratory frames, and the description of collinear boosts by rapidity, whose additivity replaces the awkward velocity-addition law.\n",{"path":20335,"title":20336,"module":20328,"summary":20337},"\u002Fparticle-physics\u002Funits-kinematics\u002Fdecay-scattering-kinematics-mandelstam","Decay, Scattering, and Mandelstam Variables","Two-body decay in the rest frame fixes the daughter momenta from the three masses alone; production thresholds follow from the minimum invariant mass. This lesson works both, then introduces the Mandelstam invariants $s$, $t$, $u$ for $2\\to2$ scattering, proves the identity $s+t+u=\\sum m_i^2$, and maps the physical regions and the crossing that relates channels.\n",{"path":20339,"title":20340,"module":20328,"summary":20341},"\u002Fparticle-physics\u002Funits-kinematics\u002Fcross-sections-golden-rule","Cross Sections and the Golden Rule","The cross section measures how often a scattering happens and the decay width how fast a particle disintegrates. This lesson defines both, relates event rate to luminosity through $R=\\mathcal L\\,\\sigma$ and lifetime to width through $\\tau=\\hbar\u002F\\Gamma$, and states Fermi's golden rule with Lorentz-invariant phase space, giving the master formulas that turn an amplitude $\\mathcal M$ into a measurable rate for $1\\to2$ decay and $2\\to2$ scattering.\n",{"path":20343,"title":20344,"module":20345,"summary":20346},"\u002Fparticle-physics\u002Fsymmetries\u002Fconservation-laws-symmetries","Conservation Laws and Symmetries","Symmetries and Conservation Laws","Which decays occur is decided by conservation laws, each tied by Noether's theorem to a symmetry of physical law. Energy, charge, baryon number, and lepton number are conserved universally; strangeness, isospin, and parity hold in the strong and electromagnetic interactions but break in the weak one, whose parity and CP violation distinguish matter from antimatter.\n",{"path":20348,"title":20349,"module":20345,"summary":20350},"\u002Fparticle-physics\u002Fsymmetries\u002Fdiscrete-symmetries-cpt","Discrete Symmetries — C, P, T, and CPT","Parity reflects space, charge conjugation swaps particle for antiparticle, and time reversal runs the clock backward. Each assigns multiplicative quantum numbers that act as selection rules — intrinsic parities, the photon's C = −1, the C-parity argument fixing the pion's two-photon decay. Their product CPT is a theorem of any local relativistic field theory, forcing particle and antiparticle to share mass and lifetime.\n",{"path":20352,"title":20353,"module":20345,"summary":20354},"\u002Fparticle-physics\u002Fsymmetries\u002Fparity-violation-weak","Parity Violation and the Weak Force","The tau–theta puzzle forced a choice: two particles with identical mass but opposite parity, or one particle whose decay violates parity. Lee and Yang proposed the latter, Wu's polarized cobalt-60 confirmed it, and the violation proved maximal. The charged weak force couples only to left-handed chirality — the Goldhaber experiment showed the neutrino is left-handed — which is why the mirror image of a weak decay is something nature never produces.\n",{"path":20356,"title":20357,"module":20345,"summary":20358},"\u002Fparticle-physics\u002Fsymmetries\u002Fsu2-su3-flavor-symmetry","Isospin, SU(2), and Flavor SU(3)","The near-equal masses of the proton and neutron, and of the three pions, signal a continuous internal symmetry of the strong force: isospin, an SU(2) whose ladder operators move between the members of a multiplet. Adding strangeness enlarges it to an approximate SU(3) flavor symmetry, and the Gell-Mann–Nishijima relation Q = I3 + Y\u002F2 places every hadron on a weight diagram in the isospin–hypercharge plane — the language in which the quark model is written.\n",{"path":20360,"title":20361,"module":20362,"summary":20363},"\u002Fparticle-physics\u002Fquark-model\u002Feightfold-way-su3","The Eightfold Way and SU(3) Flavor","The Quark Model","Gell-Mann and Ne'eman's classification of the hadrons into geometric multiplets, read as representations of an approximate flavor SU(3). The fundamental triplet (u, d, s) and its antitriplet combine into the meson nonet from 3⊗3̄ = 8⊕1 and the baryon octet and decuplet from 3⊗3⊗3, and the empty corner of the decuplet forecast the Ω⁻.\n",{"path":20365,"title":20366,"module":20362,"summary":20367},"\u002Fparticle-physics\u002Fquark-model\u002Fmeson-spectroscopy","Meson Multiplets and Quantum Numbers","Mesons as quark–antiquark bound states. The spin singlet and triplet, orbital excitations, and the assignment of J^PC from the quark spins and orbital angular momentum, giving the pseudoscalar and vector nonets. The η–η' and ω–φ mixing problems, and the charmonium and bottomonium spectra read as heavy-quark positronium.\n",{"path":20369,"title":20370,"module":20362,"summary":20371},"\u002Fparticle-physics\u002Fquark-model\u002Fbaryon-spectroscopy","Baryon Multiplets, Spin, and the Color Puzzle","Baryons as three-quark states, with a wavefunction factored into space, spin, flavor, and color. The spin-3\u002F2 Δ⁺⁺ = uuu forces a totally symmetric state that the Pauli principle forbids, and the resolution is an antisymmetric color factor — the first evidence for color. The octet and decuplet spin content, and baryon magnetic moments as a quantitative test of the model.\n",{"path":20373,"title":20374,"module":20362,"summary":20375},"\u002Fparticle-physics\u002Fquark-model\u002Fcolor-confinement-exotics","Color, Confinement, and Exotic Hadrons","Color as the gauged SU(3) charge, and the requirement that every physical hadron be a color singlet — which selects q-qbar mesons and qqq baryons as the simplest states. The R-ratio of e⁺e⁻ annihilation measures three colors directly. Beyond the simplest singlets lie glueballs, tetraquarks, and pentaquarks, and the recent XYZ states, read as either compact multiquarks or loose hadronic molecules.\n",{"path":20377,"title":20378,"module":20379,"summary":20380},"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fklein-gordon-equation","The Klein-Gordon Equation","Relativistic Wave Equations","Quantizing the relativistic energy relation $E^2 = p^2 + m^2$ produces the Klein-Gordon equation for a scalar field. Its plane-wave solutions come in positive- and negative-energy branches, and the conserved density it supplies is not positive-definite — the two difficulties that first drove physicists to seek a first-order equation. The static Klein-Gordon equation with a point source gives the Yukawa potential, and the free equation gives the scalar propagator that later modules attach to exchanged lines.\n",{"path":20382,"title":20383,"module":20379,"summary":20384},"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fdirac-equation-spinors","The Dirac Equation and Spinors","Dirac demanded a wave equation first order in time to fix the Klein-Gordon density problem. Factorizing $E^2 = p^2 + m^2$ into a linear form forces the coefficients to be anticommuting matrices — the gamma matrices of the Clifford algebra — so the wavefunction becomes a four-component spinor. The plane-wave solutions split into two particle and two antiparticle states, spin appears automatically with the correct $g = 2$ magnetic moment, and the chirality projectors that the weak interaction later needs fall straight out of the fifth gamma matrix.\n",{"path":20386,"title":20387,"module":20379,"summary":20388},"\u002Fparticle-physics\u002Frelativistic-wave-equations\u002Fantiparticles-hole-theory","Antiparticles and Hole Theory","The negative-energy solutions of the Dirac equation refuse to go away, so they must mean something. Dirac read them as a filled sea of occupied negative-energy states whose holes are positive-energy antiparticles, predicting the positron before its discovery. The picture works for fermions but not bosons, and the Feynman-Stückelberg interpretation replaces it: an antiparticle is a negative-energy solution propagating backward in time, equivalent to a positive-energy antiparticle going forward. Crossing symmetry ties incoming particles to outgoing antiparticles in a single amplitude.\n",{"path":20390,"title":20391,"module":20392,"summary":20393},"\u002Fparticle-physics\u002Fqed\u002Ffeynman-rules-qed","Feynman Rules for QED","Quantum Electrodynamics","Quantum electrodynamics computes a process by summing diagrams, each a term in a power series in the coupling. Every diagram translates into an amplitude by a fixed dictionary: spinors and polarization vectors for external lines, propagators for internal lines, and the vertex factor $ie\\gamma^\\mu$ for each photon-fermion junction. Squaring the amplitude and feeding it to Fermi's golden rule produces a cross section or decay rate, with each extra vertex costing one power of $\\alpha$.\n",{"path":20395,"title":20396,"module":20392,"summary":20397},"\u002Fparticle-physics\u002Fqed\u002Fqed-tree-processes","Tree-Level QED Processes","The Feynman rules become numbers on the reference reactions of QED. Muon pair production $e^+e^-\\to\\mu^+\\mu^-$ sets the scale with its $1+\\cos^2\\theta$ distribution and $4\\pi\\alpha^2\u002F3s$ total cross section, and its ratio to hadron production counts colors. Compton scattering gives the Klein-Nishina formula and the Thomson limit; Bhabha scattering shows $s$- and $t$-channel interference. Casimir's trick turns every spin-averaged square into a trace of gamma matrices.\n",{"path":20399,"title":20400,"module":20392,"summary":20401},"\u002Fparticle-physics\u002Fqed\u002Frenormalization-running-coupling","Renormalization and the Running Coupling","Beyond tree level, QED loops diverge. The three primitive one-loop diagrams — vacuum polarization, electron self-energy, and vertex correction — carry ultraviolet divergences that regularization exposes as logarithms of a cutoff. Renormalization absorbs them into the measured mass, charge, and field normalization, leaving finite predictions. The surviving physical content is that the coupling runs: vacuum polarization screens charge, so $\\alpha$ grows from $1\u002F137$ at low energy to about $1\u002F128$ at the $Z$ mass.\n",{"path":20403,"title":20404,"module":20392,"summary":20405},"\u002Fparticle-physics\u002Fqed\u002Felectron-g-2","The Anomalous Magnetic Moment","The Dirac equation predicts $g=2$; loops shift it. Schwinger's one-loop vertex correction gives the anomaly $a=(g-2)\u002F2=\\alpha\u002F2\\pi$, and the QED series continues to five loops. The electron $a_e$ agrees with theory to better than a part in a billion, the most precise confrontation of theory and experiment in physics. The muon $a_\\mu$, heavier and so more sensitive to virtual heavy states, is dominated by hadronic uncertainty and sits at the center of a long-running comparison with the Standard Model prediction.\n",{"path":20407,"title":20408,"module":20409,"summary":20410},"\u002Fparticle-physics\u002Fweak-interaction\u002Fva-structure-weak","The V–A Charged Weak Current","The Weak Interaction","Fermi modelled beta decay as a four-fermion contact interaction, but a coupling with dimensions of inverse mass squared makes cross sections grow without bound and the theory fails near 300 GeV. The cure is a heavy mediator: the $W$ boson, whose propagator collapses to Fermi's contact term at low energy and fixes $G_F\u002F\\sqrt2 = g^2\u002F8M_W^2$. Parity violation dictates the current's form — vector minus axial-vector, coupling only to left-chiral fields — and universality of the coupling ties muon decay, beta decay, and pion decay to one constant. Pion decay's helicity suppression of the electron channel is the sharpest test.\n",{"path":20412,"title":20413,"module":20409,"summary":20414},"\u002Fparticle-physics\u002Fweak-interaction\u002Fw-z-bosons-decays","The W and Z Bosons","The contact theory hides a massive mediator. The charged $W^\\pm$ carries the current that changes flavour; the neutral $Z^0$ carries a current that does not. Both were found at CERN's proton–antiproton collider in 1983 at the masses the electroweak theory demanded. Their decay widths partition into leptonic and hadronic channels, and the $Z$ carries a decisive extra: an invisible width from decays to neutrinos that counts the number of light generations at exactly three. Beta decay and muon decay are re-read at the parton level as $W$ exchange.\n",{"path":20416,"title":20417,"module":20409,"summary":20418},"\u002Fparticle-physics\u002Fweak-interaction\u002Fckm-matrix","Quark Mixing and the CKM Matrix","The quark eigenstates the weak force acts on are not the mass eigenstates. Cabibbo captured this with one rotation angle; the GIM mechanism added a fourth quark to cancel dangerous flavour-changing neutral currents and predicted charm before its discovery. Three generations promote the rotation to the unitary Cabibbo–Kobayashi–Maskawa matrix — three angles and one irreducible complex phase, the sole source of Standard-Model CP violation. The Wolfenstein parametrization exposes its steep hierarchy, and unitarity closes into a triangle whose area measures the phase.\n",{"path":20420,"title":20421,"module":20409,"summary":20422},"\u002Fparticle-physics\u002Fweak-interaction\u002Fcp-violation-kaons-b-mesons","CP Violation in Kaons and B Mesons","The neutral kaon is its own laboratory for CP. Weak box diagrams mix $K^0$ and its antiparticle into short- and long-lived states that should be pure CP eigenstates decaying to two and three pions. In 1964 Cronin and Fitch caught the long-lived kaon decaying to two pions — CP is violated, at the two-per-mille level of $\\epsilon$. Direct violation ($\\epsilon'$) followed, and the $B$ factories turned the CKM phase into a large, clean time-dependent asymmetry measuring $\\sin 2\\beta$. The effect is real but far too small to explain why the universe is made of matter.\n",{"path":20424,"title":20425,"module":20426,"summary":20427},"\u002Fparticle-physics\u002Fqcd\u002Fcolor-su3-gluons","Color SU(3), Gluons, and the QCD Lagrangian","Quantum Chromodynamics","Color is the exact gauged SU(3) charge of the strong force. Gauging it forces eight massless gluons in the adjoint representation and, because the gauge group is non-abelian, three- and four-gluon self-couplings absent from QED. This lesson builds the QCD Lagrangian from the covariant derivative and the non-abelian field strength, states the Feynman rules with their color factors, and computes the Casimir invariants that set the strength of quark-gluon and gluon-gluon coupling.\n",{"path":20429,"title":20430,"module":20426,"summary":20431},"\u002Fparticle-physics\u002Fqcd\u002Fasymptotic-freedom-confinement","Asymptotic Freedom and Confinement","The QCD beta function is negative: gluon self-interaction antiscreens color, so the coupling weakens at short distance (asymptotic freedom) and strengthens at long distance (confinement). This lesson computes the one-loop beta coefficient, solves for the running of alpha_s and the emergent scale Lambda_QCD, and reads the strong-coupling regime as the linear quark-antiquark potential of a color flux tube that breaks by pair creation.\n",{"path":20433,"title":20434,"module":20426,"summary":20435},"\u002Fparticle-physics\u002Fqcd\u002Fdeep-inelastic-scattering-partons","Deep Inelastic Scattering and the Parton Model","Scattering electrons hard off a proton resolves pointlike constituents. This lesson sets up the deep-inelastic kinematics, defines the structure functions F1 and F2, and reads Bjorken scaling as the signature of free spin-half partons. The Callan-Gross relation fixes the parton spin, the structure function becomes a charge-weighted sum of parton distributions, and the slow logarithmic scaling violations expose the gluon through DGLAP evolution.\n",{"path":20437,"title":20438,"module":20426,"summary":20439},"\u002Fparticle-physics\u002Fqcd\u002Fjets-hadronization","Jets, Hadronization, and Testing QCD","Quarks and gluons produced in a collision fragment into collimated sprays of hadrons — jets — whose directions track the underlying partons. This lesson reads two-jet events as the quark and antiquark of electron-positron annihilation, three-jet events as direct evidence of the radiated gluon, and the hadronization step as the flux tube breaking into color singlets. Jet algorithms and event-shape variables turn the pattern into precision measurements of alpha_s.\n",{"path":20441,"title":20442,"module":20443,"summary":20444},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Felectroweak-su2-u1","The Electroweak Theory","Electroweak Unification and the Higgs","The electromagnetic and weak interactions are two faces of a single gauge theory built on $SU(2)_L \\times U(1)_Y$. Left-handed fermions sit in weak-isospin doublets and right-handed fermions in singlets, each carrying a hypercharge fixed by the Gell-Mann–Nishijima relation $Q = T_3 + Y\u002F2$. The four gauge fields $W^{1,2,3}$ and $B$ mix: the charged combinations $W^\\pm$ mediate the charged current, while $W^3$ and $B$ rotate through the Weinberg angle into the massless photon and the massive $Z$. The single angle $\\theta_W$ ties the couplings, the boson masses, and the neutral-current strengths together.\n",{"path":20446,"title":20447,"module":20443,"summary":20448},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fspontaneous-symmetry-breaking","Spontaneous Symmetry Breaking","A symmetry of the Lagrangian need not be a symmetry of the ground state. When the lowest-energy configuration sits away from the symmetric point, the symmetry is spontaneously broken and the vacuum is one of a degenerate family. Breaking a continuous global symmetry produces one massless scalar — a Goldstone boson — for every broken generator, the flat direction along the vacuum manifold. The Mexican-hat potential and the ferromagnet below its Curie point are the working pictures.\n",{"path":20450,"title":20451,"module":20443,"summary":20452},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-mechanism","The Higgs Mechanism","Gauging a spontaneously broken symmetry converts the would-be Goldstone bosons into the longitudinal polarizations of the gauge fields, which thereby acquire mass. Applied to $SU(2)_L \\times U(1)_Y$ with a single Higgs doublet, three of the four scalar degrees of freedom are eaten by the $W^\\pm$ and $Z$; the fourth survives as the physical Higgs boson, and the photon stays massless. Fermion masses come from Yukawa couplings to the same field, each mass proportional to its coupling times the vacuum expectation value $v \\approx 246$ GeV.\n",{"path":20454,"title":20455,"module":20443,"summary":20456},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fhiggs-boson-discovery","The Higgs Boson","The Higgs boson is produced at the LHC chiefly through gluon fusion, with vector-boson fusion and associated production as cleaner but rarer channels. It decays most often to $b\\bar b$ and $WW^\\ast$, but the discovery rested on two rare clean modes, $H \\to \\gamma\\gamma$ and $H \\to ZZ^\\ast \\to 4\\ell$, whose narrow invariant-mass peaks emerged over smooth backgrounds. ATLAS and CMS announced a boson near 125 GeV in 2012; its measured spin-parity $0^+$ and its couplings, which scale with particle mass, identify it as the Standard Model Higgs.\n",{"path":20458,"title":20459,"module":20443,"summary":20460},"\u002Fparticle-physics\u002Felectroweak-higgs\u002Fstandard-model","The Standard Model","The Standard Model combines the quark model, quantum chromodynamics, and the electroweak theory. SU(3) symmetry sorts the hadrons and predicted the omega; color explains why only colorless quark combinations exist; QCD gives asymptotic freedom and confinement; and spontaneous symmetry breaking through the Higgs field gives the weak bosons their mass.\n",{"path":20462,"title":20463,"module":20464,"summary":20465},"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-oscillations","Neutrino Oscillations","Neutrino Physics","Neutrinos are produced and detected in flavour states, but they propagate as mass states, and the two bases are misaligned. A flavour therefore evolves coherently into a superposition of other flavours with a probability set by the mass-squared splitting and the ratio L\u002FE. This lesson derives the two-flavour oscillation formula, applies it to the solar and atmospheric neutrino deficits, shows how the SNO neutral-current measurement resolved the solar problem, and works out the MSW resonance that amplifies mixing inside the Sun.\n",{"path":20467,"title":20468,"module":20464,"summary":20469},"\u002Fparticle-physics\u002Fneutrinos\u002Fneutrino-mass-pmns","Neutrino Mass and the PMNS Matrix","Three-flavour mixing promotes the single oscillation angle to the unitary Pontecorvo–Maki–Nakagawa–Sakata matrix, parametrised by three angles and a Dirac CP phase. This lesson decomposes the PMNS matrix into three rotations, records the measured angles and mass-squared splittings, lays out the normal and inverted mass orderings, contrasts the large leptonic mixing with the near-diagonal CKM matrix, and collects the absolute-mass bounds from beta decay and cosmology.\n",{"path":20471,"title":20472,"module":20464,"summary":20473},"\u002Fparticle-physics\u002Fneutrinos\u002Fdirac-majorana-experiments","Dirac, Majorana, and Neutrino Experiments","A neutral fermion can carry a mass term forbidden to every charged particle, so the neutrino may be its own antiparticle. This lesson contrasts the Dirac and Majorana mass terms and their state content, derives the seesaw mechanism that ties a tiny light mass to a heavy right-handed partner, presents neutrinoless double-beta decay as the decisive lepton-number test, surveys the reactor, accelerator, solar, and atmospheric sources on a baseline–energy map, and explains why neutrino mass is physics beyond the original Standard Model.\n",{"path":20475,"title":20476,"module":20477,"summary":20478},"\u002Fparticle-physics\u002Fexperiment\u002Faccelerators-luminosity","Accelerators, Colliders, and Luminosity","Accelerators and Detectors","Fixed-target machines waste energy in the center-of-mass motion of the whole system, so the reachable $\\sqrt s$ grows only as the square root of the beam energy, while colliders put the full beam energy into the collision. Circular electron machines are limited by synchrotron radiation scaling as $E^4\u002Fm^4R$; proton machines are limited by bending fields. Luminosity, set by beam current and focusing, converts a cross section into an event rate through $R=\\mathcal L\\,\\sigma$, and integrated luminosity sets the total event count.\n",{"path":20480,"title":20481,"module":20477,"summary":20482},"\u002Fparticle-physics\u002Fexperiment\u002Fdetectors-subsystems","Particle Detectors and Subsystems","A detector reads a collision by the energy particles deposit as they cross matter. Charged particles ionize at the Bethe-Bloch rate, radiate in the field of nuclei above a critical energy, and emit Cherenkov light above a velocity threshold; electrons and photons build electromagnetic showers over a radiation length, and hadrons build wider showers over a nuclear interaction length. The onion of tracker, electromagnetic and hadronic calorimeters, and outer muon chambers turns these processes into momentum, energy, and identity, with neutrinos inferred from missing transverse momentum.\n",{"path":20484,"title":20485,"module":20477,"summary":20486},"\u002Fparticle-physics\u002Fexperiment\u002Fhow-discoveries-are-made","From Collisions to Discoveries","A discovery is a peak that survives statistics. Events are reconstructed into invariant masses, a signal accumulates as a bump over a smooth background, and its significance is judged by a p-value; the field's threshold is five sigma. The expected yield is a product — luminosity times cross section times branching ratio times acceptance and efficiency — that must be balanced by a trigger and data-reduction chain against an overwhelming rate. Worked reconstructions of $Z\\to\\ell\\ell$, the $J\u002F\\psi$, and the Higgs show the same peak-over-background logic at three scales.\n",{"path":20488,"title":20489,"module":20489,"summary":20490},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fbeyond-standard-model","Beyond the Standard Model","The Standard Model leaves the four interactions ununified and the neutrinos massless, both now known to be wrong. Grand unification predicts the couplings merge near ten-to-the-sixteen GeV and the proton decays; supersymmetry pairs each particle with a superpartner; and the confirmed oscillation of neutrinos proves they carry mass, the first crack in the model.\n",{"path":20492,"title":20493,"module":20489,"summary":20494},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fgrand-unified-theories","Grand Unified Theories and Proton Decay","The Standard Model gauge group is a product of three factors with three independent couplings. A grand unified theory embeds them in a single simple group — SU(5) is the minimal choice — so that one coupling runs into all three and the fractional quark charges follow from a tracelessness condition. The same embedding places quarks and leptons in shared multiplets, mediates baryon-number violation through superheavy gauge bosons, and predicts the proton decays with a lifetime that Super-Kamiokande has pushed past ten-to-the-thirty-four years.\n",{"path":20496,"title":20497,"module":20489,"summary":20498},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fsupersymmetry","Supersymmetry","Supersymmetry relates fermions and bosons, pairing every Standard Model particle with a superpartner whose spin differs by one half. The pairing makes the scalar and fermion loop corrections to the Higgs mass cancel, removing the quadratic sensitivity to high scales; it sharpens the meeting of the three gauge couplings; and, when R-parity is conserved, it leaves the lightest superpartner stable and neutral, a natural dark-matter candidate. The LHC has excluded gluinos and light squarks below roughly two TeV.\n",{"path":20500,"title":20501,"module":20489,"summary":20502},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fhierarchy-problem-naturalness","The Hierarchy Problem and Naturalness","The electroweak scale sits sixteen orders of magnitude below the Planck scale, and nothing in the Standard Model protects that gap. The Higgs mass squared picks up quadratic corrections proportional to the highest scale in the theory, so keeping it at the observed value requires the bare mass and its counterterm to cancel to some thirty significant figures. Naturalness treats that cancellation as a symptom of missing physics. Supersymmetry, compositeness, and extra dimensions each remove the quadratic sensitivity, but the LHC has found none of them at the predicted scale.\n",{"path":20504,"title":20505,"module":20489,"summary":20506},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fdark-matter-candidates","Dark Matter and Particle Candidates","Flat galactic rotation curves, gravitational lensing, the cosmic microwave background, and structure formation all require about five times more matter than the visible baryons, none of it interacting electromagnetically. A stable weakly interacting particle of roughly weak-scale mass freezes out of the early universe with close to the observed abundance — the WIMP miracle — and is the leading candidate, with axions and sterile neutrinos as alternatives. Direct, indirect, and collider searches have so far only tightened the limits.\n",{"path":20508,"title":20509,"module":20489,"summary":20510},"\u002Fparticle-physics\u002Fbeyond-standard-model\u002Fmatter-antimatter-open-questions","Matter-Antimatter Asymmetry and Open Questions","The universe is made of matter, with about one extra baryon for every billion photons and no antimatter regions. Sakharov identified the three conditions any dynamical explanation must meet: baryon-number violation, C and CP violation, and a departure from thermal equilibrium. The Standard Model contains all three in principle, but its CP violation falls short by some ten orders of magnitude, so baryogenesis requires new physics — leptogenesis being the leading route. A closing survey collects the open questions and the experiments aimed at them.\n",{"path":20512,"title":20513,"module":6,"summary":6},"\u002Fparticle-physics","Particle Physics",{"path":20515,"title":20516,"module":20517,"summary":20518},"\u002Fastrophysics-cosmology\u002Forientation\u002Fthe-sun-and-stars","The Sun and the Life of Stars","Orientation","The Sun is the one star close enough to study in detail: its luminosity fixes a surface temperature of 5780 K, and the proton-proton fusion cycle in its 1.5-million-kelvin core supplies its power. Measuring other stars needs the magnitude scale, parallax, and the distance ladder; plotting luminosity against temperature builds the Hertzsprung-Russell diagram, on which a star's mass sets its lifetime and its evolutionary track off the main sequence.\n",{"path":20520,"title":20521,"module":20517,"summary":20522},"\u002Fastrophysics-cosmology\u002Forientation\u002Fstellar-death-final-states","Cataclysmic Events and the Final States of Stars","A star's death is set by its mass. In close binaries, matter poured across the Roche lobe onto a white dwarf produces novae and, at the Chandrasekhar limit of 1.4 solar masses, a Type Ia supernova; a massive star fusing to an iron core collapses into a Type II supernova. The remnant is a white dwarf held by electron degeneracy, a neutron star held by neutron degeneracy, or, above the neutron-star limit, a black hole inside its Schwarzschild radius.\n",{"path":20524,"title":20525,"module":20517,"summary":20526},"\u002Fastrophysics-cosmology\u002Forientation\u002Fgalaxies-and-cosmology","Galaxies, Cosmology, and the Evolving Universe","Galaxies come in elliptical, spiral, and irregular forms, and their redshifts obey Hubble's law, evidence that space itself is expanding. The critical density and the density parameter decide whether the universe is open, flat, or closed; baryons, dark matter, and dark energy each contribute. The cosmic microwave background and primordial helium anchor the Big Bang, whose thermal history runs from inflation through nucleosynthesis to the atoms of today.\n",{"path":20528,"title":20529,"module":20530,"summary":20531},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fmagnitudes-fluxes-and-the-distance-modulus","Magnitudes, Fluxes, and the Distance Modulus","Observational Foundations","The brightness of a star reaches us as a radiant flux that falls off as the inverse square of distance. The magnitude scale encodes flux logarithmically through the Pogson ratio; the apparent and absolute magnitudes differ by the distance modulus, which converts a measured brightness into a distance. The bolometric correction folds a filtered magnitude into a total luminosity, and the difference of two magnitudes in different bands, the color index, measures surface temperature.\n",{"path":20533,"title":20534,"module":20530,"summary":20535},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fstellar-spectra-and-spectral-classification","Stellar Spectra and Spectral Classification","A stellar spectrum is a continuum crossed by absorption lines whose strengths are set by the temperature of the atmosphere. The Boltzmann factor governs how atoms populate excited states, and the Saha equation governs how they ionize; their product explains why each line, such as the hydrogen Balmer series, peaks in strength at a characteristic temperature. This behavior orders stars into the OBAFGKM sequence, and the luminosity classes of the MK system add a second dimension for surface gravity.\n",{"path":20537,"title":20538,"module":20530,"summary":20539},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Ftelescopes-and-detectors-across-the-spectrum","Telescopes and Detectors Across the Spectrum","A telescope collects light in proportion to its collecting area and resolves detail down to the diffraction limit set by its aperture and the observing wavelength. The atmosphere blurs and blocks large parts of the spectrum, which drives the choice between ground and space and between refractors, reflectors, and radio dishes. CCDs record the light with high quantum efficiency, and interferometry synthesizes an aperture as large as the separation of two telescopes.\n",{"path":20541,"title":20542,"module":20530,"summary":20543},"\u002Fastrophysics-cosmology\u002Fobservational-foundations\u002Fthe-cosmic-distance-ladder","The Cosmic Distance Ladder","No single method measures distances from the nearest stars to the far reaches of the universe. Instead a ladder of overlapping techniques, each calibrated by the one below it, extends the scale rung by rung: trigonometric parallax, main-sequence fitting, pulsating variables, the tip of the red-giant branch, the Tully-Fisher relation, and Type Ia supernovae. Each rung inherits the uncertainty of every rung beneath it, so the whole chain sets the accuracy of the Hubble constant.\n",{"path":20545,"title":20546,"module":20547,"summary":20548},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fblackbody-radiation-and-specific-intensity","Blackbody Radiation and Specific Intensity","Radiation and Matter","Specific intensity is the fundamental measure of a radiation field: energy per unit area, time, frequency, and solid angle. It is conserved along a ray in empty space, and its angular moments give the mean intensity, flux, and radiation pressure. In thermal equilibrium the intensity equals the Planck function, whose limits and integrals reproduce the Rayleigh-Jeans law, the Wien law, Stefan-Boltzmann, and Wien's displacement law.\n",{"path":20550,"title":20551,"module":20547,"summary":20552},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fradiative-transfer-and-the-transfer-equation","Radiative Transfer and the Transfer Equation","Along a ray, matter adds intensity through emission and removes it through absorption. Measuring path length in optical depth turns this into the transfer equation, whose formal solution superposes an attenuated background on the source function integrated along the line of sight. In local thermodynamic equilibrium the source function is the Planck function, and the Eddington-Barbier relation shows that the emergent intensity samples the source function at optical depth of order unity, explaining absorption lines and solar limb darkening.\n",{"path":20554,"title":20555,"module":20547,"summary":20556},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fspectral-line-formation-and-broadening","Spectral-Line Formation and Broadening","A spectral line is a bound-bound transition whose strength is set by an oscillator strength and whose shape is set by three broadening mechanisms: the Lorentzian natural and collisional wings, the Gaussian thermal Doppler core, and their Voigt convolution. Equivalent width measures the total absorption, and the curve of growth relates it to the number of absorbers through a linear, saturated, and damping regime, turning line strengths into abundances.\n",{"path":20558,"title":20559,"module":20547,"summary":20560},"\u002Fastrophysics-cosmology\u002Fradiation-and-matter\u002Fopacity-and-the-rosseland-mean","Opacity Sources and the Rosseland Mean","Stellar opacity comes from four processes: bound-bound line absorption, bound-free photoionization, free-free absorption, and electron scattering. The bound-free and free-free terms follow a Kramers law, electron scattering sets a frequency-flat floor, and the negative hydrogen ion dominates cool photospheres. The Rosseland mean averages these harmonically, weighting transparent frequencies because they carry the flux, and its value fixes the radiative temperature gradient and decides where a star becomes convective.\n",{"path":20562,"title":20563,"module":20564,"summary":20565},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fhydrostatic-equilibrium-and-the-virial-theorem","Hydrostatic Equilibrium and the Virial Theorem","Stellar Structure","A star holds itself up by balancing the inward pull of gravity against an outward pressure gradient. This balance, hydrostatic equilibrium, fixes a lower bound on the central pressure and, combined with the gravitational potential energy, yields the virial theorem. The virial relation gives a star a negative heat capacity, so that losing energy makes it hotter, and sets the Kelvin-Helmholtz timescale over which contraction alone can power the Sun.\n",{"path":20567,"title":20568,"module":20564,"summary":20569},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equations-of-stellar-structure","The Equations of Stellar Structure","A static star is described by four coupled first-order differential equations in the interior mass or radius: mass conservation, hydrostatic equilibrium, energy generation, and energy transport. Closed with an equation of state, opacity, and reaction rates, and subject to central and surface boundary conditions, they determine the structure uniquely from mass and composition, the Vogt-Russell theorem. Energy moves by radiation until the temperature gradient exceeds the Schwarzschild limit, where convection takes over.\n",{"path":20571,"title":20572,"module":20564,"summary":20573},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-equation-of-state-and-polytropes","The Equation of State and Polytropes","Stellar pressure comes from gas, radiation, and, at high density, degenerate electrons. When pressure depends on density as a power law, hydrostatic equilibrium reduces to the Lane-Emden equation, whose solutions describe polytropes of index n. The relativistic degenerate case, n equal to three, gives a mass independent of radius, the Chandrasekhar mass. Eddington's standard model treats a radiation-supported star as an n equal to three polytrope and yields the quartic relating radiation fraction to mass.\n",{"path":20575,"title":20576,"module":20564,"summary":20577},"\u002Fastrophysics-cosmology\u002Fstellar-structure\u002Fthe-standard-solar-model","The Standard Solar Model","The standard solar model integrates the structure equations for one solar mass and calibrates the composition and convection parameter to reproduce the Sun's observed luminosity, radius, and age. Helioseismology tests the model's sound speed through the Sun's acoustic p-mode oscillations, and the model predicts a neutrino flux by production channel. The measured deficit, the solar-neutrino problem, is resolved by matter-enhanced flavor oscillation, confirmed when SNO measured the total flux across all flavors.\n",{"path":20579,"title":20580,"module":20581,"summary":20582},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fthermonuclear-reaction-rates-and-the-gamow-peak","Thermonuclear Reaction Rates and the Gamow Peak","Nuclear Astrophysics","Stellar fusion proceeds only by quantum tunneling through the Coulomb barrier, because thermal energies are a thousand times smaller than the barrier height. The reaction rate is an integral over the Maxwell–Boltzmann distribution and the tunneling probability, whose product is sharply peaked at the Gamow energy. The astrophysical S-factor isolates the nuclear physics from the barrier penetration, and the steep temperature dependence follows from the width and position of the Gamow peak.\n",{"path":20584,"title":20585,"module":20581,"summary":20586},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhydrogen-burning-pp-chains-and-cno","Hydrogen Burning: pp Chains and the CNO Cycle","Four protons fuse into one helium-4 nucleus, releasing 26.7 MeV, through two competing networks. The pp chain begins with a weak-interaction bottleneck and branches three ways; the CNO cycle uses carbon, nitrogen, and oxygen as catalysts and is limited by nitrogen-14 proton capture. Their steep and gentle temperature dependences cross near 1.8e7 K, which divides pp-powered lower-main-sequence stars from CNO-powered upper-main-sequence stars.\n",{"path":20588,"title":20589,"module":20581,"summary":20590},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fhelium-burning-and-the-triple-alpha-process","Helium Burning and the Triple-Alpha Process","Helium fuses to carbon in two steps through the unbound beryllium-8 nucleus and a resonant excited state of carbon-12, the Hoyle state, whose existence was predicted from the observed carbon abundance. The rate scales as roughly the fortieth power of temperature, and in a degenerate low-mass core this drives the runaway helium flash. A competing alpha capture on carbon-12 sets the carbon-to-oxygen ratio and the composition of the resulting white dwarf.\n",{"path":20592,"title":20593,"module":20581,"summary":20594},"\u002Fastrophysics-cosmology\u002Fnuclear-astrophysics\u002Fadvanced-burning-and-neutron-capture-nucleosynthesis","Advanced Burning, the Iron Peak, and the s\u002Fr Processes","Massive stars burn carbon, neon, oxygen, and silicon in ever-shorter stages, building an onion-shell interior and reaching nuclear statistical equilibrium at the iron peak, where the binding-energy-per-nucleon curve turns over and fusion can release no more energy. Elements beyond iron form by neutron capture: the slow s-process in AGB stars tracks the valley of stability, while the rapid r-process in supernovae and neutron-star mergers builds the heaviest nuclei far from it.\n",{"path":20596,"title":20597,"module":20598,"summary":20599},"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fphases-of-the-interstellar-medium","The Phases of the Interstellar Medium","The Interstellar Medium","The gas between the stars separates into distinct thermal phases, from cold molecular clouds at 10 K to a diffuse million-degree corona, held near a common pressure by a balance of photoelectric heating and radiative cooling. Neutral hydrogen is traced by the 21-cm hyperfine line, dust reddens and extinguishes starlight along a characteristic wavelength law, and the ultraviolet output of hot stars carves ionized Strömgren spheres out of the surrounding gas.\n",{"path":20601,"title":20602,"module":20598,"summary":20603},"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fmolecular-clouds-and-gravitational-collapse","Molecular Clouds and Gravitational Collapse","Stars form in cold, dense molecular clouds when self-gravity overcomes thermal and magnetic support. The virial theorem fixes the Jeans mass and length at which a clump becomes unstable, the free-fall time sets how fast it collapses, and a fragmentation cascade — cut off at a minimum mass by the onset of opacity — turns one cloud into a whole cluster, imprinting the stellar initial mass function.\n",{"path":20605,"title":20606,"module":20598,"summary":20607},"\u002Fastrophysics-cosmology\u002Fism-and-star-formation\u002Fprotostars-and-the-pre-main-sequence","Protostars and Pre-Main-Sequence Evolution","A collapsing core becomes optically thick and forms a protostar that grows by accretion through a disk while driving bipolar outflows. The newborn star appears on the birthline and contracts down the fully convective Hayashi track, then crosses the radiative Henyey track to the zero-age main sequence, powered by gravitational contraction until hydrogen ignites. Below about 0.08 solar masses degeneracy halts contraction before ignition, dividing stars from brown dwarfs.\n",{"path":20609,"title":20610,"module":20611,"summary":20612},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-main-sequence-and-its-structure","The Main Sequence and Its Structure","Stellar Evolution","A star settles onto the zero-age main sequence when core hydrogen ignition halts contraction. Homology scaling of the structure equations reproduces the mass–luminosity relation, and the burning mode splits the sequence into an upper branch with a convective core and a lower branch with a convective envelope. The main-sequence lifetime falls steeply with mass, and the turnoff of a coeval cluster serves as a clock.\n",{"path":20614,"title":20615,"module":20611,"summary":20616},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fpost-main-sequence-low-mass-evolution","Post-Main-Sequence Evolution of Low-Mass Stars","When a low-mass star exhausts core hydrogen, burning moves to a shell, the core contracts, and the envelope swells into a red giant. A degenerate helium core ignites in a flash, settles onto the horizontal branch, and after a second contraction the star climbs the asymptotic giant branch with two burning shells. Thermal pulses and dredge-up enrich the surface, and mass loss ejects a planetary nebula, leaving a carbon–oxygen white dwarf.\n",{"path":20618,"title":20619,"module":20611,"summary":20620},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fthe-evolution-of-massive-stars","The Evolution of Massive Stars","Stars above about eight solar masses burn through hydrogen, helium, carbon, neon, oxygen, and silicon in stages that grow shorter as neutrino losses accelerate contraction. The interior becomes an onion of concentric burning shells around an inert iron core. Radiation pressure near the Eddington limit drives fierce winds that can strip the hydrogen envelope entirely, and silicon burning builds an iron core toward the threshold of collapse.\n",{"path":20622,"title":20623,"module":20611,"summary":20624},"\u002Fastrophysics-cosmology\u002Fstellar-evolution\u002Fstellar-pulsation-and-the-instability-strip","Stellar Pulsation and the Instability Strip","Radial pulsation is a standing sound wave whose period scales inversely with the square root of the mean density. The kappa mechanism, an opacity valve seated in the helium partial-ionization zone, turns a star into a heat engine that pumps the oscillation. Stars in the instability strip pulsate as Cepheids, RR Lyrae, and Mira variables, and the Cepheid period–luminosity relation calibrates the distance ladder.\n",{"path":20626,"title":19042,"module":20627,"summary":20628},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fwhite-dwarfs-and-the-chandrasekhar-limit","Stellar Death and Compact Remnants","A white dwarf is held up by the degeneracy pressure of its electrons, a quantum-mechanical stiffness that survives to zero temperature. Filling the Fermi sea sets a pressure that scales as density to the five-thirds power when the electrons are slow and only four-thirds when they are relativistic. The softer relativistic law produces the inverted mass-radius relation and a maximum mass, the Chandrasekhar limit near 1.4 solar masses, above which no cold equilibrium exists. Cooling and crystallization then turn the white-dwarf population into a clock for the Galactic disk.\n",{"path":20630,"title":20631,"module":20627,"summary":20632},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fcore-collapse-supernovae","Core-Collapse Supernovae","When a massive star builds an iron core past the Chandrasekhar mass, degeneracy fails and the core collapses in less than a second. Photodisintegration and electron capture remove pressure support and neutronize the matter; the collapse halts abruptly at nuclear density, launching a shock that stalls and is revived by neutrino heating. The event is a Type II or stripped-envelope Ib\u002FIc supernova, and the neutrinos from SN 1987A confirmed the picture directly.\n",{"path":20634,"title":20635,"module":20627,"summary":20636},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fthermonuclear-supernovae-type-ia","Thermonuclear Supernovae","A carbon-oxygen white dwarf driven toward the Chandrasekhar mass ignites its degenerate fuel and unbinds itself in a thermonuclear runaway, the Type Ia supernova. The light curve is powered by the radioactive decay of nickel-56 to cobalt-56 to iron-56, and the Phillips relation between peak brightness and decline rate makes these events standardizable candles. Their near-uniform luminosity turns them into the distance indicators that revealed cosmic acceleration.\n",{"path":20638,"title":20639,"module":20627,"summary":20640},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fneutron-stars-and-pulsars","Neutron Stars and Pulsars","A neutron star is held up by neutron degeneracy and the repulsive nuclear force, with a maximum mass, the Tolman-Oppenheimer-Volkoff limit, set by an uncertain dense-matter equation of state. Its rotating magnetic dipole sweeps a beam past Earth as a pulsar, and magnetic braking traces a track across the period-period- derivative diagram. Millisecond pulsars, magnetars, glitches, and the orbital decay of the Hulse-Taylor binary follow from the same structure.\n",{"path":20642,"title":20643,"module":20627,"summary":20644},"\u002Fastrophysics-cosmology\u002Fstellar-death-and-compact-remnants\u002Fblack-holes-schwarzschild-and-kerr","Black Holes, Schwarzschild and Kerr","Above the neutron-star mass limit gravity wins completely and the remnant is a black hole. The Schwarzschild solution gives the event horizon, gravitational redshift, and time dilation; the innermost stable circular orbit sets the efficiency of accretion. Rotating Kerr black holes drag spacetime and carry an ergosphere. Stellar-mass black holes are found in X-ray binaries, and the Event Horizon Telescope has imaged the shadow of a supermassive one.\n",{"path":20646,"title":20647,"module":20648,"summary":20649},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fbinary-systems-and-mass-transfer","Binary Systems and Mass Transfer","Binaries and Gravitational Waves","Most stars are born in pairs, and a binary is the only setting where a stellar mass can be measured directly. Visual, spectroscopic, and eclipsing binaries each expose a different combination of the orbital elements, and together they calibrate the mass-luminosity relation. When one star swells to fill its Roche lobe, gas streams through the inner Lagrange point onto its companion. Conservative transfer widens or shrinks the orbit depending on the mass ratio, and the sign of that response explains the Algol paradox.\n",{"path":20651,"title":20652,"module":20648,"summary":20653},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Faccreting-compact-objects","Accreting Compact Objects","Gas falling onto a compact object converts gravitational binding energy into radiation with an efficiency set by the depth of the potential well, up to tens of percent of the rest mass for a neutron star or black hole. Angular momentum forces the flow into a disk, and viscous dissipation gives a temperature profile that falls as radius to the minus three-quarters, producing a multicolor blackbody spectrum. Radiation pressure caps the steady luminosity at the Eddington limit. Unstable nuclear burning of the accreted fuel powers classical novae on white dwarfs and Type I X-ray bursts on neutron stars.\n",{"path":20655,"title":20656,"module":20648,"summary":20657},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fgravitational-waves-from-inspiraling-binaries","Gravitational Waves from Inspiraling Binaries","A time-varying mass quadrupole radiates gravitational waves, ripples in spacetime that stretch and squeeze a ring of free masses along two polarizations. The radiated power drains a binary's orbital energy, shrinking the orbit and sweeping the wave frequency upward in a chirp whose rate fixes the chirp mass. Laser interferometers with kilometre arms measure the resulting strain of order ten to the minus twenty-one. The first detection, GW150914, matched a template for two merging black holes near thirty solar masses each.\n",{"path":20659,"title":20660,"module":20648,"summary":20661},"\u002Fastrophysics-cosmology\u002Fbinaries-and-gravitational-waves\u002Fmultimessenger-astronomy-and-gamma-ray-bursts","Multimessenger Astronomy and Gamma-Ray Bursts","Gamma-ray bursts split into two populations: long bursts from the collapse of massive stars and short bursts from merging compact objects. The compactness problem forces the emitting plasma to move at ultra-relativistic speed, beaming the radiation into a narrow jet. The neutron-star merger GW170817 tied a gravitational chirp to a short gamma-ray burst, a radioactive kilonova, and a broadband afterglow, confirming that mergers forge r-process elements. A merger with a measured redshift is a standard siren that reads the Hubble constant from gravitational data alone.\n",{"path":20663,"title":20664,"module":20665,"summary":20666},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fthe-milky-way","The Milky Way Galaxy","Galaxies and Dark Matter","The Galaxy resolves into a thin disk of gas and young stars, a central bar and bulge, and a diffuse old halo studded with globular clusters. Star counts and the reddening of distant light map these components, while the differential rotation of the disk — encoded in the Oort constants and the flat rotation curve — measures the enclosed mass and reveals more than the stars can account for. Spiral arms are density waves, not material structures, and the innermost stellar orbits around Sgr A* weigh a four-million-solar-mass black hole.\n",{"path":20668,"title":20669,"module":20665,"summary":20670},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-morphology-and-classification","Galaxy Morphology and Classification","Galaxies sort along the Hubble tuning fork from smooth ellipticals through lenticulars to grand-design and barred spirals, with irregulars off the end. The light of a spheroid follows the de Vaucouleurs quarter-power law while a disk fades exponentially, and the general Sérsic profile interpolates between them. Virial scaling relations — Tully–Fisher for disks, Faber–Jackson and the fundamental plane for spheroids — tie luminosity to internal motions, and the Schechter function fixes the abundance of galaxies as a function of luminosity.\n",{"path":20672,"title":20673,"module":20665,"summary":20674},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-rotation-curves-and-dark-matter","Galaxy Rotation Curves and Dark Matter","The rotation curves of disk galaxies stay flat far beyond the light, demanding an extended halo whose density falls as the inverse square of radius. Decomposing the curve into disk, bulge, and halo, and fitting isothermal or NFW profiles, quantifies the missing mass. Gravitational lensing weighs the same mass without dynamics, the mass-to-light ratio climbs from stars to clusters, and the Bullet Cluster separates the collisionless dark matter from the colliding gas — evidence that MOND strains to match.\n",{"path":20676,"title":20677,"module":20665,"summary":20678},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Factive-galactic-nuclei-and-supermassive-black-holes","Active Galactic Nuclei","A small fraction of galaxies pour out enormous luminosity from a region smaller than the solar system. Accretion onto a supermassive black hole, limited by the Eddington balance of radiation pressure and gravity, powers the Seyferts, quasars, radio galaxies, and blazars — one engine seen from different angles through an obscuring torus. Relativistic jets produce apparent superluminal motion, reverberation mapping and stellar dynamics weigh the central mass, and the M–sigma relation ties that mass to the host bulge.\n",{"path":20680,"title":20681,"module":20665,"summary":20682},"\u002Fastrophysics-cosmology\u002Fgalaxies\u002Fgalaxy-clusters-and-large-scale-structure","Galaxy Clusters and Large-Scale Structure","Galaxies gather into groups and rich clusters bound by a common dark halo and filled with hot X-ray gas. Three independent probes — the virial theorem, the hydrostatic X-ray temperature, and gravitational lensing — agree on a mass that dwarfs the stars. On the largest scales galaxies trace a cosmic web of filaments, walls, and voids, quantified by the two-point correlation function, whose baryon acoustic oscillation bump provides a standard ruler for cosmology.\n",{"path":20684,"title":20685,"module":20686,"summary":20687},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-expanding-universe-and-hubbles-law","The Expanding Universe and Hubble's Law","Cosmic Expansion and Dynamics","The universe is homogeneous and isotropic on large scales, so its expansion is captured by a single function of time, the scale factor. Comoving coordinates stay fixed while proper distances grow in proportion to the scale factor, producing Hubble's law and a cosmological redshift that measures stretched space rather than a Doppler shift. A Newtonian energy argument reproduces the dynamics, and the same finite, expanding cosmos resolves Olbers' paradox.\n",{"path":20689,"title":20690,"module":20686,"summary":20691},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-frw-metric-and-cosmological-redshift","The FRW Metric and Cosmological Redshift","The geometry of a homogeneous, isotropic universe is fixed by symmetry to the Robertson-Walker metric, with the entire freedom reduced to a scale factor and a single curvature constant selecting an open, flat, or closed space. From the metric the null geodesic of light gives comoving distance, the exact cosmological redshift, and the distinction between the proper distance we cannot measure and the redshift we can.\n",{"path":20693,"title":17769,"module":20686,"summary":20694},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fthe-friedmann-equations-and-cosmic-dynamics","The scale factor obeys the Friedmann equation, the acceleration equation, and the fluid equation, only two of which are independent. An equation of state fixes how each component behaves under expansion, so radiation dilutes as the inverse fourth power of the scale factor, matter as the inverse cube, and vacuum energy not at all. The critical density defines the density parameters, and the deceleration parameter encodes whether gravity or dark energy is winning.\n",{"path":20696,"title":20697,"module":20686,"summary":20698},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fcosmological-models-and-distances","Cosmological Models and Distances","Integrating the Friedmann equation for particular mixtures gives the benchmark models, from the matter-only Einstein-de Sitter universe to the concordance Lambda-CDM, each with its own scale-factor history and age. Because the redshift is the only direct observable, several distance measures diverge at high redshift, and the angular-diameter distance even turns over so that the most distant objects look larger. The horizon and lookback time set what is causally and observationally reachable.\n",{"path":20700,"title":20701,"module":20686,"summary":20702},"\u002Fastrophysics-cosmology\u002Fcosmology-expansion-and-dynamics\u002Fdark-energy-and-the-accelerating-universe","Dark Energy and the Accelerating Universe","In 1998 two teams found that distant Type Ia supernovae are fainter than a decelerating universe predicts, revealing that the expansion is accelerating and that a component with negative pressure dominates the energy budget. The simplest candidate is the cosmological constant, or vacuum energy, with an equation of state near minus one. It works observationally but leaves two deep puzzles: why the vacuum energy is a hundred and twenty orders of magnitude smaller than expected, and why it is comparable to the matter density just now.\n",{"path":20704,"title":20705,"module":20706,"summary":20707},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fthe-thermal-history-of-the-universe","The Thermal History of the Universe","The Hot Big Bang","Running the expansion backward compresses and heats the universe, so its past is a sequence of thermal epochs set by temperature. Temperature scales as the inverse scale factor; species stay in equilibrium while their interaction rate exceeds the expansion rate and freeze out when it drops below. The effective degrees of freedom count the relativistic species and step down through mass thresholds, and neutrino decoupling just before electron-positron annihilation leaves a relic neutrino background slightly cooler than the photons.\n",{"path":20709,"title":20710,"module":20706,"summary":20711},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fbig-bang-nucleosynthesis","Big Bang Nucleosynthesis","In the first three minutes the weak interactions freeze out the neutron-to-proton ratio, and once deuterium survives photodissociation a fast reaction network converts nearly all free neutrons into helium-4. The primordial abundances of deuterium, helium-3, helium-4, and lithium-7 depend on a single free parameter, the baryon-to-photon ratio, so measuring them fixes the baryon density. The predictions match observation across nine decades of abundance, with a persistent discrepancy in lithium-7.\n",{"path":20713,"title":20714,"module":20706,"summary":20715},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Frecombination-and-the-cosmic-microwave-background","Recombination and the Cosmic Microwave Background","As the universe cooled through a few thousand kelvin the free electrons bound to protons, and the Saha equation tracks the falling ionization fraction. Once the plasma neutralized, photons stopped scattering and streamed freely from a spherical surface of last scattering at redshift about 1100. Those photons are the cosmic microwave background, an almost perfect blackbody at 2.725 kelvin with a dipole from our motion through it.\n",{"path":20717,"title":20718,"module":20706,"summary":20719},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcmb-anisotropies-and-cosmological-parameters","CMB Anisotropies and Cosmological Parameters","The cosmic microwave background carries temperature fluctuations at the ten-parts-per-million level, imprinted by sound waves in the photon-baryon plasma before recombination. Decomposed into spherical harmonics, the fluctuations form an angular power spectrum whose acoustic peaks encode the geometry and contents of the universe: the first peak fixes spatial flatness, the odd-even peak ratio the baryon density, and the third peak the dark-matter density. Polarization adds an independent channel, and the Planck measurements pin the concordance parameters.\n",{"path":20721,"title":20722,"module":20706,"summary":20723},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fcosmic-inflation","Cosmic Inflation","The hot Big Bang leaves three initial-condition puzzles unexplained: why causally disconnected patches share a temperature, why the geometry is so nearly flat, and why no magnetic monopoles are seen. A brief epoch of accelerated expansion driven by a slowly rolling scalar field solves all three by stretching a small causal patch across the observable universe. The same accelerated expansion freezes quantum fluctuations into a near-scale-invariant spectrum of density perturbations, seeding all later structure.\n",{"path":20725,"title":20726,"module":20706,"summary":20727},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fstructure-formation-and-the-growth-of-perturbations","Structure Formation and the Growth of Perturbations","The near-uniform early universe grew its galaxies and clusters by gravitational instability acting on the tiny inflationary perturbations. In an expanding background the growth is slowed to a power law rather than the exponential of a static medium; perturbations stall during radiation domination and grow with the scale factor once matter dominates. The transfer function turns the primordial spectrum into the processed matter power spectrum, and cold dark matter builds structure from the bottom up.\n",{"path":20729,"title":20730,"module":20706,"summary":20731},"\u002Fastrophysics-cosmology\u002Fthe-hot-big-bang\u002Fdark-matter-dark-energy-and-open-questions","Dark Matter, Dark Energy, and Open Questions","Five independent lines of evidence converge on a universe whose energy budget is dominated by dark energy and dark matter, with ordinary baryons a small remainder. The candidate particles for dark matter range from WIMPs to axions to sterile neutrinos, each with its own detection strategy. The concordance model fits the data with six parameters but leaves the nature of dark energy, the Hubble tension, small-scale structure, and the matter-antimatter asymmetry unexplained.\n",{"path":20733,"title":20734,"module":6,"summary":6},"\u002Fastrophysics-cosmology","Astrophysics & Cosmology",{"path":20736,"title":20737,"module":6,"summary":6},"\u002Fcolophon","Colophon",{"path":3985,"title":20739,"module":6,"summary":6},"Study Notes",[20741,20752,20761,20774,20787,20798,20820,20833,20850,20859,20877,20903],{"module":18615,"moduleNumber":9829,"slug":20742,"lessons":20743},"mathematical-background",[20744,20746,20748,20750],{"title":17256,"path":18614,"lessonNumber":9829,"topics":20745,"summary":18616},[18615],{"title":18619,"path":18618,"lessonNumber":9835,"topics":20747,"summary":18620},[18615],{"title":18623,"path":18622,"lessonNumber":9841,"topics":20749,"summary":18624},[18615],{"title":16615,"path":18626,"lessonNumber":9847,"topics":20751,"summary":18627},[18615],{"module":16062,"moduleNumber":9835,"slug":20753,"lessons":20754},"foundations",[20755,20757,20759],{"title":18630,"path":18629,"lessonNumber":9829,"topics":20756,"summary":18631},[16062],{"title":18634,"path":18633,"lessonNumber":9835,"topics":20758,"summary":18635},[16062],{"title":18638,"path":18637,"lessonNumber":9841,"topics":20760,"summary":18639},[16062],{"module":18643,"moduleNumber":9841,"slug":20762,"lessons":20763},"neural-networks",[20764,20766,20768,20770,20772],{"title":18642,"path":18641,"lessonNumber":9829,"topics":20765,"summary":18644},[18643],{"title":18647,"path":18646,"lessonNumber":9835,"topics":20767,"summary":18648},[18643],{"title":18651,"path":18650,"lessonNumber":9841,"topics":20769,"summary":18652},[18643],{"title":18655,"path":18654,"lessonNumber":9847,"topics":20771,"summary":18656},[18643],{"title":18659,"path":18658,"lessonNumber":9853,"topics":20773,"summary":18660},[18643],{"module":18664,"moduleNumber":9847,"slug":20775,"lessons":20776},"optimization",[20777,20779,20781,20783,20785],{"title":18663,"path":18662,"lessonNumber":9829,"topics":20778,"summary":18665},[18664],{"title":18668,"path":18667,"lessonNumber":9835,"topics":20780,"summary":18669},[18664],{"title":18672,"path":18671,"lessonNumber":9841,"topics":20782,"summary":18673},[18664],{"title":18676,"path":18675,"lessonNumber":9847,"topics":20784,"summary":18677},[18664],{"title":18680,"path":18679,"lessonNumber":9853,"topics":20786,"summary":18681},[18664],{"module":18685,"moduleNumber":9853,"slug":20788,"lessons":20789},"regularization",[20790,20792,20794,20796],{"title":18684,"path":18683,"lessonNumber":9829,"topics":20791,"summary":18686},[18685],{"title":18689,"path":18688,"lessonNumber":9835,"topics":20793,"summary":18690},[18685],{"title":18693,"path":18692,"lessonNumber":9841,"topics":20795,"summary":18694},[18685],{"title":18696,"path":115,"lessonNumber":9847,"topics":20797,"summary":18697},[18685],{"module":15125,"moduleNumber":9859,"slug":20799,"lessons":20800},"architectures",[20801,20803,20805,20807,20809,20811,20813,20815,20817],{"title":18700,"path":18699,"lessonNumber":9829,"topics":20802,"summary":18701},[15125],{"title":18704,"path":18703,"lessonNumber":9835,"topics":20804,"summary":18705},[15125],{"title":18708,"path":18707,"lessonNumber":9841,"topics":20806,"summary":18709},[15125],{"title":18712,"path":18711,"lessonNumber":9847,"topics":20808,"summary":18713},[15125],{"title":18715,"path":17,"lessonNumber":9853,"topics":20810,"summary":18716},[15125],{"title":5,"path":15127,"lessonNumber":9859,"topics":20812,"summary":15143},[15125],{"title":14485,"path":14484,"lessonNumber":9865,"topics":20814,"summary":18719},[15125],{"title":18722,"path":18721,"lessonNumber":9871,"topics":20816,"summary":18723},[15125],{"title":18726,"path":18725,"lessonNumber":20818,"topics":20819,"summary":18727},9,[15125],{"module":18731,"moduleNumber":9865,"slug":20821,"lessons":20822},"theory",[20823,20825,20827,20829,20831],{"title":18730,"path":18729,"lessonNumber":9829,"topics":20824,"summary":18732},[18731],{"title":18735,"path":18734,"lessonNumber":9835,"topics":20826,"summary":18736},[18731],{"title":18739,"path":18738,"lessonNumber":9841,"topics":20828,"summary":18740},[18731],{"title":18743,"path":18742,"lessonNumber":9847,"topics":20830,"summary":18744},[18731],{"title":18747,"path":18746,"lessonNumber":9853,"topics":20832,"summary":18748},[18731],{"module":18752,"moduleNumber":9871,"slug":20834,"lessons":20835},"generative-models",[20836,20838,20840,20842,20844,20846,20848],{"title":18751,"path":18750,"lessonNumber":9829,"topics":20837,"summary":18753},[18752],{"title":18756,"path":18755,"lessonNumber":9835,"topics":20839,"summary":18757},[18752],{"title":18760,"path":18759,"lessonNumber":9841,"topics":20841,"summary":18761},[18752],{"title":18764,"path":18763,"lessonNumber":9847,"topics":20843,"summary":18765},[18752],{"title":18768,"path":18767,"lessonNumber":9853,"topics":20845,"summary":18769},[18752],{"title":18772,"path":18771,"lessonNumber":9859,"topics":20847,"summary":18773},[18752],{"title":18776,"path":18775,"lessonNumber":9865,"topics":20849,"summary":18777},[18752],{"module":18781,"moduleNumber":20818,"slug":20851,"lessons":20852},"probabilistic-methods",[20853,20855,20857],{"title":18780,"path":18779,"lessonNumber":9829,"topics":20854,"summary":18782},[18781],{"title":18785,"path":18784,"lessonNumber":9835,"topics":20856,"summary":18786},[18781],{"title":18789,"path":18788,"lessonNumber":9841,"topics":20858,"summary":18790},[18781],{"module":18794,"moduleNumber":20860,"slug":20861,"lessons":20862},10,"practical",[20863,20865,20867,20869,20871,20873,20875],{"title":18793,"path":18792,"lessonNumber":9829,"topics":20864,"summary":18795},[18794],{"title":18798,"path":18797,"lessonNumber":9835,"topics":20866,"summary":18799},[18794],{"title":18802,"path":18801,"lessonNumber":9841,"topics":20868,"summary":18803},[18794],{"title":18806,"path":18805,"lessonNumber":9847,"topics":20870,"summary":18807},[18794],{"title":18810,"path":18809,"lessonNumber":9853,"topics":20872,"summary":18811},[18794],{"title":18814,"path":18813,"lessonNumber":9859,"topics":20874,"summary":18815},[18794],{"title":18818,"path":18817,"lessonNumber":9865,"topics":20876,"summary":18819},[18794],{"module":18823,"moduleNumber":20878,"slug":20879,"lessons":20880},11,"large-models-and-agents",[20881,20883,20885,20887,20889,20891,20893,20895,20897,20899,20901],{"title":18822,"path":18821,"lessonNumber":9829,"topics":20882,"summary":18824},[18823],{"title":18827,"path":18826,"lessonNumber":9835,"topics":20884,"summary":18828},[18823],{"title":18831,"path":18830,"lessonNumber":9841,"topics":20886,"summary":18832},[18823],{"title":18835,"path":18834,"lessonNumber":9847,"topics":20888,"summary":18836},[18823],{"title":18839,"path":18838,"lessonNumber":9853,"topics":20890,"summary":18840},[18823],{"title":18843,"path":18842,"lessonNumber":9859,"topics":20892,"summary":18844},[18823],{"title":18847,"path":18846,"lessonNumber":9865,"topics":20894,"summary":18848},[18823],{"title":18851,"path":18850,"lessonNumber":9871,"topics":20896,"summary":18852},[18823],{"title":18855,"path":18854,"lessonNumber":20818,"topics":20898,"summary":18856},[18823],{"title":18859,"path":18858,"lessonNumber":20860,"topics":20900,"summary":18860},[18823],{"title":18863,"path":18862,"lessonNumber":20878,"topics":20902,"summary":18864},[18823],{"module":18868,"moduleNumber":20904,"slug":20905,"lessons":20906},12,"reinforcement-learning",[20907,20909,20911,20913,20915],{"title":18867,"path":18866,"lessonNumber":9829,"topics":20908,"summary":18869},[18868],{"title":18872,"path":18871,"lessonNumber":9835,"topics":20910,"summary":18873},[18868],{"title":18876,"path":18875,"lessonNumber":9841,"topics":20912,"summary":18877},[18868],{"title":18880,"path":18879,"lessonNumber":9847,"topics":20914,"summary":18881},[18868],{"title":18884,"path":18883,"lessonNumber":9853,"topics":20916,"summary":18885},[18868],"\u003Csvg style=\"width:100%;max-width:454.127px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 340.595 212.351\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-14.875 1.556)\">\u003Cpath d=\"M-30.643 104.645L-30.643 104.555Q-30.592 104.348-30.397 104.324L-29.358 104.324L-29.358 101.996L-30.330 101.996Q-30.530 101.973-30.580 101.754L-30.580 101.668Q-30.530 101.457-30.330 101.434L-28.963 101.434Q-28.768 101.453-28.717 101.668L-28.717 104.324L-27.803 104.324Q-27.608 104.348-27.557 104.555L-27.557 104.645Q-27.608 104.860-27.803 104.883L-30.397 104.883Q-30.592 104.860-30.643 104.645M-29.612 100.457L-29.612 100.403Q-29.612 100.231-29.475 100.110Q-29.338 99.988-29.162 99.988Q-28.990 99.988-28.854 100.110Q-28.717 100.231-28.717 100.403L-28.717 100.457Q-28.717 100.633-28.854 100.754Q-28.990 100.875-29.162 100.875Q-29.338 100.875-29.475 100.754Q-29.612 100.633-29.612 100.457M-26.944 104.645L-26.944 104.555Q-26.901 104.348-26.694 104.324L-26.272 104.324L-26.272 101.996L-26.694 101.996Q-26.901 101.973-26.944 101.754L-26.944 101.668Q-26.897 101.457-26.694 101.434L-25.877 101.434Q-25.682 101.457-25.631 101.668L-25.631 101.754L-25.639 101.778Q-25.412 101.598-25.139 101.496Q-24.865 101.395-24.573 101.395Q-24.225 101.395-23.987 101.535Q-23.748 101.676-23.633 101.934Q-23.518 102.192-23.518 102.547L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-24.487 104.883Q-24.682 104.860-24.733 104.645L-24.733 104.555Q-24.682 104.344-24.487 104.324L-24.158 104.324L-24.158 102.578Q-24.158 102.270-24.248 102.112Q-24.338 101.953-24.631 101.953Q-24.901 101.953-25.129 102.084Q-25.358 102.215-25.494 102.444Q-25.631 102.672-25.631 102.938L-25.631 104.324L-25.205 104.324Q-24.998 104.348-24.959 104.555L-24.959 104.645Q-24.998 104.860-25.205 104.883L-26.694 104.883Q-26.901 104.860-26.944 104.645M-22.698 106.426L-22.698 106.340Q-22.655 106.121-22.448 106.098L-22.026 106.098L-22.026 101.996L-22.448 101.996Q-22.655 101.973-22.698 101.754L-22.698 101.668Q-22.651 101.457-22.448 101.434L-21.631 101.434Q-21.436 101.453-21.385 101.668L-21.385 101.738Q-21.174 101.570-20.910 101.483Q-20.647 101.395-20.377 101.395Q-20.037 101.395-19.740 101.539Q-19.444 101.684-19.229 101.936Q-19.014 102.188-18.899 102.500Q-18.783 102.813-18.783 103.156Q-18.783 103.621-19.010 104.031Q-19.237 104.442-19.623 104.682Q-20.010 104.922-20.479 104.922Q-20.998 104.922-21.385 104.555L-21.385 106.098L-20.959 106.098Q-20.752 106.121-20.713 106.340L-20.713 106.426Q-20.752 106.637-20.959 106.660L-22.448 106.660Q-22.651 106.637-22.698 106.426M-20.522 104.363Q-20.213 104.363-19.963 104.194Q-19.713 104.024-19.569 103.742Q-19.424 103.461-19.424 103.156Q-19.424 102.867-19.549 102.588Q-19.674 102.309-19.906 102.131Q-20.139 101.953-20.440 101.953Q-20.760 101.953-21.022 102.139Q-21.283 102.324-21.385 102.625L-21.385 103.477Q-21.295 103.844-21.074 104.104Q-20.854 104.363-20.522 104.363M-17.780 104.028L-17.780 101.996L-18.201 101.996Q-18.408 101.973-18.451 101.754L-18.451 101.668Q-18.405 101.457-18.201 101.434L-17.385 101.434Q-17.190 101.457-17.139 101.668L-17.139 103.996Q-17.139 104.231-16.969 104.297Q-16.799 104.363-16.514 104.363Q-16.307 104.363-16.112 104.287Q-15.916 104.211-15.791 104.061Q-15.666 103.910-15.666 103.699L-15.666 101.996L-16.088 101.996Q-16.299 101.973-16.338 101.754L-16.338 101.668Q-16.299 101.457-16.088 101.434L-15.276 101.434Q-15.076 101.457-15.026 101.668L-15.026 104.324L-14.600 104.324Q-14.393 104.348-14.354 104.555L-14.354 104.645Q-14.393 104.860-14.600 104.883L-15.416 104.883Q-15.615 104.860-15.666 104.660Q-16.069 104.922-16.576 104.922Q-16.811 104.922-17.026 104.881Q-17.240 104.840-17.406 104.738Q-17.573 104.637-17.676 104.459Q-17.780 104.281-17.780 104.028M-13.076 103.778L-13.076 101.996L-13.826 101.996Q-14.026 101.973-14.076 101.754L-14.076 101.668Q-14.026 101.457-13.826 101.434L-13.076 101.434L-13.076 100.684Q-13.026 100.477-12.826 100.449L-12.682 100.449Q-12.487 100.477-12.436 100.684L-12.436 101.434L-11.076 101.434Q-10.885 101.453-10.826 101.668L-10.826 101.754Q-10.881 101.973-11.076 101.996L-12.436 101.996L-12.436 103.746Q-12.436 104.363-11.862 104.363Q-11.612 104.363-11.448 104.178Q-11.283 103.992-11.283 103.746Q-11.283 103.653-11.211 103.582Q-11.139 103.512-11.037 103.500L-10.893 103.500Q-10.694 103.524-10.643 103.731L-10.643 103.778Q-10.643 104.102-10.826 104.365Q-11.010 104.629-11.303 104.776Q-11.596 104.922-11.916 104.922Q-12.428 104.922-12.752 104.612Q-13.076 104.301-13.076 103.778\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-14.875 1.556)\">\u003Cpath d=\"M-5.502 104.645L-5.502 104.555Q-5.463 104.348-5.256 104.324L-4.850 104.324L-3.920 103.106L-4.791 101.996L-5.209 101.996Q-5.405 101.977-5.455 101.754L-5.455 101.668Q-5.405 101.457-5.209 101.434L-4.049 101.434Q-3.850 101.457-3.799 101.668L-3.799 101.754Q-3.850 101.973-4.049 101.996L-4.158 101.996L-3.662 102.653L-3.186 101.996L-3.303 101.996Q-3.502 101.973-3.553 101.754L-3.553 101.668Q-3.502 101.457-3.303 101.434L-2.143 101.434Q-1.947 101.453-1.897 101.668L-1.897 101.754Q-1.947 101.973-2.143 101.996L-2.553 101.996L-3.401 103.106L-2.440 104.324L-2.033 104.324Q-1.834 104.348-1.783 104.555L-1.783 104.645Q-1.822 104.860-2.033 104.883L-3.186 104.883Q-3.393 104.860-3.432 104.645L-3.432 104.555Q-3.393 104.348-3.186 104.324L-3.057 104.324L-3.662 103.469L-4.248 104.324L-4.104 104.324Q-3.897 104.348-3.858 104.555L-3.858 104.645Q-3.897 104.860-4.104 104.883L-5.256 104.883Q-5.451 104.863-5.502 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-65.403 73.585H2.883V50.822h-68.286Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-21.25 -41.124)\">\u003Cpath d=\"M-30.674 104.684L-30.674 103.770Q-30.647 103.563-30.436 103.539L-30.268 103.539Q-30.104 103.563-30.045 103.723Q-29.842 104.363-29.115 104.363Q-28.908 104.363-28.680 104.328Q-28.451 104.293-28.283 104.178Q-28.115 104.063-28.115 103.860Q-28.115 103.649-28.338 103.535Q-28.561 103.422-28.834 103.379L-29.533 103.266Q-30.674 103.055-30.674 102.332Q-30.674 102.043-30.530 101.854Q-30.385 101.664-30.145 101.557Q-29.905 101.449-29.649 101.410Q-29.393 101.371-29.115 101.371Q-28.865 101.371-28.672 101.401Q-28.479 101.430-28.315 101.508Q-28.237 101.391-28.108 101.371L-28.030 101.371Q-27.932 101.383-27.869 101.445Q-27.807 101.508-27.795 101.602L-27.795 102.309Q-27.807 102.403-27.869 102.469Q-27.932 102.535-28.030 102.547L-28.198 102.547Q-28.291 102.535-28.358 102.469Q-28.424 102.403-28.436 102.309Q-28.436 101.930-29.131 101.930Q-29.479 101.930-29.797 102.012Q-30.115 102.094-30.115 102.340Q-30.115 102.606-29.444 102.715L-28.740 102.836Q-28.256 102.918-27.906 103.166Q-27.557 103.414-27.557 103.860Q-27.557 104.250-27.793 104.492Q-28.030 104.735-28.379 104.828Q-28.729 104.922-29.115 104.922Q-29.694 104.922-30.092 104.668Q-30.162 104.793-30.211 104.850Q-30.260 104.906-30.365 104.922L-30.436 104.922Q-30.651 104.899-30.674 104.684M-26.272 104.028L-26.272 101.996L-26.694 101.996Q-26.901 101.973-26.944 101.754L-26.944 101.668Q-26.897 101.457-26.694 101.434L-25.877 101.434Q-25.682 101.457-25.631 101.668L-25.631 103.996Q-25.631 104.231-25.461 104.297Q-25.291 104.363-25.006 104.363Q-24.799 104.363-24.604 104.287Q-24.408 104.211-24.283 104.061Q-24.158 103.910-24.158 103.699L-24.158 101.996L-24.580 101.996Q-24.791 101.973-24.830 101.754L-24.830 101.668Q-24.791 101.457-24.580 101.434L-23.768 101.434Q-23.569 101.457-23.518 101.668L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-23.908 104.883Q-24.108 104.860-24.158 104.660Q-24.561 104.922-25.069 104.922Q-25.303 104.922-25.518 104.881Q-25.733 104.840-25.899 104.738Q-26.065 104.637-26.168 104.459Q-26.272 104.281-26.272 104.028M-22.026 104.645L-22.026 100.555L-22.448 100.555Q-22.655 100.531-22.698 100.317L-22.698 100.227Q-22.655 100.020-22.448 99.996L-21.631 99.996Q-21.436 100.020-21.385 100.227L-21.385 101.738Q-21.174 101.570-20.910 101.483Q-20.647 101.395-20.377 101.395Q-20.037 101.395-19.740 101.539Q-19.444 101.684-19.229 101.936Q-19.014 102.188-18.899 102.500Q-18.783 102.813-18.783 103.156Q-18.783 103.621-19.010 104.031Q-19.237 104.442-19.623 104.682Q-20.010 104.922-20.479 104.922Q-20.998 104.922-21.385 104.555L-21.385 104.645Q-21.436 104.863-21.631 104.883L-21.776 104.883Q-21.967 104.860-22.026 104.645M-20.522 104.363Q-20.213 104.363-19.963 104.194Q-19.713 104.024-19.569 103.742Q-19.424 103.461-19.424 103.156Q-19.424 102.867-19.549 102.588Q-19.674 102.309-19.906 102.131Q-20.139 101.953-20.440 101.953Q-20.760 101.953-21.022 102.139Q-21.283 102.324-21.385 102.625L-21.385 103.477Q-21.295 103.844-21.074 104.104Q-20.854 104.363-20.522 104.363M-18.073 104.645L-18.073 104.555Q-18.022 104.348-17.826 104.324L-16.721 104.324L-16.721 100.555L-17.826 100.555Q-18.022 100.531-18.073 100.317L-18.073 100.227Q-18.022 100.020-17.826 99.996L-16.330 99.996Q-16.139 100.020-16.080 100.227L-16.080 104.324L-14.979 104.324Q-14.780 104.348-14.729 104.555L-14.729 104.645Q-14.780 104.860-14.979 104.883L-17.826 104.883Q-18.022 104.860-18.073 104.645M-13.869 103.770Q-13.869 103.324-13.455 103.067Q-13.041 102.809-12.500 102.709Q-11.959 102.610-11.451 102.602Q-11.451 102.387-11.586 102.235Q-11.721 102.082-11.928 102.006Q-12.135 101.930-12.346 101.930Q-12.690 101.930-12.850 101.953L-12.850 102.012Q-12.850 102.180-12.969 102.295Q-13.088 102.410-13.252 102.410Q-13.428 102.410-13.543 102.287Q-13.658 102.164-13.658 101.996Q-13.658 101.590-13.278 101.481Q-12.897 101.371-12.338 101.371Q-12.069 101.371-11.801 101.449Q-11.533 101.528-11.309 101.678Q-11.084 101.828-10.948 102.049Q-10.811 102.270-10.811 102.547L-10.811 104.266Q-10.811 104.324-10.283 104.324Q-10.088 104.344-10.037 104.555L-10.037 104.645Q-10.088 104.860-10.283 104.883L-10.428 104.883Q-10.772 104.883-11 104.836Q-11.229 104.789-11.373 104.602Q-11.834 104.922-12.541 104.922Q-12.877 104.922-13.182 104.781Q-13.487 104.641-13.678 104.379Q-13.869 104.117-13.869 103.770M-13.229 103.778Q-13.229 104.051-12.987 104.207Q-12.744 104.363-12.459 104.363Q-12.240 104.363-12.008 104.305Q-11.776 104.246-11.614 104.108Q-11.451 103.969-11.451 103.746L-11.451 103.156Q-11.733 103.156-12.149 103.213Q-12.565 103.270-12.897 103.408Q-13.229 103.547-13.229 103.778M-9.686 106.004Q-9.686 105.895-9.635 105.803Q-9.584 105.711-9.492 105.660Q-9.401 105.610-9.295 105.610Q-9.186 105.610-9.094 105.660Q-9.002 105.711-8.951 105.803Q-8.901 105.895-8.901 106.004L-9.045 106.004Q-9.045 106.141-9.022 106.141Q-8.764 106.141-8.576 105.949Q-8.389 105.758-8.303 105.492L-8.092 104.883L-9.229 101.996L-9.557 101.996Q-9.752 101.973-9.807 101.754L-9.807 101.668Q-9.748 101.457-9.557 101.434L-8.397 101.434Q-8.201 101.457-8.151 101.668L-8.151 101.754Q-8.201 101.973-8.397 101.996L-8.662 101.996Q-8.326 102.844-8.082 103.498Q-7.838 104.153-7.838 104.242L-7.830 104.242Q-7.830 104.184-7.739 103.891Q-7.647 103.598-7.453 103.014Q-7.260 102.430-7.119 101.996L-7.397 101.996Q-7.608 101.973-7.647 101.754L-7.647 101.668Q-7.596 101.453-7.397 101.434L-6.244 101.434Q-6.037 101.457-5.998 101.668L-5.998 101.754Q-6.037 101.973-6.244 101.996L-6.565 101.996L-7.740 105.492Q-7.908 105.992-8.235 106.346Q-8.561 106.699-9.022 106.699Q-9.295 106.699-9.490 106.488Q-9.686 106.278-9.686 106.004M-2.272 103.395L-4.713 103.395Q-4.658 103.672-4.461 103.895Q-4.264 104.117-3.987 104.240Q-3.709 104.363-3.424 104.363Q-2.951 104.363-2.729 104.074Q-2.721 104.063-2.664 103.957Q-2.608 103.852-2.559 103.809Q-2.510 103.766-2.416 103.754L-2.272 103.754Q-2.080 103.774-2.022 103.988L-2.022 104.043Q-2.088 104.344-2.319 104.541Q-2.549 104.738-2.862 104.830Q-3.174 104.922-3.479 104.922Q-3.963 104.922-4.403 104.694Q-4.842 104.465-5.110 104.065Q-5.377 103.664-5.377 103.172L-5.377 103.113Q-5.377 102.645-5.131 102.242Q-4.885 101.840-4.477 101.606Q-4.069 101.371-3.600 101.371Q-3.096 101.371-2.742 101.594Q-2.389 101.817-2.205 102.205Q-2.022 102.594-2.022 103.098L-2.022 103.156Q-2.080 103.371-2.272 103.395M-4.705 102.844L-2.678 102.844Q-2.725 102.434-2.963 102.182Q-3.201 101.930-3.600 101.930Q-3.994 101.930-4.301 102.192Q-4.608 102.453-4.705 102.844M-1.315 104.645L-1.315 104.555Q-1.256 104.348-1.065 104.324L-0.354 104.324L-0.354 101.996L-1.065 101.996Q-1.260 101.973-1.315 101.754L-1.315 101.668Q-1.256 101.457-1.065 101.434L0.037 101.434Q0.236 101.453 0.287 101.668L0.287 101.996Q0.549 101.711 0.904 101.553Q1.260 101.395 1.646 101.395Q1.939 101.395 2.174 101.529Q2.408 101.664 2.408 101.930Q2.408 102.098 2.299 102.215Q2.189 102.332 2.021 102.332Q1.869 102.332 1.754 102.221Q1.638 102.110 1.638 101.953Q1.263 101.953 0.949 102.154Q0.635 102.356 0.461 102.690Q0.287 103.024 0.287 103.403L0.287 104.324L1.232 104.324Q1.439 104.348 1.478 104.555L1.478 104.645Q1.439 104.860 1.232 104.883L-1.065 104.883Q-1.256 104.860-1.315 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -41.124)\">\u003Cpath d=\"M7.310 104.645L7.310 104.555Q7.361 104.348 7.556 104.324L8.439 104.324L8.439 101.996L7.584 101.996Q7.385 101.973 7.334 101.754L7.334 101.668Q7.385 101.457 7.584 101.434L8.439 101.434L8.439 100.981Q8.439 100.516 8.845 100.235Q9.252 99.953 9.732 99.953Q10.045 99.953 10.289 100.074Q10.533 100.195 10.533 100.477Q10.533 100.641 10.424 100.758Q10.314 100.875 10.150 100.875Q10.002 100.875 9.881 100.770Q9.760 100.664 9.760 100.516L9.678 100.516Q9.525 100.516 9.388 100.576Q9.252 100.637 9.166 100.752Q9.080 100.867 9.080 101.012L9.080 101.434L10.111 101.434Q10.306 101.453 10.357 101.668L10.357 101.754Q10.306 101.973 10.111 101.996L9.080 101.996L9.080 104.324L9.959 104.324Q10.154 104.348 10.205 104.555L10.205 104.645Q10.154 104.860 9.959 104.883L7.556 104.883Q7.361 104.860 7.310 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M-22.724 19.524a8.536 8.536 0 1 0-17.072 0 8.536 8.536 0 0 0 17.072 0Zm-8.536 0\"\u002F>\u003Cg transform=\"translate(-3.306 -83.358)\">\u003Cpath d=\"M-28.139 103.067L-30.612 103.067Q-30.690 103.055-30.739 103.006Q-30.787 102.957-30.787 102.883Q-30.787 102.809-30.739 102.760Q-30.690 102.711-30.612 102.699L-28.139 102.699L-28.139 100.219Q-28.112 100.051-27.955 100.051Q-27.881 100.051-27.832 100.100Q-27.783 100.149-27.772 100.219L-27.772 102.699L-25.299 102.699Q-25.131 102.731-25.131 102.883Q-25.131 103.035-25.299 103.067L-27.772 103.067L-27.772 105.547Q-27.783 105.617-27.832 105.666Q-27.881 105.715-27.955 105.715Q-28.112 105.715-28.139 105.547\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-good)\">\u003Cpath fill=\"none\" d=\"M-65.403-11.774H2.883v-22.762h-68.286Z\"\u002F>\u003Cg transform=\"translate(-19.125 -126.482)\">\u003Cpath d=\"M-31.037 104.645L-31.037 104.555Q-30.979 104.348-30.787 104.324L-30.420 104.324L-30.420 100.555L-30.787 100.555Q-30.979 100.531-31.037 100.317L-31.037 100.227Q-30.979 100.020-30.787 99.996L-29.260 99.996Q-29.065 100.020-29.014 100.227L-29.014 100.317Q-29.065 100.531-29.260 100.555L-29.780 100.555L-29.780 104.324L-27.948 104.324L-27.948 103.684Q-27.897 103.477-27.701 103.449L-27.557 103.449Q-27.358 103.477-27.307 103.684L-27.307 104.645Q-27.358 104.860-27.557 104.883L-30.787 104.883Q-30.979 104.860-31.037 104.645M-26.608 103.770Q-26.608 103.324-26.194 103.067Q-25.780 102.809-25.239 102.709Q-24.698 102.610-24.190 102.602Q-24.190 102.387-24.324 102.235Q-24.459 102.082-24.666 102.006Q-24.873 101.930-25.084 101.930Q-25.428 101.930-25.588 101.953L-25.588 102.012Q-25.588 102.180-25.707 102.295Q-25.826 102.410-25.990 102.410Q-26.166 102.410-26.281 102.287Q-26.397 102.164-26.397 101.996Q-26.397 101.590-26.016 101.481Q-25.635 101.371-25.076 101.371Q-24.807 101.371-24.539 101.449Q-24.272 101.528-24.047 101.678Q-23.823 101.828-23.686 102.049Q-23.549 102.270-23.549 102.547L-23.549 104.266Q-23.549 104.324-23.022 104.324Q-22.826 104.344-22.776 104.555L-22.776 104.645Q-22.826 104.860-23.022 104.883L-23.166 104.883Q-23.510 104.883-23.739 104.836Q-23.967 104.789-24.112 104.602Q-24.573 104.922-25.280 104.922Q-25.615 104.922-25.920 104.781Q-26.225 104.641-26.416 104.379Q-26.608 104.117-26.608 103.770M-25.967 103.778Q-25.967 104.051-25.725 104.207Q-25.483 104.363-25.198 104.363Q-24.979 104.363-24.746 104.305Q-24.514 104.246-24.352 104.108Q-24.190 103.969-24.190 103.746L-24.190 103.156Q-24.471 103.156-24.887 103.213Q-25.303 103.270-25.635 103.408Q-25.967 103.547-25.967 103.778M-22.424 106.004Q-22.424 105.895-22.373 105.803Q-22.323 105.711-22.231 105.660Q-22.139 105.610-22.033 105.610Q-21.924 105.610-21.832 105.660Q-21.740 105.711-21.690 105.803Q-21.639 105.895-21.639 106.004L-21.783 106.004Q-21.783 106.141-21.760 106.141Q-21.502 106.141-21.315 105.949Q-21.127 105.758-21.041 105.492L-20.830 104.883L-21.967 101.996L-22.295 101.996Q-22.490 101.973-22.545 101.754L-22.545 101.668Q-22.487 101.457-22.295 101.434L-21.135 101.434Q-20.940 101.457-20.889 101.668L-20.889 101.754Q-20.940 101.973-21.135 101.996L-21.401 101.996Q-21.065 102.844-20.821 103.498Q-20.576 104.153-20.576 104.242L-20.569 104.242Q-20.569 104.184-20.477 103.891Q-20.385 103.598-20.192 103.014Q-19.998 102.430-19.858 101.996L-20.135 101.996Q-20.346 101.973-20.385 101.754L-20.385 101.668Q-20.334 101.453-20.135 101.434L-18.983 101.434Q-18.776 101.457-18.737 101.668L-18.737 101.754Q-18.776 101.973-18.983 101.996L-19.303 101.996L-20.479 105.492Q-20.647 105.992-20.973 106.346Q-21.299 106.699-21.760 106.699Q-22.033 106.699-22.229 106.488Q-22.424 106.278-22.424 106.004M-15.010 103.395L-17.451 103.395Q-17.397 103.672-17.199 103.895Q-17.002 104.117-16.725 104.240Q-16.448 104.363-16.162 104.363Q-15.690 104.363-15.467 104.074Q-15.459 104.063-15.403 103.957Q-15.346 103.852-15.297 103.809Q-15.248 103.766-15.155 103.754L-15.010 103.754Q-14.819 103.774-14.760 103.988L-14.760 104.043Q-14.826 104.344-15.057 104.541Q-15.287 104.738-15.600 104.830Q-15.912 104.922-16.217 104.922Q-16.701 104.922-17.141 104.694Q-17.580 104.465-17.848 104.065Q-18.115 103.664-18.115 103.172L-18.115 103.113Q-18.115 102.645-17.869 102.242Q-17.623 101.840-17.215 101.606Q-16.807 101.371-16.338 101.371Q-15.834 101.371-15.481 101.594Q-15.127 101.817-14.944 102.205Q-14.760 102.594-14.760 103.098L-14.760 103.156Q-14.819 103.371-15.010 103.395M-17.444 102.844L-15.416 102.844Q-15.463 102.434-15.701 102.182Q-15.940 101.930-16.338 101.930Q-16.733 101.930-17.039 102.192Q-17.346 102.453-17.444 102.844M-14.053 104.645L-14.053 104.555Q-13.994 104.348-13.803 104.324L-13.092 104.324L-13.092 101.996L-13.803 101.996Q-13.998 101.973-14.053 101.754L-14.053 101.668Q-13.994 101.457-13.803 101.434L-12.701 101.434Q-12.502 101.453-12.451 101.668L-12.451 101.996Q-12.190 101.711-11.834 101.553Q-11.479 101.395-11.092 101.395Q-10.799 101.395-10.565 101.529Q-10.330 101.664-10.330 101.930Q-10.330 102.098-10.440 102.215Q-10.549 102.332-10.717 102.332Q-10.869 102.332-10.985 102.221Q-11.100 102.110-11.100 101.953Q-11.475 101.953-11.789 102.154Q-12.104 102.356-12.278 102.690Q-12.451 103.024-12.451 103.403L-12.451 104.324L-11.506 104.324Q-11.299 104.348-11.260 104.555L-11.260 104.645Q-11.299 104.860-11.506 104.883L-13.803 104.883Q-13.994 104.860-14.053 104.645M-9.830 104.645L-9.830 104.555Q-9.780 104.348-9.580 104.324L-9.311 104.324L-9.311 100.555L-9.580 100.555Q-9.780 100.531-9.830 100.317L-9.830 100.227Q-9.780 100.020-9.580 99.996L-8.799 99.996Q-8.670 99.996-8.565 100.070Q-8.459 100.145-8.420 100.258Q-8.143 101.047-7.983 101.496Q-7.823 101.945-7.569 102.664Q-7.315 103.383-7.176 103.793Q-7.037 104.203-7.037 104.242L-7.037 100.555L-7.311 100.555Q-7.506 100.531-7.557 100.317L-7.557 100.227Q-7.506 100.020-7.311 99.996L-6.237 99.996Q-6.041 100.020-5.990 100.227L-5.990 100.317Q-6.041 100.531-6.237 100.555L-6.510 100.555L-6.510 104.645Q-6.561 104.860-6.756 104.883L-7.022 104.883Q-7.147 104.883-7.250 104.809Q-7.354 104.735-7.397 104.617Q-7.694 103.770-8.067 102.721Q-8.440 101.672-8.610 101.184Q-8.780 100.695-8.783 100.637L-8.783 104.324L-8.510 104.324Q-8.319 104.348-8.260 104.555L-8.260 104.645Q-8.319 104.860-8.510 104.883L-9.580 104.883Q-9.780 104.860-9.830 104.645M-3.662 104.922Q-4.135 104.922-4.520 104.678Q-4.905 104.434-5.127 104.024Q-5.350 103.613-5.350 103.156Q-5.350 102.813-5.225 102.490Q-5.100 102.168-4.869 101.914Q-4.639 101.660-4.332 101.516Q-4.026 101.371-3.662 101.371Q-3.299 101.371-2.987 101.518Q-2.674 101.664-2.451 101.910Q-2.229 102.156-2.102 102.477Q-1.975 102.797-1.975 103.156Q-1.975 103.613-2.199 104.026Q-2.424 104.438-2.809 104.680Q-3.194 104.922-3.662 104.922M-3.662 104.363Q-3.198 104.363-2.906 103.969Q-2.615 103.574-2.615 103.090Q-2.615 102.797-2.750 102.529Q-2.885 102.262-3.125 102.096Q-3.365 101.930-3.662 101.930Q-3.967 101.930-4.205 102.096Q-4.444 102.262-4.578 102.529Q-4.713 102.797-4.713 103.090Q-4.713 103.570-4.420 103.967Q-4.127 104.363-3.662 104.363M-1.315 104.645L-1.315 104.555Q-1.256 104.348-1.065 104.324L-0.354 104.324L-0.354 101.996L-1.065 101.996Q-1.260 101.973-1.315 101.754L-1.315 101.668Q-1.256 101.457-1.065 101.434L0.037 101.434Q0.236 101.453 0.287 101.668L0.287 101.996Q0.549 101.711 0.904 101.553Q1.260 101.395 1.646 101.395Q1.939 101.395 2.174 101.529Q2.408 101.664 2.408 101.930Q2.408 102.098 2.299 102.215Q2.189 102.332 2.021 102.332Q1.869 102.332 1.754 102.221Q1.638 102.110 1.638 101.953Q1.263 101.953 0.949 102.154Q0.635 102.356 0.461 102.690Q0.287 103.024 0.287 103.403L0.287 104.324L1.232 104.324Q1.439 104.348 1.478 104.555L1.478 104.645Q1.439 104.860 1.232 104.883L-1.065 104.883Q-1.256 104.860-1.315 104.645M2.654 104.645L2.654 104.555Q2.705 104.344 2.900 104.324L3.099 104.324L3.099 101.996L2.900 101.996Q2.693 101.973 2.654 101.754L2.654 101.668Q2.705 101.453 2.900 101.434L3.381 101.434Q3.572 101.457 3.631 101.668Q3.951 101.395 4.365 101.395Q4.556 101.395 4.724 101.504Q4.892 101.613 4.967 101.785Q5.142 101.594 5.365 101.494Q5.588 101.395 5.830 101.395Q6.248 101.395 6.402 101.737Q6.556 102.078 6.556 102.547L6.556 104.324L6.756 104.324Q6.967 104.348 7.006 104.555L7.006 104.645Q6.955 104.860 6.756 104.883L5.939 104.883Q5.744 104.860 5.693 104.645L5.693 104.555Q5.744 104.348 5.939 104.324L6.029 104.324L6.029 102.578Q6.029 101.953 5.779 101.953Q5.447 101.953 5.269 102.264Q5.092 102.574 5.092 102.938L5.092 104.324L5.295 104.324Q5.502 104.348 5.541 104.555L5.541 104.645Q5.490 104.860 5.295 104.883L4.478 104.883Q4.279 104.860 4.228 104.645L4.228 104.555Q4.279 104.348 4.478 104.324L4.564 104.324L4.564 102.578Q4.564 101.953 4.318 101.953Q3.986 101.953 3.808 102.266Q3.631 102.578 3.631 102.938L3.631 104.324L3.830 104.324Q4.037 104.348 4.076 104.555L4.076 104.645Q4.025 104.863 3.830 104.883L2.900 104.883Q2.693 104.860 2.654 104.645\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(-12.75 -169.391)\">\u003Cpath d=\"M-29.139 104.922Q-29.612 104.922-29.996 104.678Q-30.381 104.434-30.604 104.024Q-30.826 103.613-30.826 103.156Q-30.826 102.813-30.701 102.490Q-30.576 102.168-30.346 101.914Q-30.115 101.660-29.809 101.516Q-29.502 101.371-29.139 101.371Q-28.776 101.371-28.463 101.518Q-28.151 101.664-27.928 101.910Q-27.705 102.156-27.578 102.477Q-27.451 102.797-27.451 103.156Q-27.451 103.613-27.676 104.026Q-27.901 104.438-28.285 104.680Q-28.670 104.922-29.139 104.922M-29.139 104.363Q-28.674 104.363-28.383 103.969Q-28.092 103.574-28.092 103.090Q-28.092 102.797-28.227 102.529Q-28.362 102.262-28.602 102.096Q-28.842 101.930-29.139 101.930Q-29.444 101.930-29.682 102.096Q-29.920 102.262-30.055 102.529Q-30.190 102.797-30.190 103.090Q-30.190 103.570-29.897 103.967Q-29.604 104.363-29.139 104.363M-26.272 104.028L-26.272 101.996L-26.694 101.996Q-26.901 101.973-26.944 101.754L-26.944 101.668Q-26.897 101.457-26.694 101.434L-25.877 101.434Q-25.682 101.457-25.631 101.668L-25.631 103.996Q-25.631 104.231-25.461 104.297Q-25.291 104.363-25.006 104.363Q-24.799 104.363-24.604 104.287Q-24.408 104.211-24.283 104.061Q-24.158 103.910-24.158 103.699L-24.158 101.996L-24.580 101.996Q-24.791 101.973-24.830 101.754L-24.830 101.668Q-24.791 101.457-24.580 101.434L-23.768 101.434Q-23.569 101.457-23.518 101.668L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-23.908 104.883Q-24.108 104.860-24.158 104.660Q-24.561 104.922-25.069 104.922Q-25.303 104.922-25.518 104.881Q-25.733 104.840-25.899 104.738Q-26.065 104.637-26.168 104.459Q-26.272 104.281-26.272 104.028M-21.569 103.778L-21.569 101.996L-22.319 101.996Q-22.518 101.973-22.569 101.754L-22.569 101.668Q-22.518 101.457-22.319 101.434L-21.569 101.434L-21.569 100.684Q-21.518 100.477-21.319 100.449L-21.174 100.449Q-20.979 100.477-20.928 100.684L-20.928 101.434L-19.569 101.434Q-19.377 101.453-19.319 101.668L-19.319 101.754Q-19.373 101.973-19.569 101.996L-20.928 101.996L-20.928 103.746Q-20.928 104.363-20.354 104.363Q-20.104 104.363-19.940 104.178Q-19.776 103.992-19.776 103.746Q-19.776 103.653-19.703 103.582Q-19.631 103.512-19.530 103.500L-19.385 103.500Q-19.186 103.524-19.135 103.731L-19.135 103.778Q-19.135 104.102-19.319 104.365Q-19.502 104.629-19.795 104.776Q-20.088 104.922-20.408 104.922Q-20.920 104.922-21.244 104.612Q-21.569 104.301-21.569 103.778M-18.451 106.426L-18.451 106.340Q-18.408 106.121-18.201 106.098L-17.780 106.098L-17.780 101.996L-18.201 101.996Q-18.408 101.973-18.451 101.754L-18.451 101.668Q-18.405 101.457-18.201 101.434L-17.385 101.434Q-17.190 101.453-17.139 101.668L-17.139 101.738Q-16.928 101.570-16.664 101.483Q-16.401 101.395-16.131 101.395Q-15.791 101.395-15.494 101.539Q-15.198 101.684-14.983 101.936Q-14.768 102.188-14.653 102.500Q-14.537 102.813-14.537 103.156Q-14.537 103.621-14.764 104.031Q-14.990 104.442-15.377 104.682Q-15.764 104.922-16.233 104.922Q-16.752 104.922-17.139 104.555L-17.139 106.098L-16.713 106.098Q-16.506 106.121-16.467 106.340L-16.467 106.426Q-16.506 106.637-16.713 106.660L-18.201 106.660Q-18.405 106.637-18.451 106.426M-16.276 104.363Q-15.967 104.363-15.717 104.194Q-15.467 104.024-15.323 103.742Q-15.178 103.461-15.178 103.156Q-15.178 102.867-15.303 102.588Q-15.428 102.309-15.660 102.131Q-15.893 101.953-16.194 101.953Q-16.514 101.953-16.776 102.139Q-17.037 102.324-17.139 102.625L-17.139 103.477Q-17.049 103.844-16.828 104.104Q-16.608 104.363-16.276 104.363M-13.533 104.028L-13.533 101.996L-13.955 101.996Q-14.162 101.973-14.205 101.754L-14.205 101.668Q-14.158 101.457-13.955 101.434L-13.139 101.434Q-12.944 101.457-12.893 101.668L-12.893 103.996Q-12.893 104.231-12.723 104.297Q-12.553 104.363-12.268 104.363Q-12.061 104.363-11.865 104.287Q-11.670 104.211-11.545 104.061Q-11.420 103.910-11.420 103.699L-11.420 101.996L-11.842 101.996Q-12.053 101.973-12.092 101.754L-12.092 101.668Q-12.053 101.457-11.842 101.434L-11.030 101.434Q-10.830 101.457-10.780 101.668L-10.780 104.324L-10.354 104.324Q-10.147 104.348-10.108 104.555L-10.108 104.645Q-10.147 104.860-10.354 104.883L-11.170 104.883Q-11.369 104.860-11.420 104.660Q-11.823 104.922-12.330 104.922Q-12.565 104.922-12.780 104.881Q-12.994 104.840-13.160 104.738Q-13.326 104.637-13.430 104.459Q-13.533 104.281-13.533 104.028M-8.830 103.778L-8.830 101.996L-9.580 101.996Q-9.780 101.973-9.830 101.754L-9.830 101.668Q-9.780 101.457-9.580 101.434L-8.830 101.434L-8.830 100.684Q-8.780 100.477-8.580 100.449L-8.436 100.449Q-8.240 100.477-8.190 100.684L-8.190 101.434L-6.830 101.434Q-6.639 101.453-6.580 101.668L-6.580 101.754Q-6.635 101.973-6.830 101.996L-8.190 101.996L-8.190 103.746Q-8.190 104.363-7.615 104.363Q-7.365 104.363-7.201 104.178Q-7.037 103.992-7.037 103.746Q-7.037 103.653-6.965 103.582Q-6.893 103.512-6.791 103.500L-6.647 103.500Q-6.448 103.524-6.397 103.731L-6.397 103.778Q-6.397 104.102-6.580 104.365Q-6.764 104.629-7.057 104.776Q-7.350 104.922-7.670 104.922Q-8.182 104.922-8.506 104.612Q-8.830 104.301-8.830 103.778\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-31.26 98.016V76.385\"\u002F>\u003Cpath stroke=\"none\" d=\"m-31.26 73.785-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-31.26 50.622V30.86\"\u002F>\u003Cpath stroke=\"none\" d=\"m-31.26 28.26-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-31.26 10.789V-8.974\"\u002F>\u003Cpath stroke=\"none\" d=\"m-31.26-11.574-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-31.26-34.736v-21.862\"\u002F>\u003Cpath stroke=\"none\" d=\"m-31.26-59.198-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M5.729 99.192C37.026 76.43 37.026 42.287 7.83 21.054\"\u002F>\u003Cpath stroke=\"none\" d=\"m5.729 19.524 2.14 4.13-.038-2.6 2.485-.765\"\u002F>\u003Cg transform=\"translate(64.195 -43.969)\">\u003Cpath d=\"M-30.674 104.684L-30.674 103.770Q-30.647 103.563-30.436 103.539L-30.268 103.539Q-30.104 103.563-30.045 103.723Q-29.842 104.363-29.115 104.363Q-28.908 104.363-28.680 104.328Q-28.451 104.293-28.283 104.178Q-28.115 104.063-28.115 103.860Q-28.115 103.649-28.338 103.535Q-28.561 103.422-28.834 103.379L-29.533 103.266Q-30.674 103.055-30.674 102.332Q-30.674 102.043-30.530 101.854Q-30.385 101.664-30.145 101.557Q-29.905 101.449-29.649 101.410Q-29.393 101.371-29.115 101.371Q-28.865 101.371-28.672 101.401Q-28.479 101.430-28.315 101.508Q-28.237 101.391-28.108 101.371L-28.030 101.371Q-27.932 101.383-27.869 101.445Q-27.807 101.508-27.795 101.602L-27.795 102.309Q-27.807 102.403-27.869 102.469Q-27.932 102.535-28.030 102.547L-28.198 102.547Q-28.291 102.535-28.358 102.469Q-28.424 102.403-28.436 102.309Q-28.436 101.930-29.131 101.930Q-29.479 101.930-29.797 102.012Q-30.115 102.094-30.115 102.340Q-30.115 102.606-29.444 102.715L-28.740 102.836Q-28.256 102.918-27.906 103.166Q-27.557 103.414-27.557 103.860Q-27.557 104.250-27.793 104.492Q-28.030 104.735-28.379 104.828Q-28.729 104.922-29.115 104.922Q-29.694 104.922-30.092 104.668Q-30.162 104.793-30.211 104.850Q-30.260 104.906-30.365 104.922L-30.436 104.922Q-30.651 104.899-30.674 104.684M-26.869 104.645L-26.869 104.555Q-26.819 104.348-26.623 104.324L-26.158 104.324L-26.158 100.555L-26.623 100.555Q-26.819 100.531-26.869 100.317L-26.869 100.227Q-26.819 100.020-26.623 99.996L-25.877 99.996Q-25.682 100.016-25.631 100.227L-25.631 103.051L-24.487 101.996L-24.783 101.996Q-24.990 101.973-25.030 101.754L-25.030 101.668Q-24.990 101.457-24.783 101.434L-23.334 101.434Q-23.131 101.457-23.084 101.668L-23.084 101.754Q-23.127 101.973-23.334 101.996L-23.701 101.996L-24.647 102.860L-23.494 104.324L-23.158 104.324Q-22.951 104.348-22.908 104.555L-22.908 104.645Q-22.951 104.860-23.158 104.883L-24.326 104.883Q-24.522 104.860-24.573 104.645L-24.573 104.555Q-24.522 104.348-24.326 104.324L-24.166 104.324L-25.030 103.219L-25.631 103.770L-25.631 104.324L-25.166 104.324Q-24.975 104.348-24.916 104.555L-24.916 104.645Q-24.975 104.860-25.166 104.883L-26.623 104.883Q-26.819 104.860-26.869 104.645M-22.151 104.645L-22.151 104.555Q-22.100 104.348-21.905 104.324L-20.865 104.324L-20.865 101.996L-21.838 101.996Q-22.037 101.973-22.088 101.754L-22.088 101.668Q-22.037 101.457-21.838 101.434L-20.471 101.434Q-20.276 101.453-20.225 101.668L-20.225 104.324L-19.311 104.324Q-19.115 104.348-19.065 104.555L-19.065 104.645Q-19.115 104.860-19.311 104.883L-21.905 104.883Q-22.100 104.860-22.151 104.645M-21.119 100.457L-21.119 100.403Q-21.119 100.231-20.983 100.110Q-20.846 99.988-20.670 99.988Q-20.498 99.988-20.362 100.110Q-20.225 100.231-20.225 100.403L-20.225 100.457Q-20.225 100.633-20.362 100.754Q-20.498 100.875-20.670 100.875Q-20.846 100.875-20.983 100.754Q-21.119 100.633-21.119 100.457M-18.451 106.426L-18.451 106.340Q-18.408 106.121-18.201 106.098L-17.780 106.098L-17.780 101.996L-18.201 101.996Q-18.408 101.973-18.451 101.754L-18.451 101.668Q-18.405 101.457-18.201 101.434L-17.385 101.434Q-17.190 101.453-17.139 101.668L-17.139 101.738Q-16.928 101.570-16.664 101.483Q-16.401 101.395-16.131 101.395Q-15.791 101.395-15.494 101.539Q-15.198 101.684-14.983 101.936Q-14.768 102.188-14.653 102.500Q-14.537 102.813-14.537 103.156Q-14.537 103.621-14.764 104.031Q-14.990 104.442-15.377 104.682Q-15.764 104.922-16.233 104.922Q-16.752 104.922-17.139 104.555L-17.139 106.098L-16.713 106.098Q-16.506 106.121-16.467 106.340L-16.467 106.426Q-16.506 106.637-16.713 106.660L-18.201 106.660Q-18.405 106.637-18.451 106.426M-16.276 104.363Q-15.967 104.363-15.717 104.194Q-15.467 104.024-15.323 103.742Q-15.178 103.461-15.178 103.156Q-15.178 102.867-15.303 102.588Q-15.428 102.309-15.660 102.131Q-15.893 101.953-16.194 101.953Q-16.514 101.953-16.776 102.139Q-17.037 102.324-17.139 102.625L-17.139 103.477Q-17.049 103.844-16.828 104.104Q-16.608 104.363-16.276 104.363\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(-19.125 24.088)\">\u003Cpath d=\"M-31.190 106.426L-31.190 106.340Q-31.147 106.121-30.940 106.098L-30.518 106.098L-30.518 101.996L-30.940 101.996Q-31.147 101.973-31.190 101.754L-31.190 101.668Q-31.143 101.457-30.940 101.434L-30.123 101.434Q-29.928 101.453-29.877 101.668L-29.877 101.738Q-29.666 101.570-29.403 101.483Q-29.139 101.395-28.869 101.395Q-28.530 101.395-28.233 101.539Q-27.936 101.684-27.721 101.936Q-27.506 102.188-27.391 102.500Q-27.276 102.813-27.276 103.156Q-27.276 103.621-27.502 104.031Q-27.729 104.442-28.115 104.682Q-28.502 104.922-28.971 104.922Q-29.490 104.922-29.877 104.555L-29.877 106.098L-29.451 106.098Q-29.244 106.121-29.205 106.340L-29.205 106.426Q-29.244 106.637-29.451 106.660L-30.940 106.660Q-31.143 106.637-31.190 106.426M-29.014 104.363Q-28.705 104.363-28.455 104.194Q-28.205 104.024-28.061 103.742Q-27.916 103.461-27.916 103.156Q-27.916 102.867-28.041 102.588Q-28.166 102.309-28.399 102.131Q-28.631 101.953-28.932 101.953Q-29.252 101.953-29.514 102.139Q-29.776 102.324-29.877 102.625L-29.877 103.477Q-29.787 103.844-29.567 104.104Q-29.346 104.363-29.014 104.363M-24.893 104.922Q-25.365 104.922-25.750 104.678Q-26.135 104.434-26.358 104.024Q-26.580 103.613-26.580 103.156Q-26.580 102.813-26.455 102.490Q-26.330 102.168-26.100 101.914Q-25.869 101.660-25.563 101.516Q-25.256 101.371-24.893 101.371Q-24.530 101.371-24.217 101.518Q-23.905 101.664-23.682 101.910Q-23.459 102.156-23.332 102.477Q-23.205 102.797-23.205 103.156Q-23.205 103.613-23.430 104.026Q-23.655 104.438-24.039 104.680Q-24.424 104.922-24.893 104.922M-24.893 104.363Q-24.428 104.363-24.137 103.969Q-23.846 103.574-23.846 103.090Q-23.846 102.797-23.981 102.529Q-24.115 102.262-24.356 102.096Q-24.596 101.930-24.893 101.930Q-25.198 101.930-25.436 102.096Q-25.674 102.262-25.809 102.529Q-25.944 102.797-25.944 103.090Q-25.944 103.570-25.651 103.967Q-25.358 104.363-24.893 104.363M-22.182 104.684L-22.182 103.770Q-22.155 103.563-21.944 103.539L-21.776 103.539Q-21.612 103.563-21.553 103.723Q-21.350 104.363-20.623 104.363Q-20.416 104.363-20.188 104.328Q-19.959 104.293-19.791 104.178Q-19.623 104.063-19.623 103.860Q-19.623 103.649-19.846 103.535Q-20.069 103.422-20.342 103.379L-21.041 103.266Q-22.182 103.055-22.182 102.332Q-22.182 102.043-22.037 101.854Q-21.893 101.664-21.653 101.557Q-21.412 101.449-21.156 101.410Q-20.901 101.371-20.623 101.371Q-20.373 101.371-20.180 101.401Q-19.987 101.430-19.823 101.508Q-19.744 101.391-19.615 101.371L-19.537 101.371Q-19.440 101.383-19.377 101.445Q-19.315 101.508-19.303 101.602L-19.303 102.309Q-19.315 102.403-19.377 102.469Q-19.440 102.535-19.537 102.547L-19.705 102.547Q-19.799 102.535-19.865 102.469Q-19.932 102.403-19.944 102.309Q-19.944 101.930-20.639 101.930Q-20.987 101.930-21.305 102.012Q-21.623 102.094-21.623 102.340Q-21.623 102.606-20.951 102.715L-20.248 102.836Q-19.764 102.918-19.414 103.166Q-19.065 103.414-19.065 103.860Q-19.065 104.250-19.301 104.492Q-19.537 104.735-19.887 104.828Q-20.237 104.922-20.623 104.922Q-21.201 104.922-21.600 104.668Q-21.670 104.793-21.719 104.850Q-21.768 104.906-21.873 104.922L-21.944 104.922Q-22.158 104.899-22.182 104.684M-17.323 103.778L-17.323 101.996L-18.073 101.996Q-18.272 101.973-18.323 101.754L-18.323 101.668Q-18.272 101.457-18.073 101.434L-17.323 101.434L-17.323 100.684Q-17.272 100.477-17.073 100.449L-16.928 100.449Q-16.733 100.477-16.682 100.684L-16.682 101.434L-15.323 101.434Q-15.131 101.453-15.073 101.668L-15.073 101.754Q-15.127 101.973-15.323 101.996L-16.682 101.996L-16.682 103.746Q-16.682 104.363-16.108 104.363Q-15.858 104.363-15.694 104.178Q-15.530 103.992-15.530 103.746Q-15.530 103.653-15.457 103.582Q-15.385 103.512-15.283 103.500L-15.139 103.500Q-14.940 103.524-14.889 103.731L-14.889 103.778Q-14.889 104.102-15.073 104.365Q-15.256 104.629-15.549 104.776Q-15.842 104.922-16.162 104.922Q-16.674 104.922-16.998 104.612Q-17.323 104.301-17.323 103.778M-10.780 102.746L-13.522 102.746Q-13.647 102.735-13.733 102.649Q-13.819 102.563-13.819 102.434Q-13.819 102.305-13.733 102.223Q-13.647 102.141-13.522 102.129L-10.780 102.129Q-10.655 102.141-10.573 102.223Q-10.490 102.305-10.490 102.434Q-10.490 102.563-10.573 102.649Q-10.655 102.735-10.780 102.746M-9.959 104.645L-9.959 104.555Q-9.916 104.348-9.709 104.324L-9.287 104.324L-9.287 101.996L-9.709 101.996Q-9.916 101.973-9.959 101.754L-9.959 101.668Q-9.912 101.457-9.709 101.434L-8.893 101.434Q-8.698 101.457-8.647 101.668L-8.647 101.754L-8.655 101.778Q-8.428 101.598-8.155 101.496Q-7.881 101.395-7.588 101.395Q-7.240 101.395-7.002 101.535Q-6.764 101.676-6.649 101.934Q-6.533 102.192-6.533 102.547L-6.533 104.324L-6.108 104.324Q-5.901 104.348-5.862 104.555L-5.862 104.645Q-5.901 104.860-6.108 104.883L-7.502 104.883Q-7.698 104.860-7.748 104.645L-7.748 104.555Q-7.698 104.344-7.502 104.324L-7.174 104.324L-7.174 102.578Q-7.174 102.270-7.264 102.112Q-7.354 101.953-7.647 101.953Q-7.916 101.953-8.145 102.084Q-8.373 102.215-8.510 102.444Q-8.647 102.672-8.647 102.938L-8.647 104.324L-8.221 104.324Q-8.014 104.348-7.975 104.555L-7.975 104.645Q-8.014 104.860-8.221 104.883L-9.709 104.883Q-9.916 104.860-9.959 104.645M-3.662 104.922Q-4.135 104.922-4.520 104.678Q-4.905 104.434-5.127 104.024Q-5.350 103.613-5.350 103.156Q-5.350 102.813-5.225 102.490Q-5.100 102.168-4.869 101.914Q-4.639 101.660-4.332 101.516Q-4.026 101.371-3.662 101.371Q-3.299 101.371-2.987 101.518Q-2.674 101.664-2.451 101.910Q-2.229 102.156-2.102 102.477Q-1.975 102.797-1.975 103.156Q-1.975 103.613-2.199 104.026Q-2.424 104.438-2.809 104.680Q-3.194 104.922-3.662 104.922M-3.662 104.363Q-3.198 104.363-2.906 103.969Q-2.615 103.574-2.615 103.090Q-2.615 102.797-2.750 102.529Q-2.885 102.262-3.125 102.096Q-3.365 101.930-3.662 101.930Q-3.967 101.930-4.205 102.096Q-4.444 102.262-4.578 102.529Q-4.713 102.797-4.713 103.090Q-4.713 103.570-4.420 103.967Q-4.127 104.363-3.662 104.363M-1.315 104.645L-1.315 104.555Q-1.256 104.348-1.065 104.324L-0.354 104.324L-0.354 101.996L-1.065 101.996Q-1.260 101.973-1.315 101.754L-1.315 101.668Q-1.256 101.457-1.065 101.434L0.037 101.434Q0.236 101.453 0.287 101.668L0.287 101.996Q0.549 101.711 0.904 101.553Q1.260 101.395 1.646 101.395Q1.939 101.395 2.174 101.529Q2.408 101.664 2.408 101.930Q2.408 102.098 2.299 102.215Q2.189 102.332 2.021 102.332Q1.869 102.332 1.754 102.221Q1.638 102.110 1.638 101.953Q1.263 101.953 0.949 102.154Q0.635 102.356 0.461 102.690Q0.287 103.024 0.287 103.403L0.287 104.324L1.232 104.324Q1.439 104.348 1.478 104.555L1.478 104.645Q1.439 104.860 1.232 104.883L-1.065 104.883Q-1.256 104.860-1.315 104.645M2.654 104.645L2.654 104.555Q2.705 104.344 2.900 104.324L3.099 104.324L3.099 101.996L2.900 101.996Q2.693 101.973 2.654 101.754L2.654 101.668Q2.705 101.453 2.900 101.434L3.381 101.434Q3.572 101.457 3.631 101.668Q3.951 101.395 4.365 101.395Q4.556 101.395 4.724 101.504Q4.892 101.613 4.967 101.785Q5.142 101.594 5.365 101.494Q5.588 101.395 5.830 101.395Q6.248 101.395 6.402 101.737Q6.556 102.078 6.556 102.547L6.556 104.324L6.756 104.324Q6.967 104.348 7.006 104.555L7.006 104.645Q6.955 104.860 6.756 104.883L5.939 104.883Q5.744 104.860 5.693 104.645L5.693 104.555Q5.744 104.348 5.939 104.324L6.029 104.324L6.029 102.578Q6.029 101.953 5.779 101.953Q5.447 101.953 5.269 102.264Q5.092 102.574 5.092 102.938L5.092 104.324L5.295 104.324Q5.502 104.348 5.541 104.555L5.541 104.645Q5.490 104.860 5.295 104.883L4.478 104.883Q4.279 104.860 4.228 104.645L4.228 104.555Q4.279 104.348 4.478 104.324L4.564 104.324L4.564 102.578Q4.564 101.953 4.318 101.953Q3.986 101.953 3.808 102.266Q3.631 102.578 3.631 102.938L3.631 104.324L3.830 104.324Q4.037 104.348 4.076 104.555L4.076 104.645Q4.025 104.863 3.830 104.883L2.900 104.883Q2.693 104.860 2.654 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(172.913 1.556)\">\u003Cpath d=\"M-30.643 104.645L-30.643 104.555Q-30.592 104.348-30.397 104.324L-29.358 104.324L-29.358 101.996L-30.330 101.996Q-30.530 101.973-30.580 101.754L-30.580 101.668Q-30.530 101.457-30.330 101.434L-28.963 101.434Q-28.768 101.453-28.717 101.668L-28.717 104.324L-27.803 104.324Q-27.608 104.348-27.557 104.555L-27.557 104.645Q-27.608 104.860-27.803 104.883L-30.397 104.883Q-30.592 104.860-30.643 104.645M-29.612 100.457L-29.612 100.403Q-29.612 100.231-29.475 100.110Q-29.338 99.988-29.162 99.988Q-28.990 99.988-28.854 100.110Q-28.717 100.231-28.717 100.403L-28.717 100.457Q-28.717 100.633-28.854 100.754Q-28.990 100.875-29.162 100.875Q-29.338 100.875-29.475 100.754Q-29.612 100.633-29.612 100.457M-26.944 104.645L-26.944 104.555Q-26.901 104.348-26.694 104.324L-26.272 104.324L-26.272 101.996L-26.694 101.996Q-26.901 101.973-26.944 101.754L-26.944 101.668Q-26.897 101.457-26.694 101.434L-25.877 101.434Q-25.682 101.457-25.631 101.668L-25.631 101.754L-25.639 101.778Q-25.412 101.598-25.139 101.496Q-24.865 101.395-24.573 101.395Q-24.225 101.395-23.987 101.535Q-23.748 101.676-23.633 101.934Q-23.518 102.192-23.518 102.547L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-24.487 104.883Q-24.682 104.860-24.733 104.645L-24.733 104.555Q-24.682 104.344-24.487 104.324L-24.158 104.324L-24.158 102.578Q-24.158 102.270-24.248 102.112Q-24.338 101.953-24.631 101.953Q-24.901 101.953-25.129 102.084Q-25.358 102.215-25.494 102.444Q-25.631 102.672-25.631 102.938L-25.631 104.324L-25.205 104.324Q-24.998 104.348-24.959 104.555L-24.959 104.645Q-24.998 104.860-25.205 104.883L-26.694 104.883Q-26.901 104.860-26.944 104.645M-22.698 106.426L-22.698 106.340Q-22.655 106.121-22.448 106.098L-22.026 106.098L-22.026 101.996L-22.448 101.996Q-22.655 101.973-22.698 101.754L-22.698 101.668Q-22.651 101.457-22.448 101.434L-21.631 101.434Q-21.436 101.453-21.385 101.668L-21.385 101.738Q-21.174 101.570-20.910 101.483Q-20.647 101.395-20.377 101.395Q-20.037 101.395-19.740 101.539Q-19.444 101.684-19.229 101.936Q-19.014 102.188-18.899 102.500Q-18.783 102.813-18.783 103.156Q-18.783 103.621-19.010 104.031Q-19.237 104.442-19.623 104.682Q-20.010 104.922-20.479 104.922Q-20.998 104.922-21.385 104.555L-21.385 106.098L-20.959 106.098Q-20.752 106.121-20.713 106.340L-20.713 106.426Q-20.752 106.637-20.959 106.660L-22.448 106.660Q-22.651 106.637-22.698 106.426M-20.522 104.363Q-20.213 104.363-19.963 104.194Q-19.713 104.024-19.569 103.742Q-19.424 103.461-19.424 103.156Q-19.424 102.867-19.549 102.588Q-19.674 102.309-19.906 102.131Q-20.139 101.953-20.440 101.953Q-20.760 101.953-21.022 102.139Q-21.283 102.324-21.385 102.625L-21.385 103.477Q-21.295 103.844-21.074 104.104Q-20.854 104.363-20.522 104.363M-17.780 104.028L-17.780 101.996L-18.201 101.996Q-18.408 101.973-18.451 101.754L-18.451 101.668Q-18.405 101.457-18.201 101.434L-17.385 101.434Q-17.190 101.457-17.139 101.668L-17.139 103.996Q-17.139 104.231-16.969 104.297Q-16.799 104.363-16.514 104.363Q-16.307 104.363-16.112 104.287Q-15.916 104.211-15.791 104.061Q-15.666 103.910-15.666 103.699L-15.666 101.996L-16.088 101.996Q-16.299 101.973-16.338 101.754L-16.338 101.668Q-16.299 101.457-16.088 101.434L-15.276 101.434Q-15.076 101.457-15.026 101.668L-15.026 104.324L-14.600 104.324Q-14.393 104.348-14.354 104.555L-14.354 104.645Q-14.393 104.860-14.600 104.883L-15.416 104.883Q-15.615 104.860-15.666 104.660Q-16.069 104.922-16.576 104.922Q-16.811 104.922-17.026 104.881Q-17.240 104.840-17.406 104.738Q-17.573 104.637-17.676 104.459Q-17.780 104.281-17.780 104.028M-13.076 103.778L-13.076 101.996L-13.826 101.996Q-14.026 101.973-14.076 101.754L-14.076 101.668Q-14.026 101.457-13.826 101.434L-13.076 101.434L-13.076 100.684Q-13.026 100.477-12.826 100.449L-12.682 100.449Q-12.487 100.477-12.436 100.684L-12.436 101.434L-11.076 101.434Q-10.885 101.453-10.826 101.668L-10.826 101.754Q-10.881 101.973-11.076 101.996L-12.436 101.996L-12.436 103.746Q-12.436 104.363-11.862 104.363Q-11.612 104.363-11.448 104.178Q-11.283 103.992-11.283 103.746Q-11.283 103.653-11.211 103.582Q-11.139 103.512-11.037 103.500L-10.893 103.500Q-10.694 103.524-10.643 103.731L-10.643 103.778Q-10.643 104.102-10.826 104.365Q-11.010 104.629-11.303 104.776Q-11.596 104.922-11.916 104.922Q-12.428 104.922-12.752 104.612Q-13.076 104.301-13.076 103.778\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(172.913 1.556)\">\u003Cpath d=\"M-5.502 104.645L-5.502 104.555Q-5.463 104.348-5.256 104.324L-4.850 104.324L-3.920 103.106L-4.791 101.996L-5.209 101.996Q-5.405 101.977-5.455 101.754L-5.455 101.668Q-5.405 101.457-5.209 101.434L-4.049 101.434Q-3.850 101.457-3.799 101.668L-3.799 101.754Q-3.850 101.973-4.049 101.996L-4.158 101.996L-3.662 102.653L-3.186 101.996L-3.303 101.996Q-3.502 101.973-3.553 101.754L-3.553 101.668Q-3.502 101.457-3.303 101.434L-2.143 101.434Q-1.947 101.453-1.897 101.668L-1.897 101.754Q-1.947 101.973-2.143 101.996L-2.553 101.996L-3.401 103.106L-2.440 104.324L-2.033 104.324Q-1.834 104.348-1.783 104.555L-1.783 104.645Q-1.822 104.860-2.033 104.883L-3.186 104.883Q-3.393 104.860-3.432 104.645L-3.432 104.555Q-3.393 104.348-3.186 104.324L-3.057 104.324L-3.662 103.469L-4.248 104.324L-4.104 104.324Q-3.897 104.348-3.858 104.555L-3.858 104.645Q-3.897 104.860-4.104 104.883L-5.256 104.883Q-5.451 104.863-5.502 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-good)\">\u003Cpath fill=\"none\" d=\"M122.385 73.585h68.287V50.822h-68.287Z\"\u002F>\u003Cg transform=\"translate(168.663 -41.124)\">\u003Cpath d=\"M-31.037 104.645L-31.037 104.555Q-30.979 104.348-30.787 104.324L-30.420 104.324L-30.420 100.555L-30.787 100.555Q-30.979 100.531-31.037 100.317L-31.037 100.227Q-30.979 100.020-30.787 99.996L-29.260 99.996Q-29.065 100.020-29.014 100.227L-29.014 100.317Q-29.065 100.531-29.260 100.555L-29.780 100.555L-29.780 104.324L-27.948 104.324L-27.948 103.684Q-27.897 103.477-27.701 103.449L-27.557 103.449Q-27.358 103.477-27.307 103.684L-27.307 104.645Q-27.358 104.860-27.557 104.883L-30.787 104.883Q-30.979 104.860-31.037 104.645M-26.608 103.770Q-26.608 103.324-26.194 103.067Q-25.780 102.809-25.239 102.709Q-24.698 102.610-24.190 102.602Q-24.190 102.387-24.324 102.235Q-24.459 102.082-24.666 102.006Q-24.873 101.930-25.084 101.930Q-25.428 101.930-25.588 101.953L-25.588 102.012Q-25.588 102.180-25.707 102.295Q-25.826 102.410-25.990 102.410Q-26.166 102.410-26.281 102.287Q-26.397 102.164-26.397 101.996Q-26.397 101.590-26.016 101.481Q-25.635 101.371-25.076 101.371Q-24.807 101.371-24.539 101.449Q-24.272 101.528-24.047 101.678Q-23.823 101.828-23.686 102.049Q-23.549 102.270-23.549 102.547L-23.549 104.266Q-23.549 104.324-23.022 104.324Q-22.826 104.344-22.776 104.555L-22.776 104.645Q-22.826 104.860-23.022 104.883L-23.166 104.883Q-23.510 104.883-23.739 104.836Q-23.967 104.789-24.112 104.602Q-24.573 104.922-25.280 104.922Q-25.615 104.922-25.920 104.781Q-26.225 104.641-26.416 104.379Q-26.608 104.117-26.608 103.770M-25.967 103.778Q-25.967 104.051-25.725 104.207Q-25.483 104.363-25.198 104.363Q-24.979 104.363-24.746 104.305Q-24.514 104.246-24.352 104.108Q-24.190 103.969-24.190 103.746L-24.190 103.156Q-24.471 103.156-24.887 103.213Q-25.303 103.270-25.635 103.408Q-25.967 103.547-25.967 103.778M-22.424 106.004Q-22.424 105.895-22.373 105.803Q-22.323 105.711-22.231 105.660Q-22.139 105.610-22.033 105.610Q-21.924 105.610-21.832 105.660Q-21.740 105.711-21.690 105.803Q-21.639 105.895-21.639 106.004L-21.783 106.004Q-21.783 106.141-21.760 106.141Q-21.502 106.141-21.315 105.949Q-21.127 105.758-21.041 105.492L-20.830 104.883L-21.967 101.996L-22.295 101.996Q-22.490 101.973-22.545 101.754L-22.545 101.668Q-22.487 101.457-22.295 101.434L-21.135 101.434Q-20.940 101.457-20.889 101.668L-20.889 101.754Q-20.940 101.973-21.135 101.996L-21.401 101.996Q-21.065 102.844-20.821 103.498Q-20.576 104.153-20.576 104.242L-20.569 104.242Q-20.569 104.184-20.477 103.891Q-20.385 103.598-20.192 103.014Q-19.998 102.430-19.858 101.996L-20.135 101.996Q-20.346 101.973-20.385 101.754L-20.385 101.668Q-20.334 101.453-20.135 101.434L-18.983 101.434Q-18.776 101.457-18.737 101.668L-18.737 101.754Q-18.776 101.973-18.983 101.996L-19.303 101.996L-20.479 105.492Q-20.647 105.992-20.973 106.346Q-21.299 106.699-21.760 106.699Q-22.033 106.699-22.229 106.488Q-22.424 106.278-22.424 106.004M-15.010 103.395L-17.451 103.395Q-17.397 103.672-17.199 103.895Q-17.002 104.117-16.725 104.240Q-16.448 104.363-16.162 104.363Q-15.690 104.363-15.467 104.074Q-15.459 104.063-15.403 103.957Q-15.346 103.852-15.297 103.809Q-15.248 103.766-15.155 103.754L-15.010 103.754Q-14.819 103.774-14.760 103.988L-14.760 104.043Q-14.826 104.344-15.057 104.541Q-15.287 104.738-15.600 104.830Q-15.912 104.922-16.217 104.922Q-16.701 104.922-17.141 104.694Q-17.580 104.465-17.848 104.065Q-18.115 103.664-18.115 103.172L-18.115 103.113Q-18.115 102.645-17.869 102.242Q-17.623 101.840-17.215 101.606Q-16.807 101.371-16.338 101.371Q-15.834 101.371-15.481 101.594Q-15.127 101.817-14.944 102.205Q-14.760 102.594-14.760 103.098L-14.760 103.156Q-14.819 103.371-15.010 103.395M-17.444 102.844L-15.416 102.844Q-15.463 102.434-15.701 102.182Q-15.940 101.930-16.338 101.930Q-16.733 101.930-17.039 102.192Q-17.346 102.453-17.444 102.844M-14.053 104.645L-14.053 104.555Q-13.994 104.348-13.803 104.324L-13.092 104.324L-13.092 101.996L-13.803 101.996Q-13.998 101.973-14.053 101.754L-14.053 101.668Q-13.994 101.457-13.803 101.434L-12.701 101.434Q-12.502 101.453-12.451 101.668L-12.451 101.996Q-12.190 101.711-11.834 101.553Q-11.479 101.395-11.092 101.395Q-10.799 101.395-10.565 101.529Q-10.330 101.664-10.330 101.930Q-10.330 102.098-10.440 102.215Q-10.549 102.332-10.717 102.332Q-10.869 102.332-10.985 102.221Q-11.100 102.110-11.100 101.953Q-11.475 101.953-11.789 102.154Q-12.104 102.356-12.278 102.690Q-12.451 103.024-12.451 103.403L-12.451 104.324L-11.506 104.324Q-11.299 104.348-11.260 104.555L-11.260 104.645Q-11.299 104.860-11.506 104.883L-13.803 104.883Q-13.994 104.860-14.053 104.645M-9.830 104.645L-9.830 104.555Q-9.780 104.348-9.580 104.324L-9.311 104.324L-9.311 100.555L-9.580 100.555Q-9.780 100.531-9.830 100.317L-9.830 100.227Q-9.780 100.020-9.580 99.996L-8.799 99.996Q-8.670 99.996-8.565 100.070Q-8.459 100.145-8.420 100.258Q-8.143 101.047-7.983 101.496Q-7.823 101.945-7.569 102.664Q-7.315 103.383-7.176 103.793Q-7.037 104.203-7.037 104.242L-7.037 100.555L-7.311 100.555Q-7.506 100.531-7.557 100.317L-7.557 100.227Q-7.506 100.020-7.311 99.996L-6.237 99.996Q-6.041 100.020-5.990 100.227L-5.990 100.317Q-6.041 100.531-6.237 100.555L-6.510 100.555L-6.510 104.645Q-6.561 104.860-6.756 104.883L-7.022 104.883Q-7.147 104.883-7.250 104.809Q-7.354 104.735-7.397 104.617Q-7.694 103.770-8.067 102.721Q-8.440 101.672-8.610 101.184Q-8.780 100.695-8.783 100.637L-8.783 104.324L-8.510 104.324Q-8.319 104.348-8.260 104.555L-8.260 104.645Q-8.319 104.860-8.510 104.883L-9.580 104.883Q-9.780 104.860-9.830 104.645M-3.662 104.922Q-4.135 104.922-4.520 104.678Q-4.905 104.434-5.127 104.024Q-5.350 103.613-5.350 103.156Q-5.350 102.813-5.225 102.490Q-5.100 102.168-4.869 101.914Q-4.639 101.660-4.332 101.516Q-4.026 101.371-3.662 101.371Q-3.299 101.371-2.987 101.518Q-2.674 101.664-2.451 101.910Q-2.229 102.156-2.102 102.477Q-1.975 102.797-1.975 103.156Q-1.975 103.613-2.199 104.026Q-2.424 104.438-2.809 104.680Q-3.194 104.922-3.662 104.922M-3.662 104.363Q-3.198 104.363-2.906 103.969Q-2.615 103.574-2.615 103.090Q-2.615 102.797-2.750 102.529Q-2.885 102.262-3.125 102.096Q-3.365 101.930-3.662 101.930Q-3.967 101.930-4.205 102.096Q-4.444 102.262-4.578 102.529Q-4.713 102.797-4.713 103.090Q-4.713 103.570-4.420 103.967Q-4.127 104.363-3.662 104.363M-1.315 104.645L-1.315 104.555Q-1.256 104.348-1.065 104.324L-0.354 104.324L-0.354 101.996L-1.065 101.996Q-1.260 101.973-1.315 101.754L-1.315 101.668Q-1.256 101.457-1.065 101.434L0.037 101.434Q0.236 101.453 0.287 101.668L0.287 101.996Q0.549 101.711 0.904 101.553Q1.260 101.395 1.646 101.395Q1.939 101.395 2.174 101.529Q2.408 101.664 2.408 101.930Q2.408 102.098 2.299 102.215Q2.189 102.332 2.021 102.332Q1.869 102.332 1.754 102.221Q1.638 102.110 1.638 101.953Q1.263 101.953 0.949 102.154Q0.635 102.356 0.461 102.690Q0.287 103.024 0.287 103.403L0.287 104.324L1.232 104.324Q1.439 104.348 1.478 104.555L1.478 104.645Q1.439 104.860 1.232 104.883L-1.065 104.883Q-1.256 104.860-1.315 104.645M2.654 104.645L2.654 104.555Q2.705 104.344 2.900 104.324L3.099 104.324L3.099 101.996L2.900 101.996Q2.693 101.973 2.654 101.754L2.654 101.668Q2.705 101.453 2.900 101.434L3.381 101.434Q3.572 101.457 3.631 101.668Q3.951 101.395 4.365 101.395Q4.556 101.395 4.724 101.504Q4.892 101.613 4.967 101.785Q5.142 101.594 5.365 101.494Q5.588 101.395 5.830 101.395Q6.248 101.395 6.402 101.737Q6.556 102.078 6.556 102.547L6.556 104.324L6.756 104.324Q6.967 104.348 7.006 104.555L7.006 104.645Q6.955 104.860 6.756 104.883L5.939 104.883Q5.744 104.860 5.693 104.645L5.693 104.555Q5.744 104.348 5.939 104.324L6.029 104.324L6.029 102.578Q6.029 101.953 5.779 101.953Q5.447 101.953 5.269 102.264Q5.092 102.574 5.092 102.938L5.092 104.324L5.295 104.324Q5.502 104.348 5.541 104.555L5.541 104.645Q5.490 104.860 5.295 104.883L4.478 104.883Q4.279 104.860 4.228 104.645L4.228 104.555Q4.279 104.348 4.478 104.324L4.564 104.324L4.564 102.578Q4.564 101.953 4.318 101.953Q3.986 101.953 3.808 102.266Q3.631 102.578 3.631 102.938L3.631 104.324L3.830 104.324Q4.037 104.348 4.076 104.555L4.076 104.645Q4.025 104.863 3.830 104.883L2.900 104.883Q2.693 104.860 2.654 104.645\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M122.385 30.905h68.287V8.143h-68.287Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(166.538 -83.803)\">\u003Cpath d=\"M-30.674 104.684L-30.674 103.770Q-30.647 103.563-30.436 103.539L-30.268 103.539Q-30.104 103.563-30.045 103.723Q-29.842 104.363-29.115 104.363Q-28.908 104.363-28.680 104.328Q-28.451 104.293-28.283 104.178Q-28.115 104.063-28.115 103.860Q-28.115 103.649-28.338 103.535Q-28.561 103.422-28.834 103.379L-29.533 103.266Q-30.674 103.055-30.674 102.332Q-30.674 102.043-30.530 101.854Q-30.385 101.664-30.145 101.557Q-29.905 101.449-29.649 101.410Q-29.393 101.371-29.115 101.371Q-28.865 101.371-28.672 101.401Q-28.479 101.430-28.315 101.508Q-28.237 101.391-28.108 101.371L-28.030 101.371Q-27.932 101.383-27.869 101.445Q-27.807 101.508-27.795 101.602L-27.795 102.309Q-27.807 102.403-27.869 102.469Q-27.932 102.535-28.030 102.547L-28.198 102.547Q-28.291 102.535-28.358 102.469Q-28.424 102.403-28.436 102.309Q-28.436 101.930-29.131 101.930Q-29.479 101.930-29.797 102.012Q-30.115 102.094-30.115 102.340Q-30.115 102.606-29.444 102.715L-28.740 102.836Q-28.256 102.918-27.906 103.166Q-27.557 103.414-27.557 103.860Q-27.557 104.250-27.793 104.492Q-28.030 104.735-28.379 104.828Q-28.729 104.922-29.115 104.922Q-29.694 104.922-30.092 104.668Q-30.162 104.793-30.211 104.850Q-30.260 104.906-30.365 104.922L-30.436 104.922Q-30.651 104.899-30.674 104.684M-26.272 104.028L-26.272 101.996L-26.694 101.996Q-26.901 101.973-26.944 101.754L-26.944 101.668Q-26.897 101.457-26.694 101.434L-25.877 101.434Q-25.682 101.457-25.631 101.668L-25.631 103.996Q-25.631 104.231-25.461 104.297Q-25.291 104.363-25.006 104.363Q-24.799 104.363-24.604 104.287Q-24.408 104.211-24.283 104.061Q-24.158 103.910-24.158 103.699L-24.158 101.996L-24.580 101.996Q-24.791 101.973-24.830 101.754L-24.830 101.668Q-24.791 101.457-24.580 101.434L-23.768 101.434Q-23.569 101.457-23.518 101.668L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-23.908 104.883Q-24.108 104.860-24.158 104.660Q-24.561 104.922-25.069 104.922Q-25.303 104.922-25.518 104.881Q-25.733 104.840-25.899 104.738Q-26.065 104.637-26.168 104.459Q-26.272 104.281-26.272 104.028M-22.026 104.645L-22.026 100.555L-22.448 100.555Q-22.655 100.531-22.698 100.317L-22.698 100.227Q-22.655 100.020-22.448 99.996L-21.631 99.996Q-21.436 100.020-21.385 100.227L-21.385 101.738Q-21.174 101.570-20.910 101.483Q-20.647 101.395-20.377 101.395Q-20.037 101.395-19.740 101.539Q-19.444 101.684-19.229 101.936Q-19.014 102.188-18.899 102.500Q-18.783 102.813-18.783 103.156Q-18.783 103.621-19.010 104.031Q-19.237 104.442-19.623 104.682Q-20.010 104.922-20.479 104.922Q-20.998 104.922-21.385 104.555L-21.385 104.645Q-21.436 104.863-21.631 104.883L-21.776 104.883Q-21.967 104.860-22.026 104.645M-20.522 104.363Q-20.213 104.363-19.963 104.194Q-19.713 104.024-19.569 103.742Q-19.424 103.461-19.424 103.156Q-19.424 102.867-19.549 102.588Q-19.674 102.309-19.906 102.131Q-20.139 101.953-20.440 101.953Q-20.760 101.953-21.022 102.139Q-21.283 102.324-21.385 102.625L-21.385 103.477Q-21.295 103.844-21.074 104.104Q-20.854 104.363-20.522 104.363M-18.073 104.645L-18.073 104.555Q-18.022 104.348-17.826 104.324L-16.721 104.324L-16.721 100.555L-17.826 100.555Q-18.022 100.531-18.073 100.317L-18.073 100.227Q-18.022 100.020-17.826 99.996L-16.330 99.996Q-16.139 100.020-16.080 100.227L-16.080 104.324L-14.979 104.324Q-14.780 104.348-14.729 104.555L-14.729 104.645Q-14.780 104.860-14.979 104.883L-17.826 104.883Q-18.022 104.860-18.073 104.645M-13.869 103.770Q-13.869 103.324-13.455 103.067Q-13.041 102.809-12.500 102.709Q-11.959 102.610-11.451 102.602Q-11.451 102.387-11.586 102.235Q-11.721 102.082-11.928 102.006Q-12.135 101.930-12.346 101.930Q-12.690 101.930-12.850 101.953L-12.850 102.012Q-12.850 102.180-12.969 102.295Q-13.088 102.410-13.252 102.410Q-13.428 102.410-13.543 102.287Q-13.658 102.164-13.658 101.996Q-13.658 101.590-13.278 101.481Q-12.897 101.371-12.338 101.371Q-12.069 101.371-11.801 101.449Q-11.533 101.528-11.309 101.678Q-11.084 101.828-10.948 102.049Q-10.811 102.270-10.811 102.547L-10.811 104.266Q-10.811 104.324-10.283 104.324Q-10.088 104.344-10.037 104.555L-10.037 104.645Q-10.088 104.860-10.283 104.883L-10.428 104.883Q-10.772 104.883-11 104.836Q-11.229 104.789-11.373 104.602Q-11.834 104.922-12.541 104.922Q-12.877 104.922-13.182 104.781Q-13.487 104.641-13.678 104.379Q-13.869 104.117-13.869 103.770M-13.229 103.778Q-13.229 104.051-12.987 104.207Q-12.744 104.363-12.459 104.363Q-12.240 104.363-12.008 104.305Q-11.776 104.246-11.614 104.108Q-11.451 103.969-11.451 103.746L-11.451 103.156Q-11.733 103.156-12.149 103.213Q-12.565 103.270-12.897 103.408Q-13.229 103.547-13.229 103.778M-9.686 106.004Q-9.686 105.895-9.635 105.803Q-9.584 105.711-9.492 105.660Q-9.401 105.610-9.295 105.610Q-9.186 105.610-9.094 105.660Q-9.002 105.711-8.951 105.803Q-8.901 105.895-8.901 106.004L-9.045 106.004Q-9.045 106.141-9.022 106.141Q-8.764 106.141-8.576 105.949Q-8.389 105.758-8.303 105.492L-8.092 104.883L-9.229 101.996L-9.557 101.996Q-9.752 101.973-9.807 101.754L-9.807 101.668Q-9.748 101.457-9.557 101.434L-8.397 101.434Q-8.201 101.457-8.151 101.668L-8.151 101.754Q-8.201 101.973-8.397 101.996L-8.662 101.996Q-8.326 102.844-8.082 103.498Q-7.838 104.153-7.838 104.242L-7.830 104.242Q-7.830 104.184-7.739 103.891Q-7.647 103.598-7.453 103.014Q-7.260 102.430-7.119 101.996L-7.397 101.996Q-7.608 101.973-7.647 101.754L-7.647 101.668Q-7.596 101.453-7.397 101.434L-6.244 101.434Q-6.037 101.457-5.998 101.668L-5.998 101.754Q-6.037 101.973-6.244 101.996L-6.565 101.996L-7.740 105.492Q-7.908 105.992-8.235 106.346Q-8.561 106.699-9.022 106.699Q-9.295 106.699-9.490 106.488Q-9.686 106.278-9.686 106.004M-2.272 103.395L-4.713 103.395Q-4.658 103.672-4.461 103.895Q-4.264 104.117-3.987 104.240Q-3.709 104.363-3.424 104.363Q-2.951 104.363-2.729 104.074Q-2.721 104.063-2.664 103.957Q-2.608 103.852-2.559 103.809Q-2.510 103.766-2.416 103.754L-2.272 103.754Q-2.080 103.774-2.022 103.988L-2.022 104.043Q-2.088 104.344-2.319 104.541Q-2.549 104.738-2.862 104.830Q-3.174 104.922-3.479 104.922Q-3.963 104.922-4.403 104.694Q-4.842 104.465-5.110 104.065Q-5.377 103.664-5.377 103.172L-5.377 103.113Q-5.377 102.645-5.131 102.242Q-4.885 101.840-4.477 101.606Q-4.069 101.371-3.600 101.371Q-3.096 101.371-2.742 101.594Q-2.389 101.817-2.205 102.205Q-2.022 102.594-2.022 103.098L-2.022 103.156Q-2.080 103.371-2.272 103.395M-4.705 102.844L-2.678 102.844Q-2.725 102.434-2.963 102.182Q-3.201 101.930-3.600 101.930Q-3.994 101.930-4.301 102.192Q-4.608 102.453-4.705 102.844M-1.315 104.645L-1.315 104.555Q-1.256 104.348-1.065 104.324L-0.354 104.324L-0.354 101.996L-1.065 101.996Q-1.260 101.973-1.315 101.754L-1.315 101.668Q-1.256 101.457-1.065 101.434L0.037 101.434Q0.236 101.453 0.287 101.668L0.287 101.996Q0.549 101.711 0.904 101.553Q1.260 101.395 1.646 101.395Q1.939 101.395 2.174 101.529Q2.408 101.664 2.408 101.930Q2.408 102.098 2.299 102.215Q2.189 102.332 2.021 102.332Q1.869 102.332 1.754 102.221Q1.638 102.110 1.638 101.953Q1.263 101.953 0.949 102.154Q0.635 102.356 0.461 102.690Q0.287 103.024 0.287 103.403L0.287 104.324L1.232 104.324Q1.439 104.348 1.478 104.555L1.478 104.645Q1.439 104.860 1.232 104.883L-1.065 104.883Q-1.256 104.860-1.315 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(166.538 -83.803)\">\u003Cpath d=\"M7.310 104.645L7.310 104.555Q7.361 104.348 7.556 104.324L8.439 104.324L8.439 101.996L7.584 101.996Q7.385 101.973 7.334 101.754L7.334 101.668Q7.385 101.457 7.584 101.434L8.439 101.434L8.439 100.981Q8.439 100.516 8.845 100.235Q9.252 99.953 9.732 99.953Q10.045 99.953 10.289 100.074Q10.533 100.195 10.533 100.477Q10.533 100.641 10.424 100.758Q10.314 100.875 10.150 100.875Q10.002 100.875 9.881 100.770Q9.760 100.664 9.760 100.516L9.678 100.516Q9.525 100.516 9.388 100.576Q9.252 100.637 9.166 100.752Q9.080 100.867 9.080 101.012L9.080 101.434L10.111 101.434Q10.306 101.453 10.357 101.668L10.357 101.754Q10.306 101.973 10.111 101.996L9.080 101.996L9.080 104.324L9.959 104.324Q10.154 104.348 10.205 104.555L10.205 104.645Q10.154 104.860 9.959 104.883L7.556 104.883Q7.361 104.860 7.310 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M165.064-23.155a8.536 8.536 0 1 0-17.071 0 8.536 8.536 0 0 0 17.071 0Zm-8.536 0\"\u002F>\u003Cg transform=\"translate(184.483 -126.037)\">\u003Cpath d=\"M-28.139 103.067L-30.612 103.067Q-30.690 103.055-30.739 103.006Q-30.787 102.957-30.787 102.883Q-30.787 102.809-30.739 102.760Q-30.690 102.711-30.612 102.699L-28.139 102.699L-28.139 100.219Q-28.112 100.051-27.955 100.051Q-27.881 100.051-27.832 100.100Q-27.783 100.149-27.772 100.219L-27.772 102.699L-25.299 102.699Q-25.131 102.731-25.131 102.883Q-25.131 103.035-25.299 103.067L-27.772 103.067L-27.772 105.547Q-27.783 105.617-27.832 105.666Q-27.881 105.715-27.955 105.715Q-28.112 105.715-28.139 105.547\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(175.038 -169.391)\">\u003Cpath d=\"M-29.139 104.922Q-29.612 104.922-29.996 104.678Q-30.381 104.434-30.604 104.024Q-30.826 103.613-30.826 103.156Q-30.826 102.813-30.701 102.490Q-30.576 102.168-30.346 101.914Q-30.115 101.660-29.809 101.516Q-29.502 101.371-29.139 101.371Q-28.776 101.371-28.463 101.518Q-28.151 101.664-27.928 101.910Q-27.705 102.156-27.578 102.477Q-27.451 102.797-27.451 103.156Q-27.451 103.613-27.676 104.026Q-27.901 104.438-28.285 104.680Q-28.670 104.922-29.139 104.922M-29.139 104.363Q-28.674 104.363-28.383 103.969Q-28.092 103.574-28.092 103.090Q-28.092 102.797-28.227 102.529Q-28.362 102.262-28.602 102.096Q-28.842 101.930-29.139 101.930Q-29.444 101.930-29.682 102.096Q-29.920 102.262-30.055 102.529Q-30.190 102.797-30.190 103.090Q-30.190 103.570-29.897 103.967Q-29.604 104.363-29.139 104.363M-26.272 104.028L-26.272 101.996L-26.694 101.996Q-26.901 101.973-26.944 101.754L-26.944 101.668Q-26.897 101.457-26.694 101.434L-25.877 101.434Q-25.682 101.457-25.631 101.668L-25.631 103.996Q-25.631 104.231-25.461 104.297Q-25.291 104.363-25.006 104.363Q-24.799 104.363-24.604 104.287Q-24.408 104.211-24.283 104.061Q-24.158 103.910-24.158 103.699L-24.158 101.996L-24.580 101.996Q-24.791 101.973-24.830 101.754L-24.830 101.668Q-24.791 101.457-24.580 101.434L-23.768 101.434Q-23.569 101.457-23.518 101.668L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-23.908 104.883Q-24.108 104.860-24.158 104.660Q-24.561 104.922-25.069 104.922Q-25.303 104.922-25.518 104.881Q-25.733 104.840-25.899 104.738Q-26.065 104.637-26.168 104.459Q-26.272 104.281-26.272 104.028M-21.569 103.778L-21.569 101.996L-22.319 101.996Q-22.518 101.973-22.569 101.754L-22.569 101.668Q-22.518 101.457-22.319 101.434L-21.569 101.434L-21.569 100.684Q-21.518 100.477-21.319 100.449L-21.174 100.449Q-20.979 100.477-20.928 100.684L-20.928 101.434L-19.569 101.434Q-19.377 101.453-19.319 101.668L-19.319 101.754Q-19.373 101.973-19.569 101.996L-20.928 101.996L-20.928 103.746Q-20.928 104.363-20.354 104.363Q-20.104 104.363-19.940 104.178Q-19.776 103.992-19.776 103.746Q-19.776 103.653-19.703 103.582Q-19.631 103.512-19.530 103.500L-19.385 103.500Q-19.186 103.524-19.135 103.731L-19.135 103.778Q-19.135 104.102-19.319 104.365Q-19.502 104.629-19.795 104.776Q-20.088 104.922-20.408 104.922Q-20.920 104.922-21.244 104.612Q-21.569 104.301-21.569 103.778M-18.451 106.426L-18.451 106.340Q-18.408 106.121-18.201 106.098L-17.780 106.098L-17.780 101.996L-18.201 101.996Q-18.408 101.973-18.451 101.754L-18.451 101.668Q-18.405 101.457-18.201 101.434L-17.385 101.434Q-17.190 101.453-17.139 101.668L-17.139 101.738Q-16.928 101.570-16.664 101.483Q-16.401 101.395-16.131 101.395Q-15.791 101.395-15.494 101.539Q-15.198 101.684-14.983 101.936Q-14.768 102.188-14.653 102.500Q-14.537 102.813-14.537 103.156Q-14.537 103.621-14.764 104.031Q-14.990 104.442-15.377 104.682Q-15.764 104.922-16.233 104.922Q-16.752 104.922-17.139 104.555L-17.139 106.098L-16.713 106.098Q-16.506 106.121-16.467 106.340L-16.467 106.426Q-16.506 106.637-16.713 106.660L-18.201 106.660Q-18.405 106.637-18.451 106.426M-16.276 104.363Q-15.967 104.363-15.717 104.194Q-15.467 104.024-15.323 103.742Q-15.178 103.461-15.178 103.156Q-15.178 102.867-15.303 102.588Q-15.428 102.309-15.660 102.131Q-15.893 101.953-16.194 101.953Q-16.514 101.953-16.776 102.139Q-17.037 102.324-17.139 102.625L-17.139 103.477Q-17.049 103.844-16.828 104.104Q-16.608 104.363-16.276 104.363M-13.533 104.028L-13.533 101.996L-13.955 101.996Q-14.162 101.973-14.205 101.754L-14.205 101.668Q-14.158 101.457-13.955 101.434L-13.139 101.434Q-12.944 101.457-12.893 101.668L-12.893 103.996Q-12.893 104.231-12.723 104.297Q-12.553 104.363-12.268 104.363Q-12.061 104.363-11.865 104.287Q-11.670 104.211-11.545 104.061Q-11.420 103.910-11.420 103.699L-11.420 101.996L-11.842 101.996Q-12.053 101.973-12.092 101.754L-12.092 101.668Q-12.053 101.457-11.842 101.434L-11.030 101.434Q-10.830 101.457-10.780 101.668L-10.780 104.324L-10.354 104.324Q-10.147 104.348-10.108 104.555L-10.108 104.645Q-10.147 104.860-10.354 104.883L-11.170 104.883Q-11.369 104.860-11.420 104.660Q-11.823 104.922-12.330 104.922Q-12.565 104.922-12.780 104.881Q-12.994 104.840-13.160 104.738Q-13.326 104.637-13.430 104.459Q-13.533 104.281-13.533 104.028M-8.830 103.778L-8.830 101.996L-9.580 101.996Q-9.780 101.973-9.830 101.754L-9.830 101.668Q-9.780 101.457-9.580 101.434L-8.830 101.434L-8.830 100.684Q-8.780 100.477-8.580 100.449L-8.436 100.449Q-8.240 100.477-8.190 100.684L-8.190 101.434L-6.830 101.434Q-6.639 101.453-6.580 101.668L-6.580 101.754Q-6.635 101.973-6.830 101.996L-8.190 101.996L-8.190 103.746Q-8.190 104.363-7.615 104.363Q-7.365 104.363-7.201 104.178Q-7.037 103.992-7.037 103.746Q-7.037 103.653-6.965 103.582Q-6.893 103.512-6.791 103.500L-6.647 103.500Q-6.448 103.524-6.397 103.731L-6.397 103.778Q-6.397 104.102-6.580 104.365Q-6.764 104.629-7.057 104.776Q-7.350 104.922-7.670 104.922Q-8.182 104.922-8.506 104.612Q-8.830 104.301-8.830 103.778\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M156.528 98.016V76.385\"\u002F>\u003Cpath stroke=\"none\" d=\"m156.528 73.785-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M156.528 50.622V33.705\"\u002F>\u003Cpath stroke=\"none\" d=\"m156.528 31.105-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M156.528 7.943v-19.762\"\u002F>\u003Cpath stroke=\"none\" d=\"m156.528-14.419-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M156.528-31.89v-24.708\"\u002F>\u003Cpath stroke=\"none\" d=\"m156.528-59.198-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M193.517 99.192c36.989-39.834 36.989-79.668 1.703-120.382\"\u002F>\u003Cpath stroke=\"none\" d=\"m193.517-23.155 1.153 4.506.55-2.541 2.593-.183\"\u002F>\u003Cg transform=\"translate(256.251 -64.241)\">\u003Cpath d=\"M-30.643 104.645L-30.643 104.555Q-30.592 104.348-30.397 104.324L-29.358 104.324L-29.358 101.996L-30.330 101.996Q-30.530 101.973-30.580 101.754L-30.580 101.668Q-30.530 101.457-30.330 101.434L-28.963 101.434Q-28.768 101.453-28.717 101.668L-28.717 104.324L-27.803 104.324Q-27.608 104.348-27.557 104.555L-27.557 104.645Q-27.608 104.860-27.803 104.883L-30.397 104.883Q-30.592 104.860-30.643 104.645M-29.612 100.457L-29.612 100.403Q-29.612 100.231-29.475 100.110Q-29.338 99.988-29.162 99.988Q-28.990 99.988-28.854 100.110Q-28.717 100.231-28.717 100.403L-28.717 100.457Q-28.717 100.633-28.854 100.754Q-28.990 100.875-29.162 100.875Q-29.338 100.875-29.475 100.754Q-29.612 100.633-29.612 100.457M-25.151 104.922Q-25.615 104.922-25.981 104.672Q-26.346 104.422-26.551 104.018Q-26.756 103.613-26.756 103.156Q-26.756 102.813-26.631 102.492Q-26.506 102.172-26.274 101.922Q-26.041 101.672-25.737 101.533Q-25.432 101.395-25.076 101.395Q-24.565 101.395-24.158 101.715L-24.158 100.555L-24.580 100.555Q-24.791 100.531-24.830 100.317L-24.830 100.227Q-24.791 100.020-24.580 99.996L-23.768 99.996Q-23.569 100.020-23.518 100.227L-23.518 104.324L-23.092 104.324Q-22.885 104.348-22.846 104.555L-22.846 104.645Q-22.885 104.860-23.092 104.883L-23.908 104.883Q-24.108 104.860-24.158 104.645L-24.158 104.516Q-24.354 104.707-24.615 104.815Q-24.877 104.922-25.151 104.922M-25.112 104.363Q-24.752 104.363-24.500 104.094Q-24.248 103.824-24.158 103.449L-24.158 102.617Q-24.217 102.430-24.344 102.279Q-24.471 102.129-24.649 102.041Q-24.826 101.953-25.022 101.953Q-25.330 101.953-25.580 102.123Q-25.830 102.293-25.975 102.578Q-26.119 102.863-26.119 103.164Q-26.119 103.613-25.834 103.988Q-25.549 104.363-25.112 104.363M-19.256 103.395L-21.698 103.395Q-21.643 103.672-21.446 103.895Q-21.248 104.117-20.971 104.240Q-20.694 104.363-20.408 104.363Q-19.936 104.363-19.713 104.074Q-19.705 104.063-19.649 103.957Q-19.592 103.852-19.543 103.809Q-19.494 103.766-19.401 103.754L-19.256 103.754Q-19.065 103.774-19.006 103.988L-19.006 104.043Q-19.073 104.344-19.303 104.541Q-19.533 104.738-19.846 104.830Q-20.158 104.922-20.463 104.922Q-20.948 104.922-21.387 104.694Q-21.826 104.465-22.094 104.065Q-22.362 103.664-22.362 103.172L-22.362 103.113Q-22.362 102.645-22.115 102.242Q-21.869 101.840-21.461 101.606Q-21.053 101.371-20.584 101.371Q-20.080 101.371-19.727 101.594Q-19.373 101.817-19.190 102.205Q-19.006 102.594-19.006 103.098L-19.006 103.156Q-19.065 103.371-19.256 103.395M-21.690 102.844L-19.662 102.844Q-19.709 102.434-19.948 102.182Q-20.186 101.930-20.584 101.930Q-20.979 101.930-21.285 102.192Q-21.592 102.453-21.690 102.844M-18.451 104.645L-18.451 104.555Q-18.408 104.348-18.201 104.324L-17.780 104.324L-17.780 101.996L-18.201 101.996Q-18.408 101.973-18.451 101.754L-18.451 101.668Q-18.405 101.457-18.201 101.434L-17.385 101.434Q-17.190 101.457-17.139 101.668L-17.139 101.754L-17.147 101.778Q-16.920 101.598-16.647 101.496Q-16.373 101.395-16.080 101.395Q-15.733 101.395-15.494 101.535Q-15.256 101.676-15.141 101.934Q-15.026 102.192-15.026 102.547L-15.026 104.324L-14.600 104.324Q-14.393 104.348-14.354 104.555L-14.354 104.645Q-14.393 104.860-14.600 104.883L-15.994 104.883Q-16.190 104.860-16.240 104.645L-16.240 104.555Q-16.190 104.344-15.994 104.324L-15.666 104.324L-15.666 102.578Q-15.666 102.270-15.756 102.112Q-15.846 101.953-16.139 101.953Q-16.408 101.953-16.637 102.084Q-16.865 102.215-17.002 102.444Q-17.139 102.672-17.139 102.938L-17.139 104.324L-16.713 104.324Q-16.506 104.348-16.467 104.555L-16.467 104.645Q-16.506 104.860-16.713 104.883L-18.201 104.883Q-18.408 104.860-18.451 104.645M-13.076 103.778L-13.076 101.996L-13.826 101.996Q-14.026 101.973-14.076 101.754L-14.076 101.668Q-14.026 101.457-13.826 101.434L-13.076 101.434L-13.076 100.684Q-13.026 100.477-12.826 100.449L-12.682 100.449Q-12.487 100.477-12.436 100.684L-12.436 101.434L-11.076 101.434Q-10.885 101.453-10.826 101.668L-10.826 101.754Q-10.881 101.973-11.076 101.996L-12.436 101.996L-12.436 103.746Q-12.436 104.363-11.862 104.363Q-11.612 104.363-11.448 104.178Q-11.283 103.992-11.283 103.746Q-11.283 103.653-11.211 103.582Q-11.139 103.512-11.037 103.500L-10.893 103.500Q-10.694 103.524-10.643 103.731L-10.643 103.778Q-10.643 104.102-10.826 104.365Q-11.010 104.629-11.303 104.776Q-11.596 104.922-11.916 104.922Q-12.428 104.922-12.752 104.612Q-13.076 104.301-13.076 103.778M-9.412 104.645L-9.412 104.555Q-9.362 104.348-9.166 104.324L-8.127 104.324L-8.127 101.996L-9.100 101.996Q-9.299 101.973-9.350 101.754L-9.350 101.668Q-9.299 101.457-9.100 101.434L-7.733 101.434Q-7.537 101.453-7.487 101.668L-7.487 104.324L-6.573 104.324Q-6.377 104.348-6.326 104.555L-6.326 104.645Q-6.377 104.860-6.573 104.883L-9.166 104.883Q-9.362 104.860-9.412 104.645M-8.381 100.457L-8.381 100.403Q-8.381 100.231-8.244 100.110Q-8.108 99.988-7.932 99.988Q-7.760 99.988-7.623 100.110Q-7.487 100.231-7.487 100.403L-7.487 100.457Q-7.487 100.633-7.623 100.754Q-7.760 100.875-7.932 100.875Q-8.108 100.875-8.244 100.754Q-8.381 100.633-8.381 100.457M-4.584 103.778L-4.584 101.996L-5.334 101.996Q-5.533 101.973-5.584 101.754L-5.584 101.668Q-5.533 101.457-5.334 101.434L-4.584 101.434L-4.584 100.684Q-4.533 100.477-4.334 100.449L-4.190 100.449Q-3.994 100.477-3.944 100.684L-3.944 101.434L-2.584 101.434Q-2.393 101.453-2.334 101.668L-2.334 101.754Q-2.389 101.973-2.584 101.996L-3.944 101.996L-3.944 103.746Q-3.944 104.363-3.369 104.363Q-3.119 104.363-2.955 104.178Q-2.791 103.992-2.791 103.746Q-2.791 103.653-2.719 103.582Q-2.647 103.512-2.545 103.500L-2.401 103.500Q-2.201 103.524-2.151 103.731L-2.151 103.778Q-2.151 104.102-2.334 104.365Q-2.518 104.629-2.811 104.776Q-3.104 104.922-3.424 104.922Q-3.936 104.922-4.260 104.612Q-4.584 104.301-4.584 103.778M-1.194 106.004Q-1.194 105.895-1.143 105.803Q-1.092 105.711-1 105.660Q-0.908 105.610-0.803 105.610Q-0.694 105.610-0.602 105.660Q-0.510 105.711-0.459 105.803Q-0.408 105.895-0.408 106.004L-0.553 106.004Q-0.553 106.141-0.530 106.141Q-0.272 106.141-0.084 105.949Q0.103 105.758 0.189 105.492L0.400 104.883L-0.737 101.996L-1.065 101.996Q-1.260 101.973-1.315 101.754L-1.315 101.668Q-1.256 101.457-1.065 101.434L0.095 101.434Q0.291 101.457 0.342 101.668L0.342 101.754Q0.291 101.973 0.095 101.996L-0.170 101.996Q0.166 102.844 0.410 103.498Q0.654 104.153 0.654 104.242L0.662 104.242Q0.662 104.184 0.754 103.891Q0.845 103.598 1.039 103.014Q1.232 102.430 1.373 101.996L1.095 101.996Q0.885 101.973 0.845 101.754L0.845 101.668Q0.896 101.453 1.095 101.434L2.248 101.434Q2.455 101.457 2.494 101.668L2.494 101.754Q2.455 101.973 2.248 101.996L1.927 101.996L0.752 105.492Q0.584 105.992 0.258 106.346Q-0.069 106.699-0.530 106.699Q-0.803 106.699-0.998 106.488Q-1.194 106.278-1.194 106.004\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(170.788 24.006)\">\u003Cpath d=\"M-31.190 106.426L-31.190 106.340Q-31.147 106.121-30.940 106.098L-30.518 106.098L-30.518 101.996L-30.940 101.996Q-31.147 101.973-31.190 101.754L-31.190 101.668Q-31.143 101.457-30.940 101.434L-30.123 101.434Q-29.928 101.453-29.877 101.668L-29.877 101.738Q-29.666 101.570-29.403 101.483Q-29.139 101.395-28.869 101.395Q-28.530 101.395-28.233 101.539Q-27.936 101.684-27.721 101.936Q-27.506 102.188-27.391 102.500Q-27.276 102.813-27.276 103.156Q-27.276 103.621-27.502 104.031Q-27.729 104.442-28.115 104.682Q-28.502 104.922-28.971 104.922Q-29.490 104.922-29.877 104.555L-29.877 106.098L-29.451 106.098Q-29.244 106.121-29.205 106.340L-29.205 106.426Q-29.244 106.637-29.451 106.660L-30.940 106.660Q-31.143 106.637-31.190 106.426M-29.014 104.363Q-28.705 104.363-28.455 104.194Q-28.205 104.024-28.061 103.742Q-27.916 103.461-27.916 103.156Q-27.916 102.867-28.041 102.588Q-28.166 102.309-28.399 102.131Q-28.631 101.953-28.932 101.953Q-29.252 101.953-29.514 102.139Q-29.776 102.324-29.877 102.625L-29.877 103.477Q-29.787 103.844-29.567 104.104Q-29.346 104.363-29.014 104.363M-26.791 104.645L-26.791 104.555Q-26.733 104.348-26.541 104.324L-25.830 104.324L-25.830 101.996L-26.541 101.996Q-26.737 101.973-26.791 101.754L-26.791 101.668Q-26.733 101.457-26.541 101.434L-25.440 101.434Q-25.240 101.453-25.190 101.668L-25.190 101.996Q-24.928 101.711-24.573 101.553Q-24.217 101.395-23.830 101.395Q-23.537 101.395-23.303 101.529Q-23.069 101.664-23.069 101.930Q-23.069 102.098-23.178 102.215Q-23.287 102.332-23.455 102.332Q-23.608 102.332-23.723 102.221Q-23.838 102.110-23.838 101.953Q-24.213 101.953-24.528 102.154Q-24.842 102.356-25.016 102.690Q-25.190 103.024-25.190 103.403L-25.190 104.324L-24.244 104.324Q-24.037 104.348-23.998 104.555L-23.998 104.645Q-24.037 104.860-24.244 104.883L-26.541 104.883Q-26.733 104.860-26.791 104.645M-19.256 103.395L-21.698 103.395Q-21.643 103.672-21.446 103.895Q-21.248 104.117-20.971 104.240Q-20.694 104.363-20.408 104.363Q-19.936 104.363-19.713 104.074Q-19.705 104.063-19.649 103.957Q-19.592 103.852-19.543 103.809Q-19.494 103.766-19.401 103.754L-19.256 103.754Q-19.065 103.774-19.006 103.988L-19.006 104.043Q-19.073 104.344-19.303 104.541Q-19.533 104.738-19.846 104.830Q-20.158 104.922-20.463 104.922Q-20.948 104.922-21.387 104.694Q-21.826 104.465-22.094 104.065Q-22.362 103.664-22.362 103.172L-22.362 103.113Q-22.362 102.645-22.115 102.242Q-21.869 101.840-21.461 101.606Q-21.053 101.371-20.584 101.371Q-20.080 101.371-19.727 101.594Q-19.373 101.817-19.190 102.205Q-19.006 102.594-19.006 103.098L-19.006 103.156Q-19.065 103.371-19.256 103.395M-21.690 102.844L-19.662 102.844Q-19.709 102.434-19.948 102.182Q-20.186 101.930-20.584 101.930Q-20.979 101.930-21.285 102.192Q-21.592 102.453-21.690 102.844M-15.026 102.746L-17.768 102.746Q-17.893 102.735-17.979 102.649Q-18.065 102.563-18.065 102.434Q-18.065 102.305-17.979 102.223Q-17.893 102.141-17.768 102.129L-15.026 102.129Q-14.901 102.141-14.819 102.223Q-14.737 102.305-14.737 102.434Q-14.737 102.563-14.819 102.649Q-14.901 102.735-15.026 102.746M-14.205 104.645L-14.205 104.555Q-14.162 104.348-13.955 104.324L-13.533 104.324L-13.533 101.996L-13.955 101.996Q-14.162 101.973-14.205 101.754L-14.205 101.668Q-14.158 101.457-13.955 101.434L-13.139 101.434Q-12.944 101.457-12.893 101.668L-12.893 101.754L-12.901 101.778Q-12.674 101.598-12.401 101.496Q-12.127 101.395-11.834 101.395Q-11.487 101.395-11.248 101.535Q-11.010 101.676-10.895 101.934Q-10.780 102.192-10.780 102.547L-10.780 104.324L-10.354 104.324Q-10.147 104.348-10.108 104.555L-10.108 104.645Q-10.147 104.860-10.354 104.883L-11.748 104.883Q-11.944 104.860-11.994 104.645L-11.994 104.555Q-11.944 104.344-11.748 104.324L-11.420 104.324L-11.420 102.578Q-11.420 102.270-11.510 102.112Q-11.600 101.953-11.893 101.953Q-12.162 101.953-12.391 102.084Q-12.619 102.215-12.756 102.444Q-12.893 102.672-12.893 102.938L-12.893 104.324L-12.467 104.324Q-12.260 104.348-12.221 104.555L-12.221 104.645Q-12.260 104.860-12.467 104.883L-13.955 104.883Q-14.162 104.860-14.205 104.645M-7.908 104.922Q-8.381 104.922-8.766 104.678Q-9.151 104.434-9.373 104.024Q-9.596 103.613-9.596 103.156Q-9.596 102.813-9.471 102.490Q-9.346 102.168-9.115 101.914Q-8.885 101.660-8.578 101.516Q-8.272 101.371-7.908 101.371Q-7.545 101.371-7.233 101.518Q-6.920 101.664-6.698 101.910Q-6.475 102.156-6.348 102.477Q-6.221 102.797-6.221 103.156Q-6.221 103.613-6.446 104.026Q-6.670 104.438-7.055 104.680Q-7.440 104.922-7.908 104.922M-7.908 104.363Q-7.444 104.363-7.153 103.969Q-6.862 103.574-6.862 103.090Q-6.862 102.797-6.996 102.529Q-7.131 102.262-7.371 102.096Q-7.612 101.930-7.908 101.930Q-8.213 101.930-8.451 102.096Q-8.690 102.262-8.824 102.529Q-8.959 102.797-8.959 103.090Q-8.959 103.570-8.666 103.967Q-8.373 104.363-7.908 104.363M-5.561 104.645L-5.561 104.555Q-5.502 104.348-5.311 104.324L-4.600 104.324L-4.600 101.996L-5.311 101.996Q-5.506 101.973-5.561 101.754L-5.561 101.668Q-5.502 101.457-5.311 101.434L-4.209 101.434Q-4.010 101.453-3.959 101.668L-3.959 101.996Q-3.698 101.711-3.342 101.553Q-2.987 101.395-2.600 101.395Q-2.307 101.395-2.073 101.529Q-1.838 101.664-1.838 101.930Q-1.838 102.098-1.948 102.215Q-2.057 102.332-2.225 102.332Q-2.377 102.332-2.492 102.221Q-2.608 102.110-2.608 101.953Q-2.983 101.953-3.297 102.154Q-3.612 102.356-3.785 102.690Q-3.959 103.024-3.959 103.403L-3.959 104.324L-3.014 104.324Q-2.807 104.348-2.768 104.555L-2.768 104.645Q-2.807 104.860-3.014 104.883L-5.311 104.883Q-5.502 104.860-5.561 104.645M-1.592 104.645L-1.592 104.555Q-1.541 104.344-1.346 104.324L-1.147 104.324L-1.147 101.996L-1.346 101.996Q-1.553 101.973-1.592 101.754L-1.592 101.668Q-1.541 101.453-1.346 101.434L-0.865 101.434Q-0.674 101.457-0.615 101.668Q-0.295 101.395 0.119 101.395Q0.310 101.395 0.478 101.504Q0.646 101.613 0.720 101.785Q0.896 101.594 1.119 101.494Q1.342 101.395 1.584 101.395Q2.002 101.395 2.156 101.737Q2.310 102.078 2.310 102.547L2.310 104.324L2.510 104.324Q2.720 104.348 2.760 104.555L2.760 104.645Q2.709 104.860 2.510 104.883L1.693 104.883Q1.498 104.860 1.447 104.645L1.447 104.555Q1.498 104.348 1.693 104.324L1.783 104.324L1.783 102.578Q1.783 101.953 1.533 101.953Q1.201 101.953 1.023 102.264Q0.845 102.574 0.845 102.938L0.845 104.324L1.049 104.324Q1.256 104.348 1.295 104.555L1.295 104.645Q1.244 104.860 1.049 104.883L0.232 104.883Q0.033 104.860-0.018 104.645L-0.018 104.555Q0.033 104.348 0.232 104.324L0.318 104.324L0.318 102.578Q0.318 101.953 0.072 101.953Q-0.260 101.953-0.438 102.266Q-0.615 102.578-0.615 102.938L-0.615 104.324L-0.416 104.324Q-0.209 104.348-0.170 104.555L-0.170 104.645Q-0.221 104.863-0.416 104.883L-1.346 104.883Q-1.553 104.860-1.592 104.645\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">Post-norm (left) routes every skip through LayerNorm; pre-norm (right) normalizes only the branch input, leaving a clean identity highway (blue) up the stack.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:355.645px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 266.733 118.288\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-68.537 26.285h202.26\"\u002F>\u003Cpath stroke=\"none\" d=\"m136.323 26.285-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003Cg transform=\"translate(208.593 93.98)\">\u003Cpath d=\"M-68.467-57.530L-68.467-57.616Q-68.424-57.835-68.217-57.858L-67.795-57.858L-67.795-61.960L-68.217-61.960Q-68.424-61.983-68.467-62.202L-68.467-62.288Q-68.420-62.499-68.217-62.522L-67.400-62.522Q-67.205-62.503-67.154-62.288L-67.154-62.218Q-66.943-62.386-66.680-62.473Q-66.416-62.561-66.146-62.561Q-65.807-62.561-65.510-62.417Q-65.213-62.272-64.998-62.020Q-64.783-61.768-64.668-61.456Q-64.553-61.143-64.553-60.800Q-64.553-60.335-64.779-59.925Q-65.006-59.514-65.392-59.274Q-65.779-59.034-66.248-59.034Q-66.767-59.034-67.154-59.401L-67.154-57.858L-66.728-57.858Q-66.521-57.835-66.482-57.616L-66.482-57.530Q-66.521-57.319-66.728-57.296L-68.217-57.296Q-68.420-57.319-68.467-57.530M-66.291-59.593Q-65.982-59.593-65.732-59.762Q-65.482-59.932-65.338-60.214Q-65.193-60.495-65.193-60.800Q-65.193-61.089-65.318-61.368Q-65.443-61.647-65.676-61.825Q-65.908-62.003-66.209-62.003Q-66.529-62.003-66.791-61.817Q-67.053-61.632-67.154-61.331L-67.154-60.479Q-67.064-60.112-66.844-59.852Q-66.623-59.593-66.291-59.593M-62.170-59.034Q-62.642-59.034-63.027-59.278Q-63.412-59.522-63.635-59.932Q-63.857-60.343-63.857-60.800Q-63.857-61.143-63.732-61.466Q-63.607-61.788-63.377-62.042Q-63.146-62.296-62.840-62.440Q-62.533-62.585-62.170-62.585Q-61.807-62.585-61.494-62.438Q-61.182-62.292-60.959-62.046Q-60.736-61.800-60.609-61.479Q-60.482-61.159-60.482-60.800Q-60.482-60.343-60.707-59.930Q-60.932-59.518-61.316-59.276Q-61.701-59.034-62.170-59.034M-62.170-59.593Q-61.705-59.593-61.414-59.987Q-61.123-60.382-61.123-60.866Q-61.123-61.159-61.258-61.427Q-61.392-61.694-61.633-61.860Q-61.873-62.026-62.170-62.026Q-62.475-62.026-62.713-61.860Q-62.951-61.694-63.086-61.427Q-63.221-61.159-63.221-60.866Q-63.221-60.386-62.928-59.989Q-62.635-59.593-62.170-59.593M-59.459-59.272L-59.459-60.186Q-59.432-60.393-59.221-60.417L-59.053-60.417Q-58.889-60.393-58.830-60.233Q-58.627-59.593-57.900-59.593Q-57.693-59.593-57.465-59.628Q-57.236-59.663-57.068-59.778Q-56.900-59.893-56.900-60.096Q-56.900-60.307-57.123-60.421Q-57.346-60.534-57.619-60.577L-58.318-60.690Q-59.459-60.901-59.459-61.624Q-59.459-61.913-59.314-62.102Q-59.170-62.292-58.930-62.399Q-58.689-62.507-58.433-62.546Q-58.178-62.585-57.900-62.585Q-57.650-62.585-57.457-62.555Q-57.264-62.526-57.100-62.448Q-57.021-62.565-56.892-62.585L-56.814-62.585Q-56.717-62.573-56.654-62.511Q-56.592-62.448-56.580-62.354L-56.580-61.647Q-56.592-61.553-56.654-61.487Q-56.717-61.421-56.814-61.409L-56.982-61.409Q-57.076-61.421-57.142-61.487Q-57.209-61.553-57.221-61.647Q-57.221-62.026-57.916-62.026Q-58.264-62.026-58.582-61.944Q-58.900-61.862-58.900-61.616Q-58.900-61.350-58.228-61.241L-57.525-61.120Q-57.041-61.038-56.691-60.790Q-56.342-60.542-56.342-60.096Q-56.342-59.706-56.578-59.464Q-56.814-59.221-57.164-59.128Q-57.514-59.034-57.900-59.034Q-58.478-59.034-58.877-59.288Q-58.947-59.163-58.996-59.106Q-59.045-59.050-59.150-59.034L-59.221-59.034Q-59.435-59.057-59.459-59.272M-55.182-59.311L-55.182-59.401Q-55.131-59.608-54.935-59.632L-53.896-59.632L-53.896-61.960L-54.869-61.960Q-55.068-61.983-55.119-62.202L-55.119-62.288Q-55.068-62.499-54.869-62.522L-53.502-62.522Q-53.307-62.503-53.256-62.288L-53.256-59.632L-52.342-59.632Q-52.146-59.608-52.096-59.401L-52.096-59.311Q-52.146-59.096-52.342-59.073L-54.935-59.073Q-55.131-59.096-55.182-59.311M-54.150-63.499L-54.150-63.553Q-54.150-63.725-54.014-63.846Q-53.877-63.968-53.701-63.968Q-53.529-63.968-53.392-63.846Q-53.256-63.725-53.256-63.553L-53.256-63.499Q-53.256-63.323-53.392-63.202Q-53.529-63.081-53.701-63.081Q-53.877-63.081-54.014-63.202Q-54.150-63.323-54.150-63.499M-50.353-60.178L-50.353-61.960L-51.103-61.960Q-51.303-61.983-51.353-62.202L-51.353-62.288Q-51.303-62.499-51.103-62.522L-50.353-62.522L-50.353-63.272Q-50.303-63.479-50.103-63.507L-49.959-63.507Q-49.764-63.479-49.713-63.272L-49.713-62.522L-48.353-62.522Q-48.162-62.503-48.103-62.288L-48.103-62.202Q-48.158-61.983-48.353-61.960L-49.713-61.960L-49.713-60.210Q-49.713-59.593-49.139-59.593Q-48.889-59.593-48.725-59.778Q-48.560-59.964-48.560-60.210Q-48.560-60.303-48.488-60.374Q-48.416-60.444-48.314-60.456L-48.170-60.456Q-47.971-60.432-47.920-60.225L-47.920-60.178Q-47.920-59.854-48.103-59.591Q-48.287-59.327-48.580-59.180Q-48.873-59.034-49.193-59.034Q-49.705-59.034-50.029-59.344Q-50.353-59.655-50.353-60.178M-46.689-59.311L-46.689-59.401Q-46.639-59.608-46.443-59.632L-45.404-59.632L-45.404-61.960L-46.377-61.960Q-46.576-61.983-46.627-62.202L-46.627-62.288Q-46.576-62.499-46.377-62.522L-45.010-62.522Q-44.814-62.503-44.764-62.288L-44.764-59.632L-43.850-59.632Q-43.654-59.608-43.603-59.401L-43.603-59.311Q-43.654-59.096-43.850-59.073L-46.443-59.073Q-46.639-59.096-46.689-59.311M-45.658-63.499L-45.658-63.553Q-45.658-63.725-45.521-63.846Q-45.385-63.968-45.209-63.968Q-45.037-63.968-44.900-63.846Q-44.764-63.725-44.764-63.553L-44.764-63.499Q-44.764-63.323-44.900-63.202Q-45.037-63.081-45.209-63.081Q-45.385-63.081-45.521-63.202Q-45.658-63.323-45.658-63.499M-40.939-59.034Q-41.412-59.034-41.797-59.278Q-42.182-59.522-42.404-59.932Q-42.627-60.343-42.627-60.800Q-42.627-61.143-42.502-61.466Q-42.377-61.788-42.146-62.042Q-41.916-62.296-41.609-62.440Q-41.303-62.585-40.939-62.585Q-40.576-62.585-40.264-62.438Q-39.951-62.292-39.728-62.046Q-39.506-61.800-39.379-61.479Q-39.252-61.159-39.252-60.800Q-39.252-60.343-39.476-59.930Q-39.701-59.518-40.086-59.276Q-40.471-59.034-40.939-59.034M-40.939-59.593Q-40.475-59.593-40.183-59.987Q-39.892-60.382-39.892-60.866Q-39.892-61.159-40.027-61.427Q-40.162-61.694-40.402-61.860Q-40.642-62.026-40.939-62.026Q-41.244-62.026-41.482-61.860Q-41.721-61.694-41.855-61.427Q-41.990-61.159-41.990-60.866Q-41.990-60.386-41.697-59.989Q-41.404-59.593-40.939-59.593M-38.744-59.311L-38.744-59.401Q-38.701-59.608-38.494-59.632L-38.072-59.632L-38.072-61.960L-38.494-61.960Q-38.701-61.983-38.744-62.202L-38.744-62.288Q-38.697-62.499-38.494-62.522L-37.678-62.522Q-37.482-62.499-37.432-62.288L-37.432-62.202L-37.439-62.178Q-37.213-62.358-36.939-62.460Q-36.666-62.561-36.373-62.561Q-36.025-62.561-35.787-62.421Q-35.549-62.280-35.433-62.022Q-35.318-61.764-35.318-61.409L-35.318-59.632L-34.892-59.632Q-34.685-59.608-34.646-59.401L-34.646-59.311Q-34.685-59.096-34.892-59.073L-36.287-59.073Q-36.482-59.096-36.533-59.311L-36.533-59.401Q-36.482-59.612-36.287-59.632L-35.959-59.632L-35.959-61.378Q-35.959-61.686-36.049-61.844Q-36.139-62.003-36.432-62.003Q-36.701-62.003-36.930-61.872Q-37.158-61.741-37.295-61.512Q-37.432-61.284-37.432-61.018L-37.432-59.632L-37.006-59.632Q-36.799-59.608-36.760-59.401L-36.760-59.311Q-36.799-59.096-37.006-59.073L-38.494-59.073Q-38.701-59.096-38.744-59.311\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"m-68.537-59.073 1.578-3.188 1.578-2.987 1.577-2.598 1.578-2.045 1.578-1.365 1.578-.596 1.577.207 1.578 1 1.578 1.729 1.577 2.348 1.578 2.821 1.578 3.115 1.578 3.212 1.577 3.11 1.578 2.808 1.578 2.332 1.577 1.709 1.578.976 1.578.184 1.578-.62 1.577-1.386 1.578-2.064 1.578-2.612 1.578-2.996 1.577-3.19 1.578-3.184 1.578-2.978 1.577-2.584 1.578-2.027 1.578-1.342 1.578-.574 1.577.232 1.578 1.023 1.578 1.749 1.577 2.364 1.578 2.832 1.578 3.121 1.578 3.212 1.577 3.102 1.578 2.798 1.578 2.316 1.577 1.688 1.578.954 1.578.16 1.578-.644 1.577-1.408 1.578-2.082 1.578-2.626 1.577-3.005 1.578-3.192 1.578-3.181 1.578-2.97 1.577-2.57 1.578-2.007 1.578-1.321 1.577-.55 1.578.256 1.578 1.046 1.578 1.768 1.577 2.381 1.578 2.844 1.578 3.126 1.577 3.212 1.578 3.096 1.578 2.786 1.578 2.298 1.577 1.668 1.578.93 1.578.137 1.578-.668 1.577-1.428 1.578-2.1 1.578-2.64 1.577-3.013 1.578-3.196 1.578-3.178 1.578-2.96 1.577-2.554 1.578-1.99 1.578-1.298 1.577-.527 1.578.28 1.578 1.068 1.578 1.788 1.577 2.398 1.578 2.854 1.578 3.132 1.577 3.211 1.578 3.09 1.578 2.774 1.578 2.281 1.577 1.647 1.578.908 1.578.113 1.577-.691 1.578-1.45 1.578-2.12 1.578-2.653 1.577-3.02 1.578-3.198 1.578-3.174 1.577-2.951 1.578-2.54 1.578-1.97 1.578-1.278 1.577-.502 1.578.304 1.578 1.09 1.577 1.809 1.578 2.413 1.578 2.865 1.578 3.137 1.577 3.21 1.578 3.084 1.578 2.761 1.577 2.265 1.578 1.626 1.578.886 1.578.088\" style=\"stroke-width:.8\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(194.166 2.444)\">\u003Cpath d=\"M-67.920-59.311L-67.920-59.401Q-67.869-59.608-67.674-59.632L-66.635-59.632L-66.635-61.960L-67.607-61.960Q-67.807-61.983-67.857-62.202L-67.857-62.288Q-67.807-62.499-67.607-62.522L-66.240-62.522Q-66.045-62.503-65.994-62.288L-65.994-59.632L-65.080-59.632Q-64.885-59.608-64.834-59.401L-64.834-59.311Q-64.885-59.096-65.080-59.073L-67.674-59.073Q-67.869-59.096-67.920-59.311M-66.889-63.499L-66.889-63.553Q-66.889-63.725-66.752-63.846Q-66.615-63.968-66.439-63.968Q-66.267-63.968-66.131-63.846Q-65.994-63.725-65.994-63.553L-65.994-63.499Q-65.994-63.323-66.131-63.202Q-66.267-63.081-66.439-63.081Q-66.615-63.081-66.752-63.202Q-66.889-63.323-66.889-63.499\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(194.166 2.444)\">\u003Cpath d=\"M-59.451-59.272L-59.451-60.186Q-59.424-60.393-59.213-60.417L-59.045-60.417Q-58.881-60.393-58.822-60.233Q-58.619-59.593-57.892-59.593Q-57.685-59.593-57.457-59.628Q-57.228-59.663-57.060-59.778Q-56.892-59.893-56.892-60.096Q-56.892-60.307-57.115-60.421Q-57.338-60.534-57.611-60.577L-58.310-60.690Q-59.451-60.901-59.451-61.624Q-59.451-61.913-59.307-62.102Q-59.162-62.292-58.922-62.399Q-58.682-62.507-58.426-62.546Q-58.170-62.585-57.892-62.585Q-57.642-62.585-57.449-62.555Q-57.256-62.526-57.092-62.448Q-57.014-62.565-56.885-62.585L-56.807-62.585Q-56.709-62.573-56.646-62.511Q-56.584-62.448-56.572-62.354L-56.572-61.647Q-56.584-61.553-56.646-61.487Q-56.709-61.421-56.807-61.409L-56.974-61.409Q-57.068-61.421-57.135-61.487Q-57.201-61.553-57.213-61.647Q-57.213-62.026-57.908-62.026Q-58.256-62.026-58.574-61.944Q-58.892-61.862-58.892-61.616Q-58.892-61.350-58.221-61.241L-57.517-61.120Q-57.033-61.038-56.683-60.790Q-56.334-60.542-56.334-60.096Q-56.334-59.706-56.570-59.464Q-56.807-59.221-57.156-59.128Q-57.506-59.034-57.892-59.034Q-58.471-59.034-58.869-59.288Q-58.939-59.163-58.988-59.106Q-59.037-59.050-59.142-59.034L-59.213-59.034Q-59.428-59.057-59.451-59.272M-55.846-59.311L-55.846-59.401Q-55.795-59.612-55.599-59.632L-55.400-59.632L-55.400-61.960L-55.599-61.960Q-55.807-61.983-55.846-62.202L-55.846-62.288Q-55.795-62.503-55.599-62.522L-55.119-62.522Q-54.928-62.499-54.869-62.288Q-54.549-62.561-54.135-62.561Q-53.943-62.561-53.775-62.452Q-53.607-62.343-53.533-62.171Q-53.357-62.362-53.135-62.462Q-52.912-62.561-52.670-62.561Q-52.252-62.561-52.098-62.219Q-51.943-61.878-51.943-61.409L-51.943-59.632L-51.744-59.632Q-51.533-59.608-51.494-59.401L-51.494-59.311Q-51.545-59.096-51.744-59.073L-52.560-59.073Q-52.756-59.096-52.807-59.311L-52.807-59.401Q-52.756-59.608-52.560-59.632L-52.471-59.632L-52.471-61.378Q-52.471-62.003-52.721-62.003Q-53.053-62.003-53.230-61.692Q-53.408-61.382-53.408-61.018L-53.408-59.632L-53.205-59.632Q-52.998-59.608-52.959-59.401L-52.959-59.311Q-53.010-59.096-53.205-59.073L-54.021-59.073Q-54.221-59.096-54.271-59.311L-54.271-59.401Q-54.221-59.608-54.021-59.632L-53.935-59.632L-53.935-61.378Q-53.935-62.003-54.182-62.003Q-54.514-62.003-54.691-61.690Q-54.869-61.378-54.869-61.018L-54.869-59.632L-54.670-59.632Q-54.463-59.608-54.424-59.401L-54.424-59.311Q-54.474-59.093-54.670-59.073L-55.599-59.073Q-55.807-59.096-55.846-59.311M-51.139-60.186Q-51.139-60.632-50.724-60.889Q-50.310-61.147-49.769-61.247Q-49.228-61.346-48.721-61.354Q-48.721-61.569-48.855-61.721Q-48.990-61.874-49.197-61.950Q-49.404-62.026-49.615-62.026Q-49.959-62.026-50.119-62.003L-50.119-61.944Q-50.119-61.776-50.238-61.661Q-50.357-61.546-50.521-61.546Q-50.697-61.546-50.812-61.669Q-50.928-61.792-50.928-61.960Q-50.928-62.366-50.547-62.475Q-50.166-62.585-49.607-62.585Q-49.338-62.585-49.070-62.507Q-48.803-62.428-48.578-62.278Q-48.353-62.128-48.217-61.907Q-48.080-61.686-48.080-61.409L-48.080-59.690Q-48.080-59.632-47.553-59.632Q-47.357-59.612-47.307-59.401L-47.307-59.311Q-47.357-59.096-47.553-59.073L-47.697-59.073Q-48.041-59.073-48.269-59.120Q-48.498-59.167-48.642-59.354Q-49.103-59.034-49.810-59.034Q-50.146-59.034-50.451-59.175Q-50.756-59.315-50.947-59.577Q-51.139-59.839-51.139-60.186M-50.498-60.178Q-50.498-59.905-50.256-59.749Q-50.014-59.593-49.728-59.593Q-49.510-59.593-49.277-59.651Q-49.045-59.710-48.883-59.848Q-48.721-59.987-48.721-60.210L-48.721-60.800Q-49.002-60.800-49.418-60.743Q-49.834-60.686-50.166-60.548Q-50.498-60.409-50.498-60.178M-46.849-59.311L-46.849-59.401Q-46.799-59.608-46.603-59.632L-45.498-59.632L-45.498-63.401L-46.603-63.401Q-46.799-63.425-46.849-63.639L-46.849-63.729Q-46.799-63.936-46.603-63.960L-45.107-63.960Q-44.916-63.936-44.857-63.729L-44.857-59.632L-43.756-59.632Q-43.557-59.608-43.506-59.401L-43.506-59.311Q-43.557-59.096-43.756-59.073L-46.603-59.073Q-46.799-59.096-46.849-59.311M-42.603-59.311L-42.603-59.401Q-42.553-59.608-42.357-59.632L-41.252-59.632L-41.252-63.401L-42.357-63.401Q-42.553-63.425-42.603-63.639L-42.603-63.729Q-42.553-63.936-42.357-63.960L-40.861-63.960Q-40.670-63.936-40.611-63.729L-40.611-59.632L-39.510-59.632Q-39.310-59.608-39.260-59.401L-39.260-59.311Q-39.310-59.096-39.510-59.073L-42.357-59.073Q-42.553-59.096-42.603-59.311\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(194.166 2.444)\">\u003Cpath d=\"M-31.423-58.432Q-31.954-58.741-32.354-59.229Q-32.755-59.718-32.966-60.311Q-33.177-60.905-33.177-61.522Q-33.177-62.139-32.968-62.727Q-32.759-63.315-32.362-63.796Q-31.966-64.276-31.431-64.600Q-31.360-64.624-31.329-64.624L-31.239-64.624Q-31.141-64.612-31.075-64.546Q-31.009-64.479-31.009-64.378Q-31.009-64.233-31.110-64.171Q-31.559-63.882-31.886-63.466Q-32.212-63.050-32.374-62.557Q-32.536-62.065-32.536-61.522Q-32.536-61.116-32.440-60.729Q-32.345-60.343-32.167-60.007Q-31.989-59.671-31.729-59.387Q-31.470-59.104-31.122-58.874Q-31.009-58.796-31.009-58.659Q-31.009-58.561-31.075-58.491Q-31.141-58.421-31.239-58.409L-31.329-58.409Q-31.388-58.409-31.423-58.432M-29.970-59.311L-29.970-59.401Q-29.919-59.608-29.724-59.632L-28.841-59.632L-28.841-61.960L-29.696-61.960Q-29.895-61.983-29.946-62.202L-29.946-62.288Q-29.895-62.499-29.696-62.522L-28.841-62.522L-28.841-62.975Q-28.841-63.440-28.434-63.721Q-28.028-64.003-27.548-64.003Q-27.235-64.003-26.991-63.882Q-26.747-63.761-26.747-63.479Q-26.747-63.315-26.856-63.198Q-26.966-63.081-27.130-63.081Q-27.278-63.081-27.399-63.186Q-27.520-63.292-27.520-63.440L-27.602-63.440Q-27.755-63.440-27.891-63.380Q-28.028-63.319-28.114-63.204Q-28.200-63.089-28.200-62.944L-28.200-62.522L-27.169-62.522Q-26.974-62.503-26.923-62.288L-26.923-62.202Q-26.974-61.983-27.169-61.960L-28.200-61.960L-28.200-59.632L-27.321-59.632Q-27.126-59.608-27.075-59.401L-27.075-59.311Q-27.126-59.096-27.321-59.073L-29.724-59.073Q-29.919-59.096-29.970-59.311M-25.638-60.186Q-25.638-60.632-25.224-60.889Q-24.809-61.147-24.268-61.247Q-23.727-61.346-23.220-61.354Q-23.220-61.569-23.354-61.721Q-23.489-61.874-23.696-61.950Q-23.903-62.026-24.114-62.026Q-24.458-62.026-24.618-62.003L-24.618-61.944Q-24.618-61.776-24.737-61.661Q-24.856-61.546-25.020-61.546Q-25.196-61.546-25.311-61.669Q-25.427-61.792-25.427-61.960Q-25.427-62.366-25.046-62.475Q-24.665-62.585-24.106-62.585Q-23.837-62.585-23.569-62.507Q-23.302-62.428-23.077-62.278Q-22.852-62.128-22.716-61.907Q-22.579-61.686-22.579-61.409L-22.579-59.690Q-22.579-59.632-22.052-59.632Q-21.856-59.612-21.806-59.401L-21.806-59.311Q-21.856-59.096-22.052-59.073L-22.196-59.073Q-22.540-59.073-22.768-59.120Q-22.997-59.167-23.141-59.354Q-23.602-59.034-24.309-59.034Q-24.645-59.034-24.950-59.175Q-25.255-59.315-25.446-59.577Q-25.638-59.839-25.638-60.186M-24.997-60.178Q-24.997-59.905-24.755-59.749Q-24.513-59.593-24.227-59.593Q-24.009-59.593-23.776-59.651Q-23.544-59.710-23.382-59.848Q-23.220-59.987-23.220-60.210L-23.220-60.800Q-23.501-60.800-23.917-60.743Q-24.333-60.686-24.665-60.548Q-24.997-60.409-24.997-60.178M-21.212-59.272L-21.212-60.186Q-21.184-60.393-20.974-60.417L-20.806-60.417Q-20.641-60.393-20.583-60.233Q-20.380-59.593-19.653-59.593Q-19.446-59.593-19.218-59.628Q-18.989-59.663-18.821-59.778Q-18.653-59.893-18.653-60.096Q-18.653-60.307-18.876-60.421Q-19.099-60.534-19.372-60.577L-20.071-60.690Q-21.212-60.901-21.212-61.624Q-21.212-61.913-21.067-62.102Q-20.923-62.292-20.682-62.399Q-20.442-62.507-20.186-62.546Q-19.931-62.585-19.653-62.585Q-19.403-62.585-19.210-62.555Q-19.016-62.526-18.852-62.448Q-18.774-62.565-18.645-62.585L-18.567-62.585Q-18.470-62.573-18.407-62.511Q-18.345-62.448-18.333-62.354L-18.333-61.647Q-18.345-61.553-18.407-61.487Q-18.470-61.421-18.567-61.409L-18.735-61.409Q-18.829-61.421-18.895-61.487Q-18.962-61.553-18.974-61.647Q-18.974-62.026-19.669-62.026Q-20.016-62.026-20.335-61.944Q-20.653-61.862-20.653-61.616Q-20.653-61.350-19.981-61.241L-19.278-61.120Q-18.794-61.038-18.444-60.790Q-18.095-60.542-18.095-60.096Q-18.095-59.706-18.331-59.464Q-18.567-59.221-18.917-59.128Q-19.266-59.034-19.653-59.034Q-20.231-59.034-20.630-59.288Q-20.700-59.163-20.749-59.106Q-20.798-59.050-20.903-59.034L-20.974-59.034Q-21.188-59.057-21.212-59.272M-16.352-60.178L-16.352-61.960L-17.102-61.960Q-17.302-61.983-17.352-62.202L-17.352-62.288Q-17.302-62.499-17.102-62.522L-16.352-62.522L-16.352-63.272Q-16.302-63.479-16.102-63.507L-15.958-63.507Q-15.763-63.479-15.712-63.272L-15.712-62.522L-14.352-62.522Q-14.161-62.503-14.102-62.288L-14.102-62.202Q-14.157-61.983-14.352-61.960L-15.712-61.960L-15.712-60.210Q-15.712-59.593-15.138-59.593Q-14.888-59.593-14.724-59.778Q-14.559-59.964-14.559-60.210Q-14.559-60.303-14.487-60.374Q-14.415-60.444-14.313-60.456L-14.169-60.456Q-13.970-60.432-13.919-60.225L-13.919-60.178Q-13.919-59.854-14.102-59.591Q-14.286-59.327-14.579-59.180Q-14.872-59.034-15.192-59.034Q-15.704-59.034-16.028-59.344Q-16.352-59.655-16.352-60.178M-12.266-58.409L-12.352-58.409Q-12.458-58.421-12.526-58.493Q-12.595-58.565-12.595-58.659Q-12.595-58.800-12.489-58.866Q-12.153-59.081-11.884-59.370Q-11.614-59.659-11.431-60.007Q-11.247-60.354-11.157-60.733Q-11.067-61.112-11.067-61.522Q-11.067-62.061-11.231-62.553Q-11.395-63.046-11.714-63.460Q-12.032-63.874-12.474-64.163Q-12.595-64.245-12.595-64.378Q-12.595-64.475-12.526-64.544Q-12.458-64.612-12.352-64.624L-12.266-64.624Q-12.212-64.624-12.177-64.600Q-11.790-64.378-11.450-64.030Q-11.110-63.682-10.890-63.288Q-10.669-62.893-10.548-62.448Q-10.427-62.003-10.427-61.522Q-10.427-61.038-10.548-60.587Q-10.669-60.136-10.893-59.739Q-11.118-59.343-11.442-59.009Q-11.766-58.675-12.169-58.432Q-12.239-58.409-12.266-58.409\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"m-68.537-24.93 1.578-1.113 1.578-1.106 1.577-1.088 1.578-1.064 1.578-1.03 1.578-.99 1.577-.94 1.578-.885 1.578-.824 1.577-.754 1.578-.68 1.578-.601 1.578-.517 1.577-.429 1.578-.337 1.578-.245 1.577-.148 1.578-.052 1.578.045 1.578.142 1.577.238 1.578.331 1.578.423 1.578.51 1.577.596 1.578.675 1.578.75 1.577.818 1.578.881 1.578.938 1.578.986 1.577 1.028 1.578 1.061 1.578 1.087 1.577 1.105 1.578 1.113 1.578 1.114 1.578 1.105 1.577 1.09 1.578 1.066 1.578 1.033 1.577.992 1.578.944 1.578.89 1.578.827 1.577.76 1.578.685 1.578.607 1.577.522 1.578.435 1.578.344 1.578.25 1.577.156 1.578.058 1.578-.038 1.577-.136 1.578-.23 1.578-.326 1.578-.417 1.577-.505 1.578-.59 1.578-.67 1.577-.744 1.578-.813 1.578-.878 1.578-.933 1.577-.984 1.578-1.025 1.578-1.06 1.578-1.085 1.577-1.103 1.578-1.113 1.578-1.114 1.577-1.107 1.578-1.09 1.578-1.068 1.578-1.036 1.577-.995 1.578-.948 1.578-.893 1.577-.832 1.578-.764 1.578-.691 1.578-.612 1.577-.528 1.578-.442 1.578-.35 1.577-.257 1.578-.161 1.578-.066 1.578.032 1.577.13 1.578.224 1.578.318 1.577.41 1.578.5 1.578.584 1.578.664 1.577.74 1.578.81 1.578.872 1.577.93 1.578.98 1.578 1.023 1.578 1.058 1.577 1.083 1.578 1.104 1.578 1.112 1.577 1.114 1.578 1.108 1.578 1.092 1.578 1.07 1.577 1.037 1.578.998 1.578.952 1.577.897 1.578.836 1.578.77 1.578.695\" style=\"stroke-width:.8\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(194.166 36.588)\">\u003Cpath d=\"M-67.920-59.311L-67.920-59.401Q-67.869-59.608-67.674-59.632L-66.635-59.632L-66.635-61.960L-67.607-61.960Q-67.807-61.983-67.857-62.202L-67.857-62.288Q-67.807-62.499-67.607-62.522L-66.240-62.522Q-66.045-62.503-65.994-62.288L-65.994-59.632L-65.080-59.632Q-64.885-59.608-64.834-59.401L-64.834-59.311Q-64.885-59.096-65.080-59.073L-67.674-59.073Q-67.869-59.096-67.920-59.311M-66.889-63.499L-66.889-63.553Q-66.889-63.725-66.752-63.846Q-66.615-63.968-66.439-63.968Q-66.267-63.968-66.131-63.846Q-65.994-63.725-65.994-63.553L-65.994-63.499Q-65.994-63.323-66.131-63.202Q-66.267-63.081-66.439-63.081Q-66.615-63.081-66.752-63.202Q-66.889-63.323-66.889-63.499\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(194.166 36.588)\">\u003Cpath d=\"M-60.092-59.311L-60.092-59.401Q-60.041-59.612-59.846-59.632L-59.646-59.632L-59.646-61.960L-59.846-61.960Q-60.053-61.983-60.092-62.202L-60.092-62.288Q-60.041-62.503-59.846-62.522L-59.365-62.522Q-59.174-62.499-59.115-62.288Q-58.795-62.561-58.381-62.561Q-58.189-62.561-58.021-62.452Q-57.853-62.343-57.779-62.171Q-57.603-62.362-57.381-62.462Q-57.158-62.561-56.916-62.561Q-56.498-62.561-56.344-62.219Q-56.189-61.878-56.189-61.409L-56.189-59.632L-55.990-59.632Q-55.779-59.608-55.740-59.401L-55.740-59.311Q-55.791-59.096-55.990-59.073L-56.807-59.073Q-57.002-59.096-57.053-59.311L-57.053-59.401Q-57.002-59.608-56.807-59.632L-56.717-59.632L-56.717-61.378Q-56.717-62.003-56.967-62.003Q-57.299-62.003-57.476-61.692Q-57.654-61.382-57.654-61.018L-57.654-59.632L-57.451-59.632Q-57.244-59.608-57.205-59.401L-57.205-59.311Q-57.256-59.096-57.451-59.073L-58.267-59.073Q-58.467-59.096-58.517-59.311L-58.517-59.401Q-58.467-59.608-58.267-59.632L-58.182-59.632L-58.182-61.378Q-58.182-62.003-58.428-62.003Q-58.760-62.003-58.937-61.690Q-59.115-61.378-59.115-61.018L-59.115-59.632L-58.916-59.632Q-58.709-59.608-58.670-59.401L-58.670-59.311Q-58.721-59.093-58.916-59.073L-59.846-59.073Q-60.053-59.096-60.092-59.311M-55.174-59.311L-55.174-59.401Q-55.123-59.608-54.928-59.632L-53.889-59.632L-53.889-61.960L-54.861-61.960Q-55.060-61.983-55.111-62.202L-55.111-62.288Q-55.060-62.499-54.861-62.522L-53.494-62.522Q-53.299-62.503-53.248-62.288L-53.248-59.632L-52.334-59.632Q-52.139-59.608-52.088-59.401L-52.088-59.311Q-52.139-59.096-52.334-59.073L-54.928-59.073Q-55.123-59.096-55.174-59.311M-54.142-63.499L-54.142-63.553Q-54.142-63.725-54.006-63.846Q-53.869-63.968-53.693-63.968Q-53.521-63.968-53.385-63.846Q-53.248-63.725-53.248-63.553L-53.248-63.499Q-53.248-63.323-53.385-63.202Q-53.521-63.081-53.693-63.081Q-53.869-63.081-54.006-63.202Q-54.142-63.323-54.142-63.499M-49.682-59.034Q-50.146-59.034-50.512-59.284Q-50.877-59.534-51.082-59.938Q-51.287-60.343-51.287-60.800Q-51.287-61.143-51.162-61.464Q-51.037-61.784-50.805-62.034Q-50.572-62.284-50.267-62.423Q-49.963-62.561-49.607-62.561Q-49.096-62.561-48.689-62.241L-48.689-63.401L-49.111-63.401Q-49.322-63.425-49.361-63.639L-49.361-63.729Q-49.322-63.936-49.111-63.960L-48.299-63.960Q-48.099-63.936-48.049-63.729L-48.049-59.632L-47.623-59.632Q-47.416-59.608-47.377-59.401L-47.377-59.311Q-47.416-59.096-47.623-59.073L-48.439-59.073Q-48.639-59.096-48.689-59.311L-48.689-59.440Q-48.885-59.249-49.146-59.141Q-49.408-59.034-49.682-59.034M-49.642-59.593Q-49.283-59.593-49.031-59.862Q-48.779-60.132-48.689-60.507L-48.689-61.339Q-48.748-61.526-48.875-61.677Q-49.002-61.827-49.180-61.915Q-49.357-62.003-49.553-62.003Q-49.861-62.003-50.111-61.833Q-50.361-61.663-50.506-61.378Q-50.650-61.093-50.650-60.792Q-50.650-60.343-50.365-59.968Q-50.080-59.593-49.642-59.593\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"m-68.537 9.213 1.578-.371 1.578-.372 1.577-.37 1.578-.37 1.578-.369 1.578-.366 1.577-.366 1.578-.363 1.578-.36 1.577-.358 1.578-.354 1.578-.352 1.578-.347 1.577-.343 1.578-.34 1.578-.335 1.577-.33 1.578-.324 1.578-.32 1.578-.313 1.577-.308 1.578-.301 1.578-.296 1.578-.288 1.577-.282 1.578-.274 1.578-.267 1.577-.26 1.578-.251 1.578-.244 1.578-.235 1.577-.227 1.578-.218 1.578-.21 1.577-.2 1.578-.19 1.578-.183 1.578-.172 1.577-.163 1.578-.152 1.578-.143 1.577-.134 1.578-.122 1.578-.113 1.578-.102 1.577-.092 1.578-.082 1.578-.07 1.577-.06 1.578-.05 1.578-.039 1.578-.028 1.577-.017 1.578-.007 1.578.005 1.577.014 1.578.026 1.578.037 1.578.047 1.577.058 1.578.069 1.578.08 1.577.089 1.578.1 1.578.11 1.578.122 1.577.13 1.578.141 1.578.151 1.578.161 1.577.17 1.578.18 1.578.19 1.577.198 1.578.207 1.578.217 1.578.225 1.577.233 1.578.242 1.578.25 1.577.258 1.578.265 1.578.273 1.578.28 1.577.288 1.578.293 1.578.3 1.577.307 1.578.313 1.578.318 1.578.324 1.577.328 1.578.334 1.578.339 1.577.342 1.578.347 1.578.35 1.578.354 1.577.357 1.578.36 1.578.363 1.577.364 1.578.367 1.578.368 1.578.37 1.577.37 1.578.372 1.578.371 1.577.371 1.578.372 1.578.37 1.578.37 1.577.37 1.578.367 1.578.366 1.577.363 1.578.36 1.578.359 1.578.355\" style=\"stroke-width:.8\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(194.166 70.175)\">\u003Cpath d=\"M-67.920-59.311L-67.920-59.401Q-67.869-59.608-67.674-59.632L-66.635-59.632L-66.635-61.960L-67.607-61.960Q-67.807-61.983-67.857-62.202L-67.857-62.288Q-67.807-62.499-67.607-62.522L-66.240-62.522Q-66.045-62.503-65.994-62.288L-65.994-59.632L-65.080-59.632Q-64.885-59.608-64.834-59.401L-64.834-59.311Q-64.885-59.096-65.080-59.073L-67.674-59.073Q-67.869-59.096-67.920-59.311M-66.889-63.499L-66.889-63.553Q-66.889-63.725-66.752-63.846Q-66.615-63.968-66.439-63.968Q-66.267-63.968-66.131-63.846Q-65.994-63.725-65.994-63.553L-65.994-63.499Q-65.994-63.323-66.131-63.202Q-66.267-63.081-66.439-63.081Q-66.615-63.081-66.752-63.202Q-66.889-63.323-66.889-63.499\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(194.166 70.175)\">\u003Cpath d=\"M-59.588-59.311L-59.588-59.401Q-59.537-59.608-59.342-59.632L-58.236-59.632L-58.236-63.401L-59.342-63.401Q-59.537-63.425-59.588-63.639L-59.588-63.729Q-59.537-63.936-59.342-63.960L-57.846-63.960Q-57.654-63.936-57.596-63.729L-57.596-59.632L-56.494-59.632Q-56.295-59.608-56.244-59.401L-56.244-59.311Q-56.295-59.096-56.494-59.073L-59.342-59.073Q-59.537-59.096-59.588-59.311M-55.385-60.186Q-55.385-60.632-54.971-60.889Q-54.557-61.147-54.016-61.247Q-53.474-61.346-52.967-61.354Q-52.967-61.569-53.101-61.721Q-53.236-61.874-53.443-61.950Q-53.650-62.026-53.861-62.026Q-54.205-62.026-54.365-62.003L-54.365-61.944Q-54.365-61.776-54.484-61.661Q-54.603-61.546-54.767-61.546Q-54.943-61.546-55.058-61.669Q-55.174-61.792-55.174-61.960Q-55.174-62.366-54.793-62.475Q-54.412-62.585-53.853-62.585Q-53.584-62.585-53.316-62.507Q-53.049-62.428-52.824-62.278Q-52.599-62.128-52.463-61.907Q-52.326-61.686-52.326-61.409L-52.326-59.690Q-52.326-59.632-51.799-59.632Q-51.603-59.612-51.553-59.401L-51.553-59.311Q-51.603-59.096-51.799-59.073L-51.943-59.073Q-52.287-59.073-52.516-59.120Q-52.744-59.167-52.889-59.354Q-53.349-59.034-54.057-59.034Q-54.392-59.034-54.697-59.175Q-55.002-59.315-55.193-59.577Q-55.385-59.839-55.385-60.186M-54.744-60.178Q-54.744-59.905-54.502-59.749Q-54.260-59.593-53.974-59.593Q-53.756-59.593-53.523-59.651Q-53.291-59.710-53.129-59.848Q-52.967-59.987-52.967-60.210L-52.967-60.800Q-53.248-60.800-53.664-60.743Q-54.080-60.686-54.412-60.548Q-54.744-60.409-54.744-60.178M-51.322-59.311L-51.322-59.401Q-51.264-59.608-51.072-59.632L-50.361-59.632L-50.361-61.960L-51.072-61.960Q-51.267-61.983-51.322-62.202L-51.322-62.288Q-51.264-62.499-51.072-62.522L-49.971-62.522Q-49.771-62.503-49.721-62.288L-49.721-61.960Q-49.459-62.245-49.103-62.403Q-48.748-62.561-48.361-62.561Q-48.068-62.561-47.834-62.427Q-47.599-62.292-47.599-62.026Q-47.599-61.858-47.709-61.741Q-47.818-61.624-47.986-61.624Q-48.139-61.624-48.254-61.735Q-48.369-61.846-48.369-62.003Q-48.744-62.003-49.058-61.802Q-49.373-61.600-49.547-61.266Q-49.721-60.932-49.721-60.553L-49.721-59.632L-48.775-59.632Q-48.568-59.608-48.529-59.401L-48.529-59.311Q-48.568-59.096-48.775-59.073L-51.072-59.073Q-51.264-59.096-51.322-59.311M-47.060-58.425Q-47.060-58.725-46.912-58.987Q-46.764-59.249-46.514-59.409Q-46.697-59.663-46.697-59.983Q-46.697-60.268-46.545-60.530Q-46.795-60.854-46.795-61.272Q-46.795-61.632-46.603-61.928Q-46.412-62.225-46.094-62.393Q-45.775-62.561-45.412-62.561Q-45.205-62.561-45.002-62.501Q-44.799-62.440-44.635-62.339Q-44.252-62.600-43.779-62.600Q-43.541-62.600-43.359-62.469Q-43.178-62.339-43.178-62.112Q-43.178-61.964-43.279-61.858Q-43.381-61.753-43.537-61.753Q-43.670-61.753-43.766-61.831Q-43.861-61.909-43.892-62.034Q-44.037-62.026-44.236-61.936Q-44.033-61.624-44.033-61.272Q-44.033-60.991-44.144-60.759Q-44.256-60.526-44.451-60.348Q-44.646-60.171-44.898-60.073Q-45.150-59.975-45.412-59.975Q-45.799-59.975-46.131-60.163Q-46.142-60.163-46.152-60.091Q-46.162-60.018-46.162-59.983Q-46.162-59.862-46.096-59.755Q-46.029-59.647-45.908-59.608Q-45.892-59.612-45.879-59.614Q-45.865-59.616-45.842-59.616Q-45.826-59.616-45.795-59.608Q-45.764-59.600-45.756-59.600L-45.162-59.600Q-44.381-59.600-43.840-59.358Q-43.299-59.116-43.299-58.425Q-43.299-58.124-43.478-57.897Q-43.658-57.671-43.955-57.526Q-44.252-57.382-44.572-57.315Q-44.892-57.249-45.178-57.249Q-45.568-57.249-46.010-57.372Q-46.451-57.495-46.756-57.762Q-47.060-58.030-47.060-58.425M-46.521-58.432Q-46.521-58.214-46.281-58.073Q-46.041-57.932-45.717-57.866Q-45.392-57.800-45.178-57.800Q-44.963-57.800-44.639-57.866Q-44.314-57.932-44.074-58.073Q-43.834-58.214-43.834-58.432Q-43.834-58.721-44.058-58.860Q-44.283-58.999-44.564-59.032Q-44.846-59.065-45.193-59.065L-45.810-59.065Q-45.994-59.065-46.156-58.985Q-46.318-58.905-46.420-58.759Q-46.521-58.612-46.521-58.432M-45.412-60.530Q-45.111-60.530-44.892-60.749Q-44.674-60.968-44.674-61.272Q-44.674-61.428-44.728-61.559Q-44.783-61.690-44.889-61.796Q-44.994-61.901-45.125-61.956Q-45.256-62.011-45.412-62.011Q-45.717-62.011-45.935-61.792Q-46.154-61.573-46.154-61.272Q-46.154-60.975-45.932-60.753Q-45.709-60.530-45.412-60.530M-39.541-60.561L-41.982-60.561Q-41.928-60.284-41.730-60.061Q-41.533-59.839-41.256-59.716Q-40.978-59.593-40.693-59.593Q-40.221-59.593-39.998-59.882Q-39.990-59.893-39.933-59.999Q-39.877-60.104-39.828-60.147Q-39.779-60.190-39.685-60.202L-39.541-60.202Q-39.349-60.182-39.291-59.968L-39.291-59.913Q-39.357-59.612-39.588-59.415Q-39.818-59.218-40.131-59.126Q-40.443-59.034-40.748-59.034Q-41.232-59.034-41.672-59.262Q-42.111-59.491-42.379-59.891Q-42.646-60.292-42.646-60.784L-42.646-60.843Q-42.646-61.311-42.400-61.714Q-42.154-62.116-41.746-62.350Q-41.338-62.585-40.869-62.585Q-40.365-62.585-40.012-62.362Q-39.658-62.139-39.474-61.751Q-39.291-61.362-39.291-60.858L-39.291-60.800Q-39.349-60.585-39.541-60.561M-41.974-61.112L-39.947-61.112Q-39.994-61.522-40.232-61.774Q-40.471-62.026-40.869-62.026Q-41.264-62.026-41.570-61.764Q-41.877-61.503-41.974-61.112\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(194.166 70.175)\">\u003Cpath d=\"M-31.423-58.432Q-31.954-58.741-32.354-59.229Q-32.755-59.718-32.966-60.311Q-33.177-60.905-33.177-61.522Q-33.177-62.139-32.968-62.727Q-32.759-63.315-32.362-63.796Q-31.966-64.276-31.431-64.600Q-31.360-64.624-31.329-64.624L-31.239-64.624Q-31.141-64.612-31.075-64.546Q-31.009-64.479-31.009-64.378Q-31.009-64.233-31.110-64.171Q-31.559-63.882-31.886-63.466Q-32.212-63.050-32.374-62.557Q-32.536-62.065-32.536-61.522Q-32.536-61.116-32.440-60.729Q-32.345-60.343-32.167-60.007Q-31.989-59.671-31.729-59.387Q-31.470-59.104-31.122-58.874Q-31.009-58.796-31.009-58.659Q-31.009-58.561-31.075-58.491Q-31.141-58.421-31.239-58.409L-31.329-58.409Q-31.388-58.409-31.423-58.432M-29.704-59.272L-29.704-60.186Q-29.677-60.393-29.466-60.417L-29.298-60.417Q-29.134-60.393-29.075-60.233Q-28.872-59.593-28.145-59.593Q-27.938-59.593-27.710-59.628Q-27.481-59.663-27.313-59.778Q-27.145-59.893-27.145-60.096Q-27.145-60.307-27.368-60.421Q-27.591-60.534-27.864-60.577L-28.563-60.690Q-29.704-60.901-29.704-61.624Q-29.704-61.913-29.559-62.102Q-29.415-62.292-29.175-62.399Q-28.934-62.507-28.679-62.546Q-28.423-62.585-28.145-62.585Q-27.895-62.585-27.702-62.555Q-27.509-62.526-27.345-62.448Q-27.266-62.565-27.138-62.585L-27.059-62.585Q-26.962-62.573-26.899-62.511Q-26.837-62.448-26.825-62.354L-26.825-61.647Q-26.837-61.553-26.899-61.487Q-26.962-61.421-27.059-61.409L-27.227-61.409Q-27.321-61.421-27.388-61.487Q-27.454-61.553-27.466-61.647Q-27.466-62.026-28.161-62.026Q-28.509-62.026-28.827-61.944Q-29.145-61.862-29.145-61.616Q-29.145-61.350-28.474-61.241L-27.770-61.120Q-27.286-61.038-26.936-60.790Q-26.587-60.542-26.587-60.096Q-26.587-59.706-26.823-59.464Q-27.059-59.221-27.409-59.128Q-27.759-59.034-28.145-59.034Q-28.724-59.034-29.122-59.288Q-29.192-59.163-29.241-59.106Q-29.290-59.050-29.395-59.034L-29.466-59.034Q-29.681-59.057-29.704-59.272M-25.595-59.311L-25.595-59.401Q-25.544-59.608-25.349-59.632L-24.243-59.632L-24.243-63.401L-25.349-63.401Q-25.544-63.425-25.595-63.639L-25.595-63.729Q-25.544-63.936-25.349-63.960L-23.852-63.960Q-23.661-63.936-23.602-63.729L-23.602-59.632L-22.501-59.632Q-22.302-59.608-22.251-59.401L-22.251-59.311Q-22.302-59.096-22.501-59.073L-25.349-59.073Q-25.544-59.096-25.595-59.311M-19.677-59.034Q-20.149-59.034-20.534-59.278Q-20.919-59.522-21.141-59.932Q-21.364-60.343-21.364-60.800Q-21.364-61.143-21.239-61.466Q-21.114-61.788-20.884-62.042Q-20.653-62.296-20.347-62.440Q-20.040-62.585-19.677-62.585Q-19.313-62.585-19.001-62.438Q-18.688-62.292-18.466-62.046Q-18.243-61.800-18.116-61.479Q-17.989-61.159-17.989-60.800Q-17.989-60.343-18.214-59.930Q-18.438-59.518-18.823-59.276Q-19.208-59.034-19.677-59.034M-19.677-59.593Q-19.212-59.593-18.921-59.987Q-18.630-60.382-18.630-60.866Q-18.630-61.159-18.765-61.427Q-18.899-61.694-19.140-61.860Q-19.380-62.026-19.677-62.026Q-19.981-62.026-20.220-61.860Q-20.458-61.694-20.593-61.427Q-20.727-61.159-20.727-60.866Q-20.727-60.386-20.434-59.989Q-20.141-59.593-19.677-59.593M-16.544-59.296L-17.009-61.960L-17.169-61.960Q-17.376-61.983-17.415-62.202L-17.415-62.288Q-17.376-62.499-17.169-62.522L-16.001-62.522Q-15.790-62.499-15.751-62.288L-15.751-62.202Q-15.790-61.983-16.001-61.960L-16.474-61.960Q-16.360-61.315-16.282-60.870Q-16.204-60.425-16.153-60.106Q-16.102-59.788-16.102-59.714Q-16.095-59.886-15.809-60.882Q-15.770-60.995-15.673-61.069Q-15.575-61.143-15.454-61.143L-15.376-61.143Q-15.255-61.143-15.157-61.069Q-15.059-60.995-15.024-60.882Q-14.915-60.499-14.833-60.175Q-14.751-59.850-14.751-59.714Q-14.739-60.003-14.391-61.960L-14.864-61.960Q-15.071-61.983-15.110-62.202L-15.110-62.288Q-15.071-62.499-14.864-62.522L-13.688-62.522Q-13.497-62.499-13.438-62.288L-13.438-62.202Q-13.493-61.983-13.688-61.960L-13.856-61.960L-14.321-59.296Q-14.345-59.178-14.432-59.106Q-14.520-59.034-14.641-59.034L-14.782-59.034Q-14.903-59.034-14.999-59.106Q-15.095-59.178-15.138-59.296Q-15.184-59.475-15.257-59.731Q-15.329-59.987-15.372-60.196Q-15.415-60.405-15.415-60.507Q-15.423-60.225-15.704-59.296Q-15.731-59.186-15.829-59.110Q-15.927-59.034-16.048-59.034L-16.224-59.034Q-16.345-59.034-16.432-59.106Q-16.520-59.178-16.544-59.296M-12.266-58.409L-12.352-58.409Q-12.458-58.421-12.526-58.493Q-12.595-58.565-12.595-58.659Q-12.595-58.800-12.489-58.866Q-12.153-59.081-11.884-59.370Q-11.614-59.659-11.431-60.007Q-11.247-60.354-11.157-60.733Q-11.067-61.112-11.067-61.522Q-11.067-62.061-11.231-62.553Q-11.395-63.046-11.714-63.460Q-12.032-63.874-12.474-64.163Q-12.595-64.245-12.595-64.378Q-12.595-64.475-12.526-64.544Q-12.458-64.612-12.352-64.624L-12.266-64.624Q-12.212-64.624-12.177-64.600Q-11.790-64.378-11.450-64.030Q-11.110-63.682-10.890-63.288Q-10.669-62.893-10.548-62.448Q-10.427-62.003-10.427-61.522Q-10.427-61.038-10.548-60.587Q-10.669-60.136-10.893-59.739Q-11.118-59.343-11.442-59.009Q-11.766-58.675-12.169-58.432Q-12.239-58.409-12.266-58.409\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">Sinusoidal positional encoding as a frequency band. Each feature slot \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> carries a sine\u002Fcosine of period \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.888em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1000\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.888em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">\u002F\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>: low-\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> channels (top) oscillate fast and separate adjacent tokens; high-\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> channels (bottom) oscillate slowly and encode coarse position.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:180.269px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 135.202 220.196\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-68.537 141.526H-5.94v-19.917h-62.596Z\"\u002F>\u003Cg transform=\"translate(-10.625 1.556)\">\u003Cpath d=\"M-36.622 131.329L-36.622 131.239Q-36.571 131.032-36.376 131.008L-35.337 131.008L-35.337 128.680L-36.309 128.680Q-36.509 128.657-36.559 128.438L-36.559 128.352Q-36.509 128.141-36.309 128.118L-34.942 128.118Q-34.747 128.137-34.696 128.352L-34.696 131.008L-33.782 131.008Q-33.587 131.032-33.536 131.239L-33.536 131.329Q-33.587 131.544-33.782 131.567L-36.376 131.567Q-36.571 131.544-36.622 131.329M-35.591 127.141L-35.591 127.087Q-35.591 126.915-35.454 126.794Q-35.317 126.672-35.141 126.672Q-34.969 126.672-34.833 126.794Q-34.696 126.915-34.696 127.087L-34.696 127.141Q-34.696 127.317-34.833 127.438Q-34.969 127.559-35.141 127.559Q-35.317 127.559-35.454 127.438Q-35.591 127.317-35.591 127.141M-32.923 131.329L-32.923 131.239Q-32.880 131.032-32.673 131.008L-32.251 131.008L-32.251 128.680L-32.673 128.680Q-32.880 128.657-32.923 128.438L-32.923 128.352Q-32.876 128.141-32.673 128.118L-31.856 128.118Q-31.661 128.141-31.610 128.352L-31.610 128.438L-31.618 128.462Q-31.391 128.282-31.118 128.180Q-30.844 128.079-30.551 128.079Q-30.204 128.079-29.966 128.219Q-29.727 128.360-29.612 128.618Q-29.497 128.876-29.497 129.231L-29.497 131.008L-29.071 131.008Q-28.864 131.032-28.825 131.239L-28.825 131.329Q-28.864 131.544-29.071 131.567L-30.466 131.567Q-30.661 131.544-30.712 131.329L-30.712 131.239Q-30.661 131.028-30.466 131.008L-30.137 131.008L-30.137 129.262Q-30.137 128.954-30.227 128.796Q-30.317 128.637-30.610 128.637Q-30.880 128.637-31.108 128.768Q-31.337 128.899-31.473 129.128Q-31.610 129.356-31.610 129.622L-31.610 131.008L-31.184 131.008Q-30.977 131.032-30.938 131.239L-30.938 131.329Q-30.977 131.544-31.184 131.567L-32.673 131.567Q-32.880 131.544-32.923 131.329M-28.676 133.110L-28.676 133.024Q-28.634 132.805-28.426 132.782L-28.005 132.782L-28.005 128.680L-28.426 128.680Q-28.634 128.657-28.676 128.438L-28.676 128.352Q-28.630 128.141-28.426 128.118L-27.610 128.118Q-27.415 128.137-27.364 128.352L-27.364 128.422Q-27.153 128.255-26.889 128.167Q-26.626 128.079-26.356 128.079Q-26.016 128.079-25.719 128.223Q-25.423 128.368-25.208 128.620Q-24.993 128.872-24.878 129.184Q-24.762 129.497-24.762 129.840Q-24.762 130.305-24.989 130.715Q-25.216 131.126-25.602 131.366Q-25.989 131.606-26.458 131.606Q-26.977 131.606-27.364 131.239L-27.364 132.782L-26.938 132.782Q-26.731 132.805-26.692 133.024L-26.692 133.110Q-26.731 133.321-26.938 133.344L-28.426 133.344Q-28.630 133.321-28.676 133.110M-26.501 131.047Q-26.192 131.047-25.942 130.878Q-25.692 130.708-25.548 130.426Q-25.403 130.145-25.403 129.840Q-25.403 129.551-25.528 129.272Q-25.653 128.993-25.885 128.815Q-26.118 128.637-26.419 128.637Q-26.739 128.637-27.001 128.823Q-27.262 129.008-27.364 129.309L-27.364 130.161Q-27.274 130.528-27.053 130.788Q-26.833 131.047-26.501 131.047M-23.759 130.712L-23.759 128.680L-24.180 128.680Q-24.387 128.657-24.430 128.438L-24.430 128.352Q-24.384 128.141-24.180 128.118L-23.364 128.118Q-23.169 128.141-23.118 128.352L-23.118 130.680Q-23.118 130.915-22.948 130.981Q-22.778 131.047-22.493 131.047Q-22.286 131.047-22.091 130.971Q-21.895 130.895-21.770 130.745Q-21.645 130.594-21.645 130.383L-21.645 128.680L-22.067 128.680Q-22.278 128.657-22.317 128.438L-22.317 128.352Q-22.278 128.141-22.067 128.118L-21.255 128.118Q-21.055 128.141-21.005 128.352L-21.005 131.008L-20.579 131.008Q-20.372 131.032-20.333 131.239L-20.333 131.329Q-20.372 131.544-20.579 131.567L-21.395 131.567Q-21.594 131.544-21.645 131.344Q-22.048 131.606-22.555 131.606Q-22.790 131.606-23.005 131.565Q-23.219 131.524-23.385 131.422Q-23.551 131.321-23.655 131.143Q-23.759 130.965-23.759 130.712M-19.055 130.462L-19.055 128.680L-19.805 128.680Q-20.005 128.657-20.055 128.438L-20.055 128.352Q-20.005 128.141-19.805 128.118L-19.055 128.118L-19.055 127.368Q-19.005 127.161-18.805 127.133L-18.661 127.133Q-18.466 127.161-18.415 127.368L-18.415 128.118L-17.055 128.118Q-16.864 128.137-16.805 128.352L-16.805 128.438Q-16.860 128.657-17.055 128.680L-18.415 128.680L-18.415 130.430Q-18.415 131.047-17.841 131.047Q-17.591 131.047-17.426 130.862Q-17.262 130.676-17.262 130.430Q-17.262 130.337-17.190 130.266Q-17.118 130.196-17.016 130.184L-16.872 130.184Q-16.673 130.208-16.622 130.415L-16.622 130.462Q-16.622 130.786-16.805 131.049Q-16.989 131.313-17.282 131.460Q-17.575 131.606-17.895 131.606Q-18.407 131.606-18.731 131.296Q-19.055 130.985-19.055 130.462\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M-68.537 93.156H-5.94V73.239h-62.596Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-23.375 -46.155)\">\u003Cpath d=\"M-36.833 130.454Q-36.833 130.008-36.419 129.751Q-36.005 129.493-35.464 129.393Q-34.923 129.294-34.415 129.286Q-34.415 129.071-34.550 128.919Q-34.684 128.766-34.891 128.690Q-35.098 128.614-35.309 128.614Q-35.653 128.614-35.813 128.637L-35.813 128.696Q-35.813 128.864-35.932 128.979Q-36.051 129.094-36.216 129.094Q-36.391 129.094-36.507 128.971Q-36.622 128.848-36.622 128.680Q-36.622 128.274-36.241 128.165Q-35.860 128.055-35.301 128.055Q-35.032 128.055-34.764 128.133Q-34.497 128.212-34.272 128.362Q-34.048 128.512-33.911 128.733Q-33.774 128.954-33.774 129.231L-33.774 130.950Q-33.774 131.008-33.247 131.008Q-33.051 131.028-33.001 131.239L-33.001 131.329Q-33.051 131.544-33.247 131.567L-33.391 131.567Q-33.735 131.567-33.964 131.520Q-34.192 131.473-34.337 131.286Q-34.798 131.606-35.505 131.606Q-35.841 131.606-36.145 131.465Q-36.450 131.325-36.641 131.063Q-36.833 130.801-36.833 130.454M-36.192 130.462Q-36.192 130.735-35.950 130.891Q-35.708 131.047-35.423 131.047Q-35.204 131.047-34.971 130.989Q-34.739 130.930-34.577 130.792Q-34.415 130.653-34.415 130.430L-34.415 129.840Q-34.696 129.840-35.112 129.897Q-35.528 129.954-35.860 130.092Q-36.192 130.231-36.192 130.462M-31.794 130.462L-31.794 128.680L-32.544 128.680Q-32.743 128.657-32.794 128.438L-32.794 128.352Q-32.743 128.141-32.544 128.118L-31.794 128.118L-31.794 127.368Q-31.743 127.161-31.544 127.133L-31.399 127.133Q-31.204 127.161-31.153 127.368L-31.153 128.118L-29.794 128.118Q-29.602 128.137-29.544 128.352L-29.544 128.438Q-29.598 128.657-29.794 128.680L-31.153 128.680L-31.153 130.430Q-31.153 131.047-30.579 131.047Q-30.329 131.047-30.165 130.862Q-30.001 130.676-30.001 130.430Q-30.001 130.337-29.928 130.266Q-29.856 130.196-29.755 130.184L-29.610 130.184Q-29.411 130.208-29.360 130.415L-29.360 130.462Q-29.360 130.786-29.544 131.049Q-29.727 131.313-30.020 131.460Q-30.313 131.606-30.634 131.606Q-31.145 131.606-31.469 131.296Q-31.794 130.985-31.794 130.462M-27.548 130.462L-27.548 128.680L-28.298 128.680Q-28.497 128.657-28.548 128.438L-28.548 128.352Q-28.497 128.141-28.298 128.118L-27.548 128.118L-27.548 127.368Q-27.497 127.161-27.298 127.133L-27.153 127.133Q-26.958 127.161-26.907 127.368L-26.907 128.118L-25.548 128.118Q-25.356 128.137-25.298 128.352L-25.298 128.438Q-25.352 128.657-25.548 128.680L-26.907 128.680L-26.907 130.430Q-26.907 131.047-26.333 131.047Q-26.083 131.047-25.919 130.862Q-25.755 130.676-25.755 130.430Q-25.755 130.337-25.682 130.266Q-25.610 130.196-25.509 130.184L-25.364 130.184Q-25.165 130.208-25.114 130.415L-25.114 130.462Q-25.114 130.786-25.298 131.049Q-25.481 131.313-25.774 131.460Q-26.067 131.606-26.387 131.606Q-26.899 131.606-27.223 131.296Q-27.548 130.985-27.548 130.462M-24.430 131.329L-24.430 131.239Q-24.387 131.032-24.180 131.008L-23.759 131.008L-23.759 128.680L-24.180 128.680Q-24.387 128.657-24.430 128.438L-24.430 128.352Q-24.384 128.141-24.180 128.118L-23.364 128.118Q-23.169 128.141-23.118 128.352L-23.118 128.438L-23.126 128.462Q-22.899 128.282-22.626 128.180Q-22.352 128.079-22.059 128.079Q-21.712 128.079-21.473 128.219Q-21.235 128.360-21.120 128.618Q-21.005 128.876-21.005 129.231L-21.005 131.008L-20.579 131.008Q-20.372 131.032-20.333 131.239L-20.333 131.329Q-20.372 131.544-20.579 131.567L-21.973 131.567Q-22.169 131.544-22.219 131.329L-22.219 131.239Q-22.169 131.028-21.973 131.008L-21.645 131.008L-21.645 129.262Q-21.645 128.954-21.735 128.796Q-21.825 128.637-22.118 128.637Q-22.387 128.637-22.616 128.768Q-22.844 128.899-22.981 129.128Q-23.118 129.356-23.118 129.622L-23.118 131.008L-22.692 131.008Q-22.485 131.032-22.446 131.239L-22.446 131.329Q-22.485 131.544-22.692 131.567L-24.180 131.567Q-24.387 131.544-24.430 131.329\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-23.375 -46.155)\">\u003Cpath d=\"M-15.402 131.368L-15.402 130.454Q-15.375 130.247-15.164 130.223L-14.996 130.223Q-14.832 130.247-14.773 130.407Q-14.570 131.047-13.843 131.047Q-13.636 131.047-13.408 131.012Q-13.179 130.977-13.011 130.862Q-12.843 130.747-12.843 130.544Q-12.843 130.333-13.066 130.219Q-13.289 130.106-13.562 130.063L-14.261 129.950Q-15.402 129.739-15.402 129.016Q-15.402 128.727-15.258 128.538Q-15.113 128.348-14.873 128.241Q-14.633 128.133-14.377 128.094Q-14.121 128.055-13.843 128.055Q-13.593 128.055-13.400 128.085Q-13.207 128.114-13.043 128.192Q-12.965 128.075-12.836 128.055L-12.758 128.055Q-12.660 128.067-12.597 128.130Q-12.535 128.192-12.523 128.286L-12.523 128.993Q-12.535 129.087-12.597 129.153Q-12.660 129.219-12.758 129.231L-12.925 129.231Q-13.019 129.219-13.086 129.153Q-13.152 129.087-13.164 128.993Q-13.164 128.614-13.859 128.614Q-14.207 128.614-14.525 128.696Q-14.843 128.778-14.843 129.024Q-14.843 129.290-14.172 129.399L-13.468 129.520Q-12.984 129.602-12.634 129.850Q-12.285 130.098-12.285 130.544Q-12.285 130.934-12.521 131.176Q-12.758 131.419-13.107 131.512Q-13.457 131.606-13.843 131.606Q-14.422 131.606-14.820 131.352Q-14.890 131.477-14.939 131.534Q-14.988 131.590-15.093 131.606L-15.164 131.606Q-15.379 131.583-15.402 131.368M-11.183 129.840Q-11.183 129.360-10.939 128.946Q-10.695 128.532-10.279 128.294Q-9.863 128.055-9.383 128.055Q-8.828 128.055-8.449 128.165Q-8.070 128.274-8.070 128.680Q-8.070 128.848-8.183 128.971Q-8.297 129.094-8.468 129.094Q-8.640 129.094-8.759 128.979Q-8.879 128.864-8.879 128.696L-8.879 128.637Q-9.039 128.614-9.375 128.614Q-9.703 128.614-9.970 128.784Q-10.238 128.954-10.390 129.237Q-10.543 129.520-10.543 129.840Q-10.543 130.161-10.371 130.442Q-10.199 130.723-9.914 130.885Q-9.629 131.047-9.300 131.047Q-8.988 131.047-8.861 130.944Q-8.734 130.840-8.617 130.651Q-8.500 130.462-8.383 130.446L-8.215 130.446Q-8.109 130.458-8.045 130.526Q-7.980 130.594-7.980 130.696Q-7.980 130.743-8 130.782Q-8.109 131.075-8.312 131.255Q-8.515 131.434-8.791 131.520Q-9.066 131.606-9.383 131.606Q-9.867 131.606-10.283 131.368Q-10.699 131.130-10.941 130.727Q-11.183 130.325-11.183 129.840M-5.375 131.606Q-5.847 131.606-6.232 131.362Q-6.617 131.118-6.840 130.708Q-7.062 130.297-7.062 129.840Q-7.062 129.497-6.937 129.174Q-6.812 128.852-6.582 128.598Q-6.351 128.344-6.045 128.200Q-5.738 128.055-5.375 128.055Q-5.011 128.055-4.699 128.202Q-4.386 128.348-4.164 128.594Q-3.941 128.840-3.814 129.161Q-3.687 129.481-3.687 129.840Q-3.687 130.297-3.912 130.710Q-4.136 131.122-4.521 131.364Q-4.906 131.606-5.375 131.606M-5.375 131.047Q-4.910 131.047-4.619 130.653Q-4.328 130.258-4.328 129.774Q-4.328 129.481-4.463 129.213Q-4.597 128.946-4.838 128.780Q-5.078 128.614-5.375 128.614Q-5.679 128.614-5.918 128.780Q-6.156 128.946-6.291 129.213Q-6.425 129.481-6.425 129.774Q-6.425 130.255-6.133 130.651Q-5.840 131.047-5.375 131.047M-3.027 131.329L-3.027 131.239Q-2.968 131.032-2.777 131.008L-2.066 131.008L-2.066 128.680L-2.777 128.680Q-2.972 128.657-3.027 128.438L-3.027 128.352Q-2.968 128.141-2.777 128.118L-1.675 128.118Q-1.476 128.137-1.425 128.352L-1.425 128.680Q-1.164 128.395-0.808 128.237Q-0.453 128.079-0.066 128.079Q0.227 128.079 0.461 128.213Q0.696 128.348 0.696 128.614Q0.696 128.782 0.586 128.899Q0.477 129.016 0.309 129.016Q0.157 129.016 0.041 128.905Q-0.074 128.794-0.074 128.637Q-0.449 128.637-0.763 128.838Q-1.078 129.040-1.252 129.374Q-1.425 129.708-1.425 130.087L-1.425 131.008L-0.480 131.008Q-0.273 131.032-0.234 131.239L-0.234 131.329Q-0.273 131.544-0.480 131.567L-2.777 131.567Q-2.968 131.544-3.027 131.329M4.508 130.079L2.067 130.079Q2.121 130.356 2.319 130.579Q2.516 130.801 2.793 130.924Q3.071 131.047 3.356 131.047Q3.828 131.047 4.051 130.758Q4.059 130.747 4.116 130.641Q4.172 130.536 4.221 130.493Q4.270 130.450 4.364 130.438L4.508 130.438Q4.700 130.458 4.758 130.672L4.758 130.727Q4.692 131.028 4.461 131.225Q4.231 131.422 3.918 131.514Q3.606 131.606 3.301 131.606Q2.817 131.606 2.377 131.378Q1.938 131.149 1.670 130.749Q1.403 130.348 1.403 129.856L1.403 129.797Q1.403 129.329 1.649 128.926Q1.895 128.524 2.303 128.290Q2.711 128.055 3.180 128.055Q3.684 128.055 4.037 128.278Q4.391 128.501 4.575 128.889Q4.758 129.278 4.758 129.782L4.758 129.840Q4.700 130.055 4.508 130.079M2.075 129.528L4.102 129.528Q4.055 129.118 3.817 128.866Q3.578 128.614 3.180 128.614Q2.785 128.614 2.479 128.876Q2.172 129.137 2.075 129.528M5.828 131.368L5.828 130.454Q5.856 130.247 6.067 130.223L6.235 130.223Q6.399 130.247 6.457 130.407Q6.660 131.047 7.387 131.047Q7.594 131.047 7.823 131.012Q8.051 130.977 8.219 130.862Q8.387 130.747 8.387 130.544Q8.387 130.333 8.164 130.219Q7.942 130.106 7.668 130.063L6.969 129.950Q5.828 129.739 5.828 129.016Q5.828 128.727 5.973 128.538Q6.117 128.348 6.358 128.241Q6.598 128.133 6.854 128.094Q7.110 128.055 7.387 128.055Q7.637 128.055 7.830 128.085Q8.024 128.114 8.188 128.192Q8.266 128.075 8.395 128.055L8.473 128.055Q8.571 128.067 8.633 128.130Q8.696 128.192 8.707 128.286L8.707 128.993Q8.696 129.087 8.633 129.153Q8.571 129.219 8.473 129.231L8.305 129.231Q8.211 129.219 8.145 129.153Q8.078 129.087 8.067 128.993Q8.067 128.614 7.371 128.614Q7.024 128.614 6.705 128.696Q6.387 128.778 6.387 129.024Q6.387 129.290 7.059 129.399L7.762 129.520Q8.246 129.602 8.596 129.850Q8.946 130.098 8.946 130.544Q8.946 130.934 8.709 131.176Q8.473 131.419 8.123 131.512Q7.774 131.606 7.387 131.606Q6.809 131.606 6.410 131.352Q6.340 131.477 6.291 131.534Q6.242 131.590 6.137 131.606L6.067 131.606Q5.852 131.583 5.828 131.368\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-68.537 44.786H-5.94V24.87h-62.596Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-21.25 -94.295)\">\u003Cpath d=\"M-35.423 130.645L-35.423 129.430L-36.637 129.430Q-36.762 129.419-36.848 129.333Q-36.934 129.247-36.934 129.118Q-36.934 128.989-36.848 128.907Q-36.762 128.825-36.637 128.813L-35.423 128.813L-35.423 127.590Q-35.411 127.465-35.325 127.383Q-35.239 127.301-35.110 127.301Q-34.981 127.301-34.899 127.383Q-34.817 127.465-34.805 127.590L-34.805 128.813L-33.591 128.813Q-33.466 128.825-33.384 128.907Q-33.301 128.989-33.301 129.118Q-33.301 129.247-33.384 129.333Q-33.466 129.419-33.591 129.430L-34.805 129.430L-34.805 130.645Q-34.817 130.770-34.899 130.856Q-34.981 130.942-35.110 130.942Q-35.239 130.942-35.325 130.856Q-35.411 130.770-35.423 130.645\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -94.295)\">\u003Cpath d=\"M-28.516 131.329L-28.516 131.239Q-28.458 131.032-28.266 131.008L-27.555 131.008L-27.555 128.680L-28.266 128.680Q-28.462 128.657-28.516 128.438L-28.516 128.352Q-28.458 128.141-28.266 128.118L-27.165 128.118Q-26.966 128.137-26.915 128.352L-26.915 128.680Q-26.653 128.395-26.298 128.237Q-25.942 128.079-25.555 128.079Q-25.262 128.079-25.028 128.213Q-24.794 128.348-24.794 128.614Q-24.794 128.782-24.903 128.899Q-25.012 129.016-25.180 129.016Q-25.333 129.016-25.448 128.905Q-25.563 128.794-25.563 128.637Q-25.938 128.637-26.253 128.838Q-26.567 129.040-26.741 129.374Q-26.915 129.708-26.915 130.087L-26.915 131.008L-25.969 131.008Q-25.762 131.032-25.723 131.239L-25.723 131.329Q-25.762 131.544-25.969 131.567L-28.266 131.567Q-28.458 131.544-28.516 131.329M-20.981 130.079L-23.423 130.079Q-23.368 130.356-23.171 130.579Q-22.973 130.801-22.696 130.924Q-22.419 131.047-22.134 131.047Q-21.661 131.047-21.438 130.758Q-21.430 130.747-21.374 130.641Q-21.317 130.536-21.268 130.493Q-21.219 130.450-21.126 130.438L-20.981 130.438Q-20.790 130.458-20.731 130.672L-20.731 130.727Q-20.798 131.028-21.028 131.225Q-21.259 131.422-21.571 131.514Q-21.884 131.606-22.188 131.606Q-22.673 131.606-23.112 131.378Q-23.552 131.149-23.819 130.749Q-24.087 130.348-24.087 129.856L-24.087 129.797Q-24.087 129.329-23.841 128.926Q-23.594 128.524-23.186 128.290Q-22.778 128.055-22.309 128.055Q-21.805 128.055-21.452 128.278Q-21.098 128.501-20.915 128.889Q-20.731 129.278-20.731 129.782L-20.731 129.840Q-20.790 130.055-20.981 130.079M-23.415 129.528L-21.387 129.528Q-21.434 129.118-21.673 128.866Q-21.911 128.614-22.309 128.614Q-22.704 128.614-23.010 128.876Q-23.317 129.137-23.415 129.528M-19.661 131.368L-19.661 130.454Q-19.634 130.247-19.423 130.223L-19.255 130.223Q-19.091 130.247-19.032 130.407Q-18.829 131.047-18.102 131.047Q-17.895 131.047-17.667 131.012Q-17.438 130.977-17.270 130.862Q-17.102 130.747-17.102 130.544Q-17.102 130.333-17.325 130.219Q-17.548 130.106-17.821 130.063L-18.520 129.950Q-19.661 129.739-19.661 129.016Q-19.661 128.727-19.516 128.538Q-19.372 128.348-19.132 128.241Q-18.891 128.133-18.635 128.094Q-18.380 128.055-18.102 128.055Q-17.852 128.055-17.659 128.085Q-17.466 128.114-17.302 128.192Q-17.223 128.075-17.094 128.055L-17.016 128.055Q-16.919 128.067-16.856 128.130Q-16.794 128.192-16.782 128.286L-16.782 128.993Q-16.794 129.087-16.856 129.153Q-16.919 129.219-17.016 129.231L-17.184 129.231Q-17.278 129.219-17.344 129.153Q-17.411 129.087-17.423 128.993Q-17.423 128.614-18.118 128.614Q-18.466 128.614-18.784 128.696Q-19.102 128.778-19.102 129.024Q-19.102 129.290-18.430 129.399L-17.727 129.520Q-17.243 129.602-16.893 129.850Q-16.544 130.098-16.544 130.544Q-16.544 130.934-16.780 131.176Q-17.016 131.419-17.366 131.512Q-17.716 131.606-18.102 131.606Q-18.680 131.606-19.079 131.352Q-19.149 131.477-19.198 131.534Q-19.247 131.590-19.352 131.606L-19.423 131.606Q-19.637 131.583-19.661 131.368M-15.384 131.329L-15.384 131.239Q-15.333 131.032-15.137 131.008L-14.098 131.008L-14.098 128.680L-15.071 128.680Q-15.270 128.657-15.321 128.438L-15.321 128.352Q-15.270 128.141-15.071 128.118L-13.704 128.118Q-13.509 128.137-13.458 128.352L-13.458 131.008L-12.544 131.008Q-12.348 131.032-12.298 131.239L-12.298 131.329Q-12.348 131.544-12.544 131.567L-15.137 131.567Q-15.333 131.544-15.384 131.329M-14.352 127.141L-14.352 127.087Q-14.352 126.915-14.216 126.794Q-14.079 126.672-13.903 126.672Q-13.731 126.672-13.594 126.794Q-13.458 126.915-13.458 127.087L-13.458 127.141Q-13.458 127.317-13.594 127.438Q-13.731 127.559-13.903 127.559Q-14.079 127.559-14.216 127.438Q-14.352 127.317-14.352 127.141M-9.891 131.606Q-10.356 131.606-10.721 131.356Q-11.087 131.106-11.292 130.702Q-11.497 130.297-11.497 129.840Q-11.497 129.497-11.372 129.176Q-11.247 128.856-11.014 128.606Q-10.782 128.356-10.477 128.217Q-10.173 128.079-9.817 128.079Q-9.305 128.079-8.899 128.399L-8.899 127.239L-9.321 127.239Q-9.532 127.215-9.571 127.001L-9.571 126.911Q-9.532 126.704-9.321 126.680L-8.509 126.680Q-8.309 126.704-8.259 126.911L-8.259 131.008L-7.833 131.008Q-7.626 131.032-7.587 131.239L-7.587 131.329Q-7.626 131.544-7.833 131.567L-8.649 131.567Q-8.848 131.544-8.899 131.329L-8.899 131.200Q-9.094 131.391-9.356 131.499Q-9.618 131.606-9.891 131.606M-9.852 131.047Q-9.493 131.047-9.241 130.778Q-8.989 130.508-8.899 130.133L-8.899 129.301Q-8.958 129.114-9.085 128.963Q-9.212 128.813-9.389 128.725Q-9.567 128.637-9.762 128.637Q-10.071 128.637-10.321 128.807Q-10.571 128.977-10.716 129.262Q-10.860 129.547-10.860 129.848Q-10.860 130.297-10.575 130.672Q-10.290 131.047-9.852 131.047M-6.766 130.712L-6.766 128.680L-7.188 128.680Q-7.395 128.657-7.438 128.438L-7.438 128.352Q-7.391 128.141-7.188 128.118L-6.372 128.118Q-6.177 128.141-6.126 128.352L-6.126 130.680Q-6.126 130.915-5.956 130.981Q-5.786 131.047-5.501 131.047Q-5.294 131.047-5.098 130.971Q-4.903 130.895-4.778 130.745Q-4.653 130.594-4.653 130.383L-4.653 128.680L-5.075 128.680Q-5.286 128.657-5.325 128.438L-5.325 128.352Q-5.286 128.141-5.075 128.118L-4.262 128.118Q-4.063 128.141-4.012 128.352L-4.012 131.008L-3.587 131.008Q-3.380 131.032-3.341 131.239L-3.341 131.329Q-3.380 131.544-3.587 131.567L-4.403 131.567Q-4.602 131.544-4.653 131.344Q-5.055 131.606-5.563 131.606Q-5.798 131.606-6.012 131.565Q-6.227 131.524-6.393 131.422Q-6.559 131.321-6.663 131.143Q-6.766 130.965-6.766 130.712M-2.856 130.454Q-2.856 130.008-2.442 129.751Q-2.028 129.493-1.487 129.393Q-0.946 129.294-0.438 129.286Q-0.438 129.071-0.573 128.919Q-0.708 128.766-0.915 128.690Q-1.122 128.614-1.333 128.614Q-1.677 128.614-1.837 128.637L-1.837 128.696Q-1.837 128.864-1.956 128.979Q-2.075 129.094-2.239 129.094Q-2.415 129.094-2.530 128.971Q-2.645 128.848-2.645 128.680Q-2.645 128.274-2.264 128.165Q-1.884 128.055-1.325 128.055Q-1.055 128.055-0.788 128.133Q-0.520 128.212-0.296 128.362Q-0.071 128.512 0.066 128.733Q0.202 128.954 0.202 129.231L0.202 130.950Q0.202 131.008 0.730 131.008Q0.925 131.028 0.976 131.239L0.976 131.329Q0.925 131.544 0.730 131.567L0.585 131.567Q0.241 131.567 0.013 131.520Q-0.216 131.473-0.360 131.286Q-0.821 131.606-1.528 131.606Q-1.864 131.606-2.169 131.465Q-2.473 131.325-2.665 131.063Q-2.856 130.801-2.856 130.454M-2.216 130.462Q-2.216 130.735-1.973 130.891Q-1.731 131.047-1.446 131.047Q-1.227 131.047-0.995 130.989Q-0.762 130.930-0.600 130.792Q-0.438 130.653-0.438 130.430L-0.438 129.840Q-0.719 129.840-1.135 129.897Q-1.552 129.954-1.884 130.092Q-2.216 130.231-2.216 130.462M1.433 131.329L1.433 131.239Q1.484 131.032 1.679 131.008L2.784 131.008L2.784 127.239L1.679 127.239Q1.484 127.215 1.433 127.001L1.433 126.911Q1.484 126.704 1.679 126.680L3.175 126.680Q3.366 126.704 3.425 126.911L3.425 131.008L4.527 131.008Q4.726 131.032 4.777 131.239L4.777 131.329Q4.726 131.544 4.527 131.567L1.679 131.567Q1.484 131.544 1.433 131.329\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M-68.537-3.584H-5.94V-23.5h-62.596Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-21.25 -142.665)\">\u003Cpath d=\"M-37.032 131.329L-37.032 131.239Q-36.993 131.032-36.782 131.008L-36.446 131.008L-36.446 127.239L-36.782 127.239Q-36.993 127.215-37.032 127.001L-37.032 126.911Q-36.993 126.704-36.782 126.680L-33.528 126.680Q-33.329 126.704-33.278 126.911L-33.278 127.751Q-33.325 127.965-33.528 127.993L-33.673 127.993Q-33.868 127.965-33.919 127.751L-33.919 127.239L-35.805 127.239L-35.805 128.840L-34.798 128.840L-34.798 128.622Q-34.747 128.415-34.551 128.391L-34.407 128.391Q-34.212 128.411-34.161 128.622L-34.161 129.606Q-34.212 129.825-34.407 129.848L-34.551 129.848Q-34.747 129.829-34.798 129.606L-34.798 129.399L-35.805 129.399L-35.805 131.008L-35.317 131.008Q-35.122 131.032-35.071 131.239L-35.071 131.329Q-35.122 131.544-35.317 131.567L-36.782 131.567Q-36.993 131.544-37.032 131.329M-32.786 131.329L-32.786 131.239Q-32.747 131.032-32.536 131.008L-32.200 131.008L-32.200 127.239L-32.536 127.239Q-32.747 127.215-32.786 127.001L-32.786 126.911Q-32.747 126.704-32.536 126.680L-29.282 126.680Q-29.083 126.704-29.032 126.911L-29.032 127.751Q-29.079 127.965-29.282 127.993L-29.426 127.993Q-29.622 127.965-29.673 127.751L-29.673 127.239L-31.559 127.239L-31.559 128.840L-30.551 128.840L-30.551 128.622Q-30.501 128.415-30.305 128.391L-30.161 128.391Q-29.966 128.411-29.915 128.622L-29.915 129.606Q-29.966 129.825-30.161 129.848L-30.305 129.848Q-30.501 129.829-30.551 129.606L-30.551 129.399L-31.559 129.399L-31.559 131.008L-31.071 131.008Q-30.876 131.032-30.825 131.239L-30.825 131.329Q-30.876 131.544-31.071 131.567L-32.536 131.567Q-32.747 131.544-32.786 131.329M-28.548 131.329L-28.548 131.239Q-28.497 131.032-28.298 131.008L-28.028 131.008L-28.028 127.239L-28.298 127.239Q-28.497 127.215-28.548 127.001L-28.548 126.911Q-28.497 126.704-28.298 126.680L-27.516 126.680Q-27.387 126.680-27.282 126.755Q-27.176 126.829-27.137 126.942Q-26.860 127.731-26.700 128.180Q-26.540 128.630-26.286 129.348Q-26.032 130.067-25.893 130.477Q-25.755 130.887-25.755 130.926L-25.755 127.239L-26.028 127.239Q-26.223 127.215-26.274 127.001L-26.274 126.911Q-26.223 126.704-26.028 126.680L-24.954 126.680Q-24.759 126.704-24.708 126.911L-24.708 127.001Q-24.759 127.215-24.954 127.239L-25.227 127.239L-25.227 131.329Q-25.278 131.544-25.473 131.567L-25.739 131.567Q-25.864 131.567-25.968 131.493Q-26.071 131.419-26.114 131.301Q-26.411 130.454-26.784 129.405Q-27.157 128.356-27.327 127.868Q-27.497 127.380-27.501 127.321L-27.501 131.008L-27.227 131.008Q-27.036 131.032-26.977 131.239L-26.977 131.329Q-27.036 131.544-27.227 131.567L-28.298 131.567Q-28.497 131.544-28.548 131.329\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -142.665)\">\u003Cpath d=\"M-20.168 131.329L-20.168 131.239Q-20.125 131.032-19.918 131.008L-19.496 131.008L-19.496 127.239L-19.918 127.239Q-20.125 127.215-20.168 127.001L-20.168 126.911Q-20.125 126.704-19.918 126.680L-19.101 126.680Q-18.906 126.704-18.855 126.911L-18.855 128.462Q-18.394 128.079-17.797 128.079Q-17.449 128.079-17.211 128.219Q-16.972 128.360-16.857 128.618Q-16.742 128.876-16.742 129.231L-16.742 131.008L-16.316 131.008Q-16.109 131.032-16.070 131.239L-16.070 131.329Q-16.109 131.544-16.316 131.567L-17.711 131.567Q-17.906 131.544-17.957 131.329L-17.957 131.239Q-17.906 131.028-17.711 131.008L-17.383 131.008L-17.383 129.262Q-17.383 128.954-17.472 128.796Q-17.562 128.637-17.855 128.637Q-18.125 128.637-18.353 128.768Q-18.582 128.899-18.718 129.128Q-18.855 129.356-18.855 129.622L-18.855 131.008L-18.429 131.008Q-18.222 131.032-18.183 131.239L-18.183 131.329Q-18.222 131.544-18.429 131.567L-19.918 131.567Q-20.125 131.544-20.168 131.329M-15.375 131.329L-15.375 131.239Q-15.324 131.032-15.129 131.008L-14.090 131.008L-14.090 128.680L-15.062 128.680Q-15.261 128.657-15.312 128.438L-15.312 128.352Q-15.261 128.141-15.062 128.118L-13.695 128.118Q-13.500 128.137-13.449 128.352L-13.449 131.008L-12.535 131.008Q-12.340 131.032-12.289 131.239L-12.289 131.329Q-12.340 131.544-12.535 131.567L-15.129 131.567Q-15.324 131.544-15.375 131.329M-14.343 127.141L-14.343 127.087Q-14.343 126.915-14.207 126.794Q-14.070 126.672-13.894 126.672Q-13.722 126.672-13.586 126.794Q-13.449 126.915-13.449 127.087L-13.449 127.141Q-13.449 127.317-13.586 127.438Q-13.722 127.559-13.894 127.559Q-14.070 127.559-14.207 127.438Q-14.343 127.317-14.343 127.141M-9.883 131.606Q-10.347 131.606-10.713 131.356Q-11.078 131.106-11.283 130.702Q-11.488 130.297-11.488 129.840Q-11.488 129.497-11.363 129.176Q-11.238 128.856-11.006 128.606Q-10.773 128.356-10.468 128.217Q-10.164 128.079-9.808 128.079Q-9.297 128.079-8.890 128.399L-8.890 127.239L-9.312 127.239Q-9.523 127.215-9.562 127.001L-9.562 126.911Q-9.523 126.704-9.312 126.680L-8.500 126.680Q-8.300 126.704-8.250 126.911L-8.250 131.008L-7.824 131.008Q-7.617 131.032-7.578 131.239L-7.578 131.329Q-7.617 131.544-7.824 131.567L-8.640 131.567Q-8.840 131.544-8.890 131.329L-8.890 131.200Q-9.086 131.391-9.347 131.499Q-9.609 131.606-9.883 131.606M-9.843 131.047Q-9.484 131.047-9.232 130.778Q-8.980 130.508-8.890 130.133L-8.890 129.301Q-8.949 129.114-9.076 128.963Q-9.203 128.813-9.381 128.725Q-9.558 128.637-9.754 128.637Q-10.062 128.637-10.312 128.807Q-10.562 128.977-10.707 129.262Q-10.851 129.547-10.851 129.848Q-10.851 130.297-10.566 130.672Q-10.281 131.047-9.843 131.047M-5.636 131.606Q-6.101 131.606-6.467 131.356Q-6.832 131.106-7.037 130.702Q-7.242 130.297-7.242 129.840Q-7.242 129.497-7.117 129.176Q-6.992 128.856-6.759 128.606Q-6.527 128.356-6.222 128.217Q-5.918 128.079-5.562 128.079Q-5.050 128.079-4.644 128.399L-4.644 127.239L-5.066 127.239Q-5.277 127.215-5.316 127.001L-5.316 126.911Q-5.277 126.704-5.066 126.680L-4.254 126.680Q-4.054 126.704-4.004 126.911L-4.004 131.008L-3.578 131.008Q-3.371 131.032-3.332 131.239L-3.332 131.329Q-3.371 131.544-3.578 131.567L-4.394 131.567Q-4.593 131.544-4.644 131.329L-4.644 131.200Q-4.840 131.391-5.101 131.499Q-5.363 131.606-5.636 131.606M-5.597 131.047Q-5.238 131.047-4.986 130.778Q-4.734 130.508-4.644 130.133L-4.644 129.301Q-4.703 129.114-4.830 128.963Q-4.957 128.813-5.134 128.725Q-5.312 128.637-5.508 128.637Q-5.816 128.637-6.066 128.807Q-6.316 128.977-6.461 129.262Q-6.605 129.547-6.605 129.848Q-6.605 130.297-6.320 130.672Q-6.035 131.047-5.597 131.047M0.258 130.079L-2.183 130.079Q-2.129 130.356-1.931 130.579Q-1.734 130.801-1.457 130.924Q-1.179 131.047-0.894 131.047Q-0.422 131.047-0.199 130.758Q-0.191 130.747-0.134 130.641Q-0.078 130.536-0.029 130.493Q0.020 130.450 0.114 130.438L0.258 130.438Q0.450 130.458 0.508 130.672L0.508 130.727Q0.442 131.028 0.211 131.225Q-0.019 131.422-0.332 131.514Q-0.644 131.606-0.949 131.606Q-1.433 131.606-1.873 131.378Q-2.312 131.149-2.580 130.749Q-2.847 130.348-2.847 129.856L-2.847 129.797Q-2.847 129.329-2.601 128.926Q-2.355 128.524-1.947 128.290Q-1.539 128.055-1.070 128.055Q-0.566 128.055-0.213 128.278Q0.141 128.501 0.325 128.889Q0.508 129.278 0.508 129.782L0.508 129.840Q0.450 130.055 0.258 130.079M-2.175 129.528L-0.148 129.528Q-0.195 129.118-0.433 128.866Q-0.672 128.614-1.070 128.614Q-1.465 128.614-1.771 128.876Q-2.078 129.137-2.175 129.528M1.063 131.329L1.063 131.239Q1.106 131.032 1.313 131.008L1.735 131.008L1.735 128.680L1.313 128.680Q1.106 128.657 1.063 128.438L1.063 128.352Q1.110 128.141 1.313 128.118L2.129 128.118Q2.325 128.141 2.375 128.352L2.375 128.438L2.367 128.462Q2.594 128.282 2.867 128.180Q3.141 128.079 3.434 128.079Q3.782 128.079 4.020 128.219Q4.258 128.360 4.373 128.618Q4.489 128.876 4.489 129.231L4.489 131.008L4.914 131.008Q5.121 131.032 5.160 131.239L5.160 131.329Q5.121 131.544 4.914 131.567L3.520 131.567Q3.325 131.544 3.274 131.329L3.274 131.239Q3.325 131.028 3.520 131.008L3.848 131.008L3.848 129.262Q3.848 128.954 3.758 128.796Q3.668 128.637 3.375 128.637Q3.106 128.637 2.877 128.768Q2.649 128.899 2.512 129.128Q2.375 129.356 2.375 129.622L2.375 131.008L2.801 131.008Q3.008 131.032 3.047 131.239L3.047 131.329Q3.008 131.544 2.801 131.567L1.313 131.567Q1.106 131.544 1.063 131.329\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-68.537-51.953H-5.94V-71.87h-62.596Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-21.25 -191.034)\">\u003Cpath d=\"M-35.423 130.645L-35.423 129.430L-36.637 129.430Q-36.762 129.419-36.848 129.333Q-36.934 129.247-36.934 129.118Q-36.934 128.989-36.848 128.907Q-36.762 128.825-36.637 128.813L-35.423 128.813L-35.423 127.590Q-35.411 127.465-35.325 127.383Q-35.239 127.301-35.110 127.301Q-34.981 127.301-34.899 127.383Q-34.817 127.465-34.805 127.590L-34.805 128.813L-33.591 128.813Q-33.466 128.825-33.384 128.907Q-33.301 128.989-33.301 129.118Q-33.301 129.247-33.384 129.333Q-33.466 129.419-33.591 129.430L-34.805 129.430L-34.805 130.645Q-34.817 130.770-34.899 130.856Q-34.981 130.942-35.110 130.942Q-35.239 130.942-35.325 130.856Q-35.411 130.770-35.423 130.645\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -191.034)\">\u003Cpath d=\"M-28.516 131.329L-28.516 131.239Q-28.458 131.032-28.266 131.008L-27.555 131.008L-27.555 128.680L-28.266 128.680Q-28.462 128.657-28.516 128.438L-28.516 128.352Q-28.458 128.141-28.266 128.118L-27.165 128.118Q-26.966 128.137-26.915 128.352L-26.915 128.680Q-26.653 128.395-26.298 128.237Q-25.942 128.079-25.555 128.079Q-25.262 128.079-25.028 128.213Q-24.794 128.348-24.794 128.614Q-24.794 128.782-24.903 128.899Q-25.012 129.016-25.180 129.016Q-25.333 129.016-25.448 128.905Q-25.563 128.794-25.563 128.637Q-25.938 128.637-26.253 128.838Q-26.567 129.040-26.741 129.374Q-26.915 129.708-26.915 130.087L-26.915 131.008L-25.969 131.008Q-25.762 131.032-25.723 131.239L-25.723 131.329Q-25.762 131.544-25.969 131.567L-28.266 131.567Q-28.458 131.544-28.516 131.329M-20.981 130.079L-23.423 130.079Q-23.368 130.356-23.171 130.579Q-22.973 130.801-22.696 130.924Q-22.419 131.047-22.134 131.047Q-21.661 131.047-21.438 130.758Q-21.430 130.747-21.374 130.641Q-21.317 130.536-21.268 130.493Q-21.219 130.450-21.126 130.438L-20.981 130.438Q-20.790 130.458-20.731 130.672L-20.731 130.727Q-20.798 131.028-21.028 131.225Q-21.259 131.422-21.571 131.514Q-21.884 131.606-22.188 131.606Q-22.673 131.606-23.112 131.378Q-23.552 131.149-23.819 130.749Q-24.087 130.348-24.087 129.856L-24.087 129.797Q-24.087 129.329-23.841 128.926Q-23.594 128.524-23.186 128.290Q-22.778 128.055-22.309 128.055Q-21.805 128.055-21.452 128.278Q-21.098 128.501-20.915 128.889Q-20.731 129.278-20.731 129.782L-20.731 129.840Q-20.790 130.055-20.981 130.079M-23.415 129.528L-21.387 129.528Q-21.434 129.118-21.673 128.866Q-21.911 128.614-22.309 128.614Q-22.704 128.614-23.010 128.876Q-23.317 129.137-23.415 129.528M-19.661 131.368L-19.661 130.454Q-19.634 130.247-19.423 130.223L-19.255 130.223Q-19.091 130.247-19.032 130.407Q-18.829 131.047-18.102 131.047Q-17.895 131.047-17.667 131.012Q-17.438 130.977-17.270 130.862Q-17.102 130.747-17.102 130.544Q-17.102 130.333-17.325 130.219Q-17.548 130.106-17.821 130.063L-18.520 129.950Q-19.661 129.739-19.661 129.016Q-19.661 128.727-19.516 128.538Q-19.372 128.348-19.132 128.241Q-18.891 128.133-18.635 128.094Q-18.380 128.055-18.102 128.055Q-17.852 128.055-17.659 128.085Q-17.466 128.114-17.302 128.192Q-17.223 128.075-17.094 128.055L-17.016 128.055Q-16.919 128.067-16.856 128.130Q-16.794 128.192-16.782 128.286L-16.782 128.993Q-16.794 129.087-16.856 129.153Q-16.919 129.219-17.016 129.231L-17.184 129.231Q-17.278 129.219-17.344 129.153Q-17.411 129.087-17.423 128.993Q-17.423 128.614-18.118 128.614Q-18.466 128.614-18.784 128.696Q-19.102 128.778-19.102 129.024Q-19.102 129.290-18.430 129.399L-17.727 129.520Q-17.243 129.602-16.893 129.850Q-16.544 130.098-16.544 130.544Q-16.544 130.934-16.780 131.176Q-17.016 131.419-17.366 131.512Q-17.716 131.606-18.102 131.606Q-18.680 131.606-19.079 131.352Q-19.149 131.477-19.198 131.534Q-19.247 131.590-19.352 131.606L-19.423 131.606Q-19.637 131.583-19.661 131.368M-15.384 131.329L-15.384 131.239Q-15.333 131.032-15.137 131.008L-14.098 131.008L-14.098 128.680L-15.071 128.680Q-15.270 128.657-15.321 128.438L-15.321 128.352Q-15.270 128.141-15.071 128.118L-13.704 128.118Q-13.509 128.137-13.458 128.352L-13.458 131.008L-12.544 131.008Q-12.348 131.032-12.298 131.239L-12.298 131.329Q-12.348 131.544-12.544 131.567L-15.137 131.567Q-15.333 131.544-15.384 131.329M-14.352 127.141L-14.352 127.087Q-14.352 126.915-14.216 126.794Q-14.079 126.672-13.903 126.672Q-13.731 126.672-13.594 126.794Q-13.458 126.915-13.458 127.087L-13.458 127.141Q-13.458 127.317-13.594 127.438Q-13.731 127.559-13.903 127.559Q-14.079 127.559-14.216 127.438Q-14.352 127.317-14.352 127.141M-9.891 131.606Q-10.356 131.606-10.721 131.356Q-11.087 131.106-11.292 130.702Q-11.497 130.297-11.497 129.840Q-11.497 129.497-11.372 129.176Q-11.247 128.856-11.014 128.606Q-10.782 128.356-10.477 128.217Q-10.173 128.079-9.817 128.079Q-9.305 128.079-8.899 128.399L-8.899 127.239L-9.321 127.239Q-9.532 127.215-9.571 127.001L-9.571 126.911Q-9.532 126.704-9.321 126.680L-8.509 126.680Q-8.309 126.704-8.259 126.911L-8.259 131.008L-7.833 131.008Q-7.626 131.032-7.587 131.239L-7.587 131.329Q-7.626 131.544-7.833 131.567L-8.649 131.567Q-8.848 131.544-8.899 131.329L-8.899 131.200Q-9.094 131.391-9.356 131.499Q-9.618 131.606-9.891 131.606M-9.852 131.047Q-9.493 131.047-9.241 130.778Q-8.989 130.508-8.899 130.133L-8.899 129.301Q-8.958 129.114-9.085 128.963Q-9.212 128.813-9.389 128.725Q-9.567 128.637-9.762 128.637Q-10.071 128.637-10.321 128.807Q-10.571 128.977-10.716 129.262Q-10.860 129.547-10.860 129.848Q-10.860 130.297-10.575 130.672Q-10.290 131.047-9.852 131.047M-6.766 130.712L-6.766 128.680L-7.188 128.680Q-7.395 128.657-7.438 128.438L-7.438 128.352Q-7.391 128.141-7.188 128.118L-6.372 128.118Q-6.177 128.141-6.126 128.352L-6.126 130.680Q-6.126 130.915-5.956 130.981Q-5.786 131.047-5.501 131.047Q-5.294 131.047-5.098 130.971Q-4.903 130.895-4.778 130.745Q-4.653 130.594-4.653 130.383L-4.653 128.680L-5.075 128.680Q-5.286 128.657-5.325 128.438L-5.325 128.352Q-5.286 128.141-5.075 128.118L-4.262 128.118Q-4.063 128.141-4.012 128.352L-4.012 131.008L-3.587 131.008Q-3.380 131.032-3.341 131.239L-3.341 131.329Q-3.380 131.544-3.587 131.567L-4.403 131.567Q-4.602 131.544-4.653 131.344Q-5.055 131.606-5.563 131.606Q-5.798 131.606-6.012 131.565Q-6.227 131.524-6.393 131.422Q-6.559 131.321-6.663 131.143Q-6.766 130.965-6.766 130.712M-2.856 130.454Q-2.856 130.008-2.442 129.751Q-2.028 129.493-1.487 129.393Q-0.946 129.294-0.438 129.286Q-0.438 129.071-0.573 128.919Q-0.708 128.766-0.915 128.690Q-1.122 128.614-1.333 128.614Q-1.677 128.614-1.837 128.637L-1.837 128.696Q-1.837 128.864-1.956 128.979Q-2.075 129.094-2.239 129.094Q-2.415 129.094-2.530 128.971Q-2.645 128.848-2.645 128.680Q-2.645 128.274-2.264 128.165Q-1.884 128.055-1.325 128.055Q-1.055 128.055-0.788 128.133Q-0.520 128.212-0.296 128.362Q-0.071 128.512 0.066 128.733Q0.202 128.954 0.202 129.231L0.202 130.950Q0.202 131.008 0.730 131.008Q0.925 131.028 0.976 131.239L0.976 131.329Q0.925 131.544 0.730 131.567L0.585 131.567Q0.241 131.567 0.013 131.520Q-0.216 131.473-0.360 131.286Q-0.821 131.606-1.528 131.606Q-1.864 131.606-2.169 131.465Q-2.473 131.325-2.665 131.063Q-2.856 130.801-2.856 130.454M-2.216 130.462Q-2.216 130.735-1.973 130.891Q-1.731 131.047-1.446 131.047Q-1.227 131.047-0.995 130.989Q-0.762 130.930-0.600 130.792Q-0.438 130.653-0.438 130.430L-0.438 129.840Q-0.719 129.840-1.135 129.897Q-1.552 129.954-1.884 130.092Q-2.216 130.231-2.216 130.462M1.433 131.329L1.433 131.239Q1.484 131.032 1.679 131.008L2.784 131.008L2.784 127.239L1.679 127.239Q1.484 127.215 1.433 127.001L1.433 126.911Q1.484 126.704 1.679 126.680L3.175 126.680Q3.366 126.704 3.425 126.911L3.425 131.008L4.527 131.008Q4.726 131.032 4.777 131.239L4.777 131.329Q4.726 131.544 4.527 131.567L1.679 131.567Q1.484 131.544 1.433 131.329\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-37.239 121.209V95.956\"\u002F>\u003Cpath stroke=\"none\" d=\"m-37.239 93.356-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-37.239 73.04V47.785\"\u002F>\u003Cpath stroke=\"none\" d=\"m-37.239 45.186-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-37.239 24.47V-.784\"\u002F>\u003Cpath stroke=\"none\" d=\"m-37.239-3.384-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-37.239-23.7v-25.253\"\u002F>\u003Cpath stroke=\"none\" d=\"m-37.239-51.553-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(46.212 1.944)\">\u003Cpath d=\"M-34.515 132.128Q-34.980 131.858-35.330 131.430Q-35.680 131.003-35.865 130.484Q-36.050 129.964-36.050 129.424Q-36.050 128.884-35.867 128.369Q-35.684 127.855-35.337 127.435Q-34.990 127.014-34.522 126.731Q-34.460 126.710-34.433 126.710L-34.354 126.710Q-34.269 126.720-34.211 126.778Q-34.153 126.837-34.153 126.925Q-34.153 127.052-34.241 127.107Q-34.635 127.359-34.920 127.723Q-35.205 128.088-35.347 128.518Q-35.489 128.949-35.489 129.424Q-35.489 129.779-35.405 130.118Q-35.322 130.456-35.166 130.750Q-35.010 131.044-34.783 131.292Q-34.556 131.540-34.252 131.741Q-34.153 131.810-34.153 131.929Q-34.153 132.015-34.211 132.076Q-34.269 132.138-34.354 132.148L-34.433 132.148Q-34.484 132.148-34.515 132.128M-33.377 131.359L-33.377 131.280Q-33.343 131.099-33.161 131.078L-32.908 131.078L-32.908 127.780L-33.161 127.780Q-33.343 127.759-33.377 127.571L-33.377 127.493Q-33.343 127.312-33.161 127.291L-31.446 127.291Q-31.210 127.291-30.999 127.375Q-30.789 127.459-30.622 127.607Q-30.454 127.756-30.359 127.956Q-30.263 128.156-30.263 128.388Q-30.263 128.710-30.473 128.963Q-30.683 129.215-31.005 129.328Q-30.759 129.383-30.555 129.535Q-30.352 129.687-30.234 129.911Q-30.116 130.135-30.116 130.384Q-30.116 130.699-30.275 130.971Q-30.434 131.242-30.709 131.405Q-30.984 131.567-31.299 131.567L-33.161 131.567Q-33.343 131.546-33.377 131.359M-32.348 129.585L-32.348 131.078L-31.446 131.078Q-31.247 131.078-31.070 130.988Q-30.892 130.897-30.782 130.740Q-30.673 130.583-30.673 130.384Q-30.673 130.183-30.762 130Q-30.851 129.817-31.010 129.701Q-31.169 129.585-31.367 129.585L-32.348 129.585M-32.348 127.780L-32.348 129.096L-31.593 129.096Q-31.292 129.096-31.056 128.891Q-30.820 128.686-30.820 128.388Q-30.820 128.224-30.906 128.084Q-30.991 127.944-31.136 127.862Q-31.281 127.780-31.446 127.780L-32.348 127.780M-28.304 132.541Q-28.404 132.541-28.482 132.463Q-28.561 132.384-28.561 132.288Q-28.561 132.134-28.393 132.069Q-28.202 132.025-28.051 131.887Q-27.901 131.748-27.843 131.553Q-27.864 131.553-27.891 131.567L-27.946 131.567Q-28.147 131.567-28.292 131.425Q-28.438 131.283-28.438 131.078Q-28.438 130.873-28.294 130.733Q-28.151 130.593-27.946 130.593Q-27.761 130.593-27.617 130.699Q-27.474 130.805-27.395 130.974Q-27.317 131.143-27.317 131.328Q-27.317 131.745-27.578 132.085Q-27.840 132.425-28.246 132.534Q-28.267 132.541-28.304 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 1.944)\">\u003Cpath d=\"M-22.301 131.359L-22.301 131.280Q-22.264 131.099-22.083 131.078L-21.714 131.078L-21.714 129.041L-22.083 129.041Q-22.264 129.021-22.301 128.829L-22.301 128.754Q-22.260 128.569-22.083 128.549L-21.368 128.549Q-21.197 128.569-21.153 128.754L-21.153 128.829L-21.160 128.850Q-20.962 128.692-20.722 128.604Q-20.483 128.515-20.227 128.515Q-19.923 128.515-19.714 128.638Q-19.506 128.761-19.405 128.986Q-19.304 129.212-19.304 129.523L-19.304 131.078L-18.931 131.078Q-18.750 131.099-18.716 131.280L-18.716 131.359Q-18.750 131.546-18.931 131.567L-20.152 131.567Q-20.322 131.546-20.367 131.359L-20.367 131.280Q-20.322 131.095-20.152 131.078L-19.864 131.078L-19.864 129.550Q-19.864 129.280-19.943 129.142Q-20.022 129.004-20.278 129.004Q-20.514 129.004-20.714 129.118Q-20.914 129.233-21.033 129.432Q-21.153 129.632-21.153 129.865L-21.153 131.078L-20.780 131.078Q-20.599 131.099-20.565 131.280L-20.565 131.359Q-20.599 131.546-20.780 131.567L-22.083 131.567Q-22.264 131.546-22.301 131.359M-17.144 132.541Q-17.243 132.541-17.321 132.463Q-17.400 132.384-17.400 132.288Q-17.400 132.134-17.233 132.069Q-17.041 132.025-16.891 131.887Q-16.740 131.748-16.682 131.553Q-16.703 131.553-16.730 131.567L-16.785 131.567Q-16.987 131.567-17.132 131.425Q-17.277 131.283-17.277 131.078Q-17.277 130.873-17.134 130.733Q-16.990 130.593-16.785 130.593Q-16.600 130.593-16.457 130.699Q-16.313 130.805-16.235 130.974Q-16.156 131.143-16.156 131.328Q-16.156 131.745-16.417 132.085Q-16.679 132.425-17.086 132.534Q-17.106 132.541-17.144 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 1.944)\">\u003Cpath d=\"M-10.212 130.798Q-10.110 130.976-9.905 131.061Q-9.700 131.147-9.471 131.147Q-9.211 131.147-8.972 131.034Q-8.732 130.921-8.580 130.714Q-8.428 130.507-8.428 130.244Q-8.428 130.022-8.532 129.810Q-8.637 129.598-8.825 129.470Q-9.013 129.342-9.249 129.342Q-9.778 129.342-10.072 129.622Q-10.141 129.697-10.188 129.738Q-10.236 129.779-10.311 129.790L-10.400 129.790Q-10.575 129.769-10.619 129.578L-10.619 127.493Q-10.575 127.312-10.400 127.291L-8.336 127.291Q-8.165 127.308-8.121 127.493L-8.121 127.571Q-8.165 127.759-8.336 127.780L-10.059 127.780L-10.059 129.027Q-9.703 128.850-9.249 128.850Q-8.873 128.850-8.553 129.039Q-8.233 129.229-8.051 129.552Q-7.868 129.875-7.868 130.244Q-7.868 130.658-8.098 130.972Q-8.329 131.287-8.700 131.461Q-9.071 131.635-9.471 131.635Q-9.693 131.635-9.936 131.570Q-10.178 131.505-10.383 131.369Q-10.588 131.232-10.711 131.027Q-10.834 130.822-10.834 130.572Q-10.834 130.425-10.734 130.318Q-10.633 130.210-10.479 130.210Q-10.407 130.210-10.346 130.236Q-10.284 130.261-10.235 130.309Q-10.185 130.357-10.158 130.424Q-10.130 130.490-10.130 130.559Q-10.130 130.699-10.212 130.798M-6.743 131.359L-6.743 131.280Q-6.699 131.099-6.524 131.078L-5.810 131.078L-5.810 128.293Q-6.142 128.563-6.538 128.563Q-6.740 128.563-6.784 128.361L-6.784 128.282Q-6.740 128.094-6.569 128.074Q-6.282 128.074-6.060 127.865Q-5.837 127.657-5.714 127.353Q-5.653 127.240-5.516 127.219L-5.468 127.219Q-5.297 127.236-5.253 127.424L-5.253 131.078L-4.539 131.078Q-4.364 131.099-4.320 131.280L-4.320 131.359Q-4.364 131.546-4.539 131.567L-6.524 131.567Q-6.699 131.546-6.743 131.359M-3.404 131.359L-3.404 131.294Q-3.376 131.147-3.288 131.106L-2.160 130.172Q-1.869 129.930-1.710 129.796Q-1.551 129.663-1.380 129.470Q-1.209 129.277-1.103 129.058Q-0.998 128.839-0.998 128.607Q-0.998 128.323-1.151 128.118Q-1.305 127.913-1.550 127.812Q-1.794 127.712-2.074 127.712Q-2.300 127.712-2.500 127.819Q-2.700 127.927-2.789 128.115Q-2.700 128.231-2.700 128.361Q-2.700 128.501-2.804 128.609Q-2.908 128.716-3.048 128.716Q-3.202 128.716-3.303 128.607Q-3.404 128.498-3.404 128.347Q-3.404 128.091-3.286 127.879Q-3.168 127.667-2.959 127.517Q-2.751 127.366-2.517 127.293Q-2.283 127.219-2.026 127.219Q-1.606 127.219-1.242 127.385Q-0.878 127.551-0.657 127.867Q-0.437 128.183-0.437 128.607Q-0.437 128.908-0.553 129.173Q-0.669 129.438-0.866 129.665Q-1.062 129.892-1.332 130.121Q-1.603 130.350-1.787 130.504L-2.495 131.078L-0.998 131.078L-0.998 130.952Q-0.953 130.767-0.779 130.747L-0.656 130.747Q-0.481 130.764-0.437 130.952L-0.437 131.359Q-0.481 131.546-0.656 131.567L-3.188 131.567Q-3.359 131.550-3.404 131.359M0.848 132.148L0.773 132.148Q0.681 132.138 0.621 132.075Q0.561 132.011 0.561 131.929Q0.561 131.806 0.653 131.748Q0.947 131.560 1.183 131.307Q1.419 131.054 1.580 130.750Q1.740 130.446 1.819 130.114Q1.897 129.783 1.897 129.424Q1.897 128.952 1.754 128.522Q1.610 128.091 1.332 127.729Q1.053 127.366 0.667 127.113Q0.561 127.042 0.561 126.925Q0.561 126.840 0.621 126.780Q0.681 126.720 0.773 126.710L0.848 126.710Q0.896 126.710 0.927 126.731Q1.265 126.925 1.563 127.230Q1.860 127.534 2.053 127.879Q2.246 128.224 2.352 128.614Q2.458 129.004 2.458 129.424Q2.458 129.848 2.352 130.243Q2.246 130.637 2.050 130.984Q1.853 131.331 1.569 131.623Q1.286 131.916 0.934 132.128Q0.872 132.148 0.848 132.148\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(46.212 -46.425)\">\u003Cpath d=\"M-34.515 132.128Q-34.980 131.858-35.330 131.430Q-35.680 131.003-35.865 130.484Q-36.050 129.964-36.050 129.424Q-36.050 128.884-35.867 128.369Q-35.684 127.855-35.337 127.435Q-34.990 127.014-34.522 126.731Q-34.460 126.710-34.433 126.710L-34.354 126.710Q-34.269 126.720-34.211 126.778Q-34.153 126.837-34.153 126.925Q-34.153 127.052-34.241 127.107Q-34.635 127.359-34.920 127.723Q-35.205 128.088-35.347 128.518Q-35.489 128.949-35.489 129.424Q-35.489 129.779-35.405 130.118Q-35.322 130.456-35.166 130.750Q-35.010 131.044-34.783 131.292Q-34.556 131.540-34.252 131.741Q-34.153 131.810-34.153 131.929Q-34.153 132.015-34.211 132.076Q-34.269 132.138-34.354 132.148L-34.433 132.148Q-34.484 132.148-34.515 132.128M-33.377 131.359L-33.377 131.280Q-33.343 131.099-33.161 131.078L-32.908 131.078L-32.908 127.780L-33.161 127.780Q-33.343 127.759-33.377 127.571L-33.377 127.493Q-33.343 127.312-33.161 127.291L-31.446 127.291Q-31.210 127.291-30.999 127.375Q-30.789 127.459-30.622 127.607Q-30.454 127.756-30.359 127.956Q-30.263 128.156-30.263 128.388Q-30.263 128.710-30.473 128.963Q-30.683 129.215-31.005 129.328Q-30.759 129.383-30.555 129.535Q-30.352 129.687-30.234 129.911Q-30.116 130.135-30.116 130.384Q-30.116 130.699-30.275 130.971Q-30.434 131.242-30.709 131.405Q-30.984 131.567-31.299 131.567L-33.161 131.567Q-33.343 131.546-33.377 131.359M-32.348 129.585L-32.348 131.078L-31.446 131.078Q-31.247 131.078-31.070 130.988Q-30.892 130.897-30.782 130.740Q-30.673 130.583-30.673 130.384Q-30.673 130.183-30.762 130Q-30.851 129.817-31.010 129.701Q-31.169 129.585-31.367 129.585L-32.348 129.585M-32.348 127.780L-32.348 129.096L-31.593 129.096Q-31.292 129.096-31.056 128.891Q-30.820 128.686-30.820 128.388Q-30.820 128.224-30.906 128.084Q-30.991 127.944-31.136 127.862Q-31.281 127.780-31.446 127.780L-32.348 127.780M-28.304 132.541Q-28.404 132.541-28.482 132.463Q-28.561 132.384-28.561 132.288Q-28.561 132.134-28.393 132.069Q-28.202 132.025-28.051 131.887Q-27.901 131.748-27.843 131.553Q-27.864 131.553-27.891 131.567L-27.946 131.567Q-28.147 131.567-28.292 131.425Q-28.438 131.283-28.438 131.078Q-28.438 130.873-28.294 130.733Q-28.151 130.593-27.946 130.593Q-27.761 130.593-27.617 130.699Q-27.474 130.805-27.395 130.974Q-27.317 131.143-27.317 131.328Q-27.317 131.745-27.578 132.085Q-27.840 132.425-28.246 132.534Q-28.267 132.541-28.304 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -46.425)\">\u003Cpath d=\"M-22.055 130.330Q-22.055 130.080-21.919 129.858Q-21.782 129.636-21.563 129.484Q-21.344 129.332-21.095 129.256Q-21.303 129.192-21.502 129.067Q-21.700 128.942-21.825 128.759Q-21.949 128.576-21.949 128.361Q-21.949 128.012-21.734 127.754Q-21.519 127.496-21.184 127.358Q-20.849 127.219-20.507 127.219Q-20.165 127.219-19.830 127.358Q-19.495 127.496-19.280 127.758Q-19.065 128.019-19.065 128.361Q-19.065 128.576-19.189 128.757Q-19.314 128.939-19.512 129.065Q-19.711 129.192-19.919 129.256Q-19.523 129.376-19.242 129.661Q-18.962 129.947-18.962 130.330Q-18.962 130.713-19.188 131.013Q-19.413 131.314-19.772 131.475Q-20.131 131.635-20.507 131.635Q-20.883 131.635-21.242 131.476Q-21.601 131.317-21.828 131.017Q-22.055 130.716-22.055 130.330M-21.495 130.330Q-21.495 130.569-21.350 130.757Q-21.204 130.945-20.975 131.046Q-20.746 131.147-20.507 131.147Q-20.268 131.147-20.040 131.046Q-19.813 130.945-19.668 130.755Q-19.523 130.566-19.523 130.330Q-19.523 130.087-19.668 129.897Q-19.813 129.708-20.040 129.605Q-20.268 129.503-20.507 129.503Q-20.746 129.503-20.975 129.605Q-21.204 129.708-21.350 129.896Q-21.495 130.084-21.495 130.330M-21.389 128.361Q-21.389 128.569-21.252 128.716Q-21.115 128.863-20.909 128.937Q-20.702 129.010-20.507 129.010Q-20.316 129.010-20.107 128.937Q-19.899 128.863-19.762 128.715Q-19.625 128.566-19.625 128.361Q-19.625 128.156-19.762 128.007Q-19.899 127.859-20.107 127.785Q-20.316 127.712-20.507 127.712Q-20.702 127.712-20.909 127.785Q-21.115 127.859-21.252 128.005Q-21.389 128.152-21.389 128.361M-17.144 132.541Q-17.243 132.541-17.321 132.463Q-17.400 132.384-17.400 132.288Q-17.400 132.134-17.233 132.069Q-17.041 132.025-16.891 131.887Q-16.740 131.748-16.682 131.553Q-16.703 131.553-16.730 131.567L-16.785 131.567Q-16.987 131.567-17.132 131.425Q-17.277 131.283-17.277 131.078Q-17.277 130.873-17.134 130.733Q-16.990 130.593-16.785 130.593Q-16.600 130.593-16.457 130.699Q-16.313 130.805-16.235 130.974Q-16.156 131.143-16.156 131.328Q-16.156 131.745-16.417 132.085Q-16.679 132.425-17.086 132.534Q-17.106 132.541-17.144 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -46.425)\">\u003Cpath d=\"M-11.145 131.359L-11.145 131.280Q-11.108 131.099-10.927 131.078L-10.558 131.078L-10.558 129.041L-10.927 129.041Q-11.108 129.021-11.145 128.829L-11.145 128.754Q-11.104 128.569-10.927 128.549L-10.212 128.549Q-10.041 128.569-9.997 128.754L-9.997 128.829L-10.004 128.850Q-9.806 128.692-9.566 128.604Q-9.327 128.515-9.071 128.515Q-8.767 128.515-8.558 128.638Q-8.350 128.761-8.249 128.986Q-8.148 129.212-8.148 129.523L-8.148 131.078L-7.775 131.078Q-7.594 131.099-7.560 131.280L-7.560 131.359Q-7.594 131.546-7.775 131.567L-8.996 131.567Q-9.166 131.546-9.211 131.359L-9.211 131.280Q-9.166 131.095-8.996 131.078L-8.708 131.078L-8.708 129.550Q-8.708 129.280-8.787 129.142Q-8.866 129.004-9.122 129.004Q-9.358 129.004-9.558 129.118Q-9.758 129.233-9.877 129.432Q-9.997 129.632-9.997 129.865L-9.997 131.078L-9.624 131.078Q-9.443 131.099-9.409 131.280L-9.409 131.359Q-9.443 131.546-9.624 131.567L-10.927 131.567Q-11.108 131.546-11.145 131.359M-5.988 132.541Q-6.087 132.541-6.165 132.463Q-6.244 132.384-6.244 132.288Q-6.244 132.134-6.077 132.069Q-5.885 132.025-5.735 131.887Q-5.584 131.748-5.526 131.553Q-5.547 131.553-5.574 131.567L-5.629 131.567Q-5.831 131.567-5.976 131.425Q-6.121 131.283-6.121 131.078Q-6.121 130.873-5.978 130.733Q-5.834 130.593-5.629 130.593Q-5.444 130.593-5.301 130.699Q-5.157 130.805-5.079 130.974Q-5 131.143-5 131.328Q-5 131.745-5.261 132.085Q-5.523 132.425-5.930 132.534Q-5.950 132.541-5.988 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -46.425)\">\u003Cpath d=\"M0.011 131.359L0.011 131.280Q0.048 131.099 0.229 131.078L0.598 131.078L0.598 129.041L0.229 129.041Q0.048 129.021 0.011 128.829L0.011 128.754Q0.052 128.569 0.229 128.549L0.944 128.549Q1.115 128.569 1.159 128.754L1.159 128.829L1.152 128.850Q1.350 128.692 1.590 128.604Q1.829 128.515 2.085 128.515Q2.389 128.515 2.598 128.638Q2.806 128.761 2.907 128.986Q3.008 129.212 3.008 129.523L3.008 131.078L3.381 131.078Q3.562 131.099 3.596 131.280L3.596 131.359Q3.562 131.546 3.381 131.567L2.160 131.567Q1.990 131.546 1.945 131.359L1.945 131.280Q1.990 131.095 2.160 131.078L2.448 131.078L2.448 129.550Q2.448 129.280 2.369 129.142Q2.290 129.004 2.034 129.004Q1.798 129.004 1.598 129.118Q1.398 129.233 1.279 129.432Q1.159 129.632 1.159 129.865L1.159 131.078L1.532 131.078Q1.713 131.099 1.747 131.280L1.747 131.359Q1.713 131.546 1.532 131.567L0.229 131.567Q0.048 131.546 0.011 131.359M4.574 132.148L4.498 132.148Q4.406 132.138 4.346 132.075Q4.286 132.011 4.286 131.929Q4.286 131.806 4.379 131.748Q4.673 131.560 4.908 131.307Q5.144 131.054 5.305 130.750Q5.466 130.446 5.544 130.114Q5.623 129.783 5.623 129.424Q5.623 128.952 5.479 128.522Q5.336 128.091 5.057 127.729Q4.779 127.366 4.392 127.113Q4.286 127.042 4.286 126.925Q4.286 126.840 4.346 126.780Q4.406 126.720 4.498 126.710L4.574 126.710Q4.621 126.710 4.652 126.731Q4.991 126.925 5.288 127.230Q5.585 127.534 5.778 127.879Q5.971 128.224 6.077 128.614Q6.183 129.004 6.183 129.424Q6.183 129.848 6.077 130.243Q5.971 130.637 5.775 130.984Q5.578 131.331 5.295 131.623Q5.011 131.916 4.659 132.128Q4.597 132.148 4.574 132.148\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(46.212 -94.795)\">\u003Cpath d=\"M-34.515 132.128Q-34.980 131.858-35.330 131.430Q-35.680 131.003-35.865 130.484Q-36.050 129.964-36.050 129.424Q-36.050 128.884-35.867 128.369Q-35.684 127.855-35.337 127.435Q-34.990 127.014-34.522 126.731Q-34.460 126.710-34.433 126.710L-34.354 126.710Q-34.269 126.720-34.211 126.778Q-34.153 126.837-34.153 126.925Q-34.153 127.052-34.241 127.107Q-34.635 127.359-34.920 127.723Q-35.205 128.088-35.347 128.518Q-35.489 128.949-35.489 129.424Q-35.489 129.779-35.405 130.118Q-35.322 130.456-35.166 130.750Q-35.010 131.044-34.783 131.292Q-34.556 131.540-34.252 131.741Q-34.153 131.810-34.153 131.929Q-34.153 132.015-34.211 132.076Q-34.269 132.138-34.354 132.148L-34.433 132.148Q-34.484 132.148-34.515 132.128M-33.377 131.359L-33.377 131.280Q-33.343 131.099-33.161 131.078L-32.908 131.078L-32.908 127.780L-33.161 127.780Q-33.343 127.759-33.377 127.571L-33.377 127.493Q-33.343 127.312-33.161 127.291L-31.446 127.291Q-31.210 127.291-30.999 127.375Q-30.789 127.459-30.622 127.607Q-30.454 127.756-30.359 127.956Q-30.263 128.156-30.263 128.388Q-30.263 128.710-30.473 128.963Q-30.683 129.215-31.005 129.328Q-30.759 129.383-30.555 129.535Q-30.352 129.687-30.234 129.911Q-30.116 130.135-30.116 130.384Q-30.116 130.699-30.275 130.971Q-30.434 131.242-30.709 131.405Q-30.984 131.567-31.299 131.567L-33.161 131.567Q-33.343 131.546-33.377 131.359M-32.348 129.585L-32.348 131.078L-31.446 131.078Q-31.247 131.078-31.070 130.988Q-30.892 130.897-30.782 130.740Q-30.673 130.583-30.673 130.384Q-30.673 130.183-30.762 130Q-30.851 129.817-31.010 129.701Q-31.169 129.585-31.367 129.585L-32.348 129.585M-32.348 127.780L-32.348 129.096L-31.593 129.096Q-31.292 129.096-31.056 128.891Q-30.820 128.686-30.820 128.388Q-30.820 128.224-30.906 128.084Q-30.991 127.944-31.136 127.862Q-31.281 127.780-31.446 127.780L-32.348 127.780M-28.304 132.541Q-28.404 132.541-28.482 132.463Q-28.561 132.384-28.561 132.288Q-28.561 132.134-28.393 132.069Q-28.202 132.025-28.051 131.887Q-27.901 131.748-27.843 131.553Q-27.864 131.553-27.891 131.567L-27.946 131.567Q-28.147 131.567-28.292 131.425Q-28.438 131.283-28.438 131.078Q-28.438 130.873-28.294 130.733Q-28.151 130.593-27.946 130.593Q-27.761 130.593-27.617 130.699Q-27.474 130.805-27.395 130.974Q-27.317 131.143-27.317 131.328Q-27.317 131.745-27.578 132.085Q-27.840 132.425-28.246 132.534Q-28.267 132.541-28.304 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -94.795)\">\u003Cpath d=\"M-22.301 131.359L-22.301 131.280Q-22.264 131.099-22.083 131.078L-21.714 131.078L-21.714 129.041L-22.083 129.041Q-22.264 129.021-22.301 128.829L-22.301 128.754Q-22.260 128.569-22.083 128.549L-21.368 128.549Q-21.197 128.569-21.153 128.754L-21.153 128.829L-21.160 128.850Q-20.962 128.692-20.722 128.604Q-20.483 128.515-20.227 128.515Q-19.923 128.515-19.714 128.638Q-19.506 128.761-19.405 128.986Q-19.304 129.212-19.304 129.523L-19.304 131.078L-18.931 131.078Q-18.750 131.099-18.716 131.280L-18.716 131.359Q-18.750 131.546-18.931 131.567L-20.152 131.567Q-20.322 131.546-20.367 131.359L-20.367 131.280Q-20.322 131.095-20.152 131.078L-19.864 131.078L-19.864 129.550Q-19.864 129.280-19.943 129.142Q-20.022 129.004-20.278 129.004Q-20.514 129.004-20.714 129.118Q-20.914 129.233-21.033 129.432Q-21.153 129.632-21.153 129.865L-21.153 131.078L-20.780 131.078Q-20.599 131.099-20.565 131.280L-20.565 131.359Q-20.599 131.546-20.780 131.567L-22.083 131.567Q-22.264 131.546-22.301 131.359M-17.144 132.541Q-17.243 132.541-17.321 132.463Q-17.400 132.384-17.400 132.288Q-17.400 132.134-17.233 132.069Q-17.041 132.025-16.891 131.887Q-16.740 131.748-16.682 131.553Q-16.703 131.553-16.730 131.567L-16.785 131.567Q-16.987 131.567-17.132 131.425Q-17.277 131.283-17.277 131.078Q-17.277 130.873-17.134 130.733Q-16.990 130.593-16.785 130.593Q-16.600 130.593-16.457 130.699Q-16.313 130.805-16.235 130.974Q-16.156 131.143-16.156 131.328Q-16.156 131.745-16.417 132.085Q-16.679 132.425-17.086 132.534Q-17.106 132.541-17.144 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -94.795)\">\u003Cpath d=\"M-10.212 130.798Q-10.110 130.976-9.905 131.061Q-9.700 131.147-9.471 131.147Q-9.211 131.147-8.972 131.034Q-8.732 130.921-8.580 130.714Q-8.428 130.507-8.428 130.244Q-8.428 130.022-8.532 129.810Q-8.637 129.598-8.825 129.470Q-9.013 129.342-9.249 129.342Q-9.778 129.342-10.072 129.622Q-10.141 129.697-10.188 129.738Q-10.236 129.779-10.311 129.790L-10.400 129.790Q-10.575 129.769-10.619 129.578L-10.619 127.493Q-10.575 127.312-10.400 127.291L-8.336 127.291Q-8.165 127.308-8.121 127.493L-8.121 127.571Q-8.165 127.759-8.336 127.780L-10.059 127.780L-10.059 129.027Q-9.703 128.850-9.249 128.850Q-8.873 128.850-8.553 129.039Q-8.233 129.229-8.051 129.552Q-7.868 129.875-7.868 130.244Q-7.868 130.658-8.098 130.972Q-8.329 131.287-8.700 131.461Q-9.071 131.635-9.471 131.635Q-9.693 131.635-9.936 131.570Q-10.178 131.505-10.383 131.369Q-10.588 131.232-10.711 131.027Q-10.834 130.822-10.834 130.572Q-10.834 130.425-10.734 130.318Q-10.633 130.210-10.479 130.210Q-10.407 130.210-10.346 130.236Q-10.284 130.261-10.235 130.309Q-10.185 130.357-10.158 130.424Q-10.130 130.490-10.130 130.559Q-10.130 130.699-10.212 130.798M-6.743 131.359L-6.743 131.280Q-6.699 131.099-6.524 131.078L-5.810 131.078L-5.810 128.293Q-6.142 128.563-6.538 128.563Q-6.740 128.563-6.784 128.361L-6.784 128.282Q-6.740 128.094-6.569 128.074Q-6.282 128.074-6.060 127.865Q-5.837 127.657-5.714 127.353Q-5.653 127.240-5.516 127.219L-5.468 127.219Q-5.297 127.236-5.253 127.424L-5.253 131.078L-4.539 131.078Q-4.364 131.099-4.320 131.280L-4.320 131.359Q-4.364 131.546-4.539 131.567L-6.524 131.567Q-6.699 131.546-6.743 131.359M-3.404 131.359L-3.404 131.294Q-3.376 131.147-3.288 131.106L-2.160 130.172Q-1.869 129.930-1.710 129.796Q-1.551 129.663-1.380 129.470Q-1.209 129.277-1.103 129.058Q-0.998 128.839-0.998 128.607Q-0.998 128.323-1.151 128.118Q-1.305 127.913-1.550 127.812Q-1.794 127.712-2.074 127.712Q-2.300 127.712-2.500 127.819Q-2.700 127.927-2.789 128.115Q-2.700 128.231-2.700 128.361Q-2.700 128.501-2.804 128.609Q-2.908 128.716-3.048 128.716Q-3.202 128.716-3.303 128.607Q-3.404 128.498-3.404 128.347Q-3.404 128.091-3.286 127.879Q-3.168 127.667-2.959 127.517Q-2.751 127.366-2.517 127.293Q-2.283 127.219-2.026 127.219Q-1.606 127.219-1.242 127.385Q-0.878 127.551-0.657 127.867Q-0.437 128.183-0.437 128.607Q-0.437 128.908-0.553 129.173Q-0.669 129.438-0.866 129.665Q-1.062 129.892-1.332 130.121Q-1.603 130.350-1.787 130.504L-2.495 131.078L-0.998 131.078L-0.998 130.952Q-0.953 130.767-0.779 130.747L-0.656 130.747Q-0.481 130.764-0.437 130.952L-0.437 131.359Q-0.481 131.546-0.656 131.567L-3.188 131.567Q-3.359 131.550-3.404 131.359M0.848 132.148L0.773 132.148Q0.681 132.138 0.621 132.075Q0.561 132.011 0.561 131.929Q0.561 131.806 0.653 131.748Q0.947 131.560 1.183 131.307Q1.419 131.054 1.580 130.750Q1.740 130.446 1.819 130.114Q1.897 129.783 1.897 129.424Q1.897 128.952 1.754 128.522Q1.610 128.091 1.332 127.729Q1.053 127.366 0.667 127.113Q0.561 127.042 0.561 126.925Q0.561 126.840 0.621 126.780Q0.681 126.720 0.773 126.710L0.848 126.710Q0.896 126.710 0.927 126.731Q1.265 126.925 1.563 127.230Q1.860 127.534 2.053 127.879Q2.246 128.224 2.352 128.614Q2.458 129.004 2.458 129.424Q2.458 129.848 2.352 130.243Q2.246 130.637 2.050 130.984Q1.853 131.331 1.569 131.623Q1.286 131.916 0.934 132.128Q0.872 132.148 0.848 132.148\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(46.212 -143.165)\">\u003Cpath d=\"M-34.515 132.128Q-34.980 131.858-35.330 131.430Q-35.680 131.003-35.865 130.484Q-36.050 129.964-36.050 129.424Q-36.050 128.884-35.867 128.369Q-35.684 127.855-35.337 127.435Q-34.990 127.014-34.522 126.731Q-34.460 126.710-34.433 126.710L-34.354 126.710Q-34.269 126.720-34.211 126.778Q-34.153 126.837-34.153 126.925Q-34.153 127.052-34.241 127.107Q-34.635 127.359-34.920 127.723Q-35.205 128.088-35.347 128.518Q-35.489 128.949-35.489 129.424Q-35.489 129.779-35.405 130.118Q-35.322 130.456-35.166 130.750Q-35.010 131.044-34.783 131.292Q-34.556 131.540-34.252 131.741Q-34.153 131.810-34.153 131.929Q-34.153 132.015-34.211 132.076Q-34.269 132.138-34.354 132.148L-34.433 132.148Q-34.484 132.148-34.515 132.128M-33.377 131.359L-33.377 131.280Q-33.343 131.099-33.161 131.078L-32.908 131.078L-32.908 127.780L-33.161 127.780Q-33.343 127.759-33.377 127.571L-33.377 127.493Q-33.343 127.312-33.161 127.291L-31.446 127.291Q-31.210 127.291-30.999 127.375Q-30.789 127.459-30.622 127.607Q-30.454 127.756-30.359 127.956Q-30.263 128.156-30.263 128.388Q-30.263 128.710-30.473 128.963Q-30.683 129.215-31.005 129.328Q-30.759 129.383-30.555 129.535Q-30.352 129.687-30.234 129.911Q-30.116 130.135-30.116 130.384Q-30.116 130.699-30.275 130.971Q-30.434 131.242-30.709 131.405Q-30.984 131.567-31.299 131.567L-33.161 131.567Q-33.343 131.546-33.377 131.359M-32.348 129.585L-32.348 131.078L-31.446 131.078Q-31.247 131.078-31.070 130.988Q-30.892 130.897-30.782 130.740Q-30.673 130.583-30.673 130.384Q-30.673 130.183-30.762 130Q-30.851 129.817-31.010 129.701Q-31.169 129.585-31.367 129.585L-32.348 129.585M-32.348 127.780L-32.348 129.096L-31.593 129.096Q-31.292 129.096-31.056 128.891Q-30.820 128.686-30.820 128.388Q-30.820 128.224-30.906 128.084Q-30.991 127.944-31.136 127.862Q-31.281 127.780-31.446 127.780L-32.348 127.780M-28.304 132.541Q-28.404 132.541-28.482 132.463Q-28.561 132.384-28.561 132.288Q-28.561 132.134-28.393 132.069Q-28.202 132.025-28.051 131.887Q-27.901 131.748-27.843 131.553Q-27.864 131.553-27.891 131.567L-27.946 131.567Q-28.147 131.567-28.292 131.425Q-28.438 131.283-28.438 131.078Q-28.438 130.873-28.294 130.733Q-28.151 130.593-27.946 130.593Q-27.761 130.593-27.617 130.699Q-27.474 130.805-27.395 130.974Q-27.317 131.143-27.317 131.328Q-27.317 131.745-27.578 132.085Q-27.840 132.425-28.246 132.534Q-28.267 132.541-28.304 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -143.165)\">\u003Cpath d=\"M-22.301 131.359L-22.301 131.280Q-22.264 131.099-22.083 131.078L-21.714 131.078L-21.714 129.041L-22.083 129.041Q-22.264 129.021-22.301 128.829L-22.301 128.754Q-22.260 128.569-22.083 128.549L-21.368 128.549Q-21.197 128.569-21.153 128.754L-21.153 128.829L-21.160 128.850Q-20.962 128.692-20.722 128.604Q-20.483 128.515-20.227 128.515Q-19.923 128.515-19.714 128.638Q-19.506 128.761-19.405 128.986Q-19.304 129.212-19.304 129.523L-19.304 131.078L-18.931 131.078Q-18.750 131.099-18.716 131.280L-18.716 131.359Q-18.750 131.546-18.931 131.567L-20.152 131.567Q-20.322 131.546-20.367 131.359L-20.367 131.280Q-20.322 131.095-20.152 131.078L-19.864 131.078L-19.864 129.550Q-19.864 129.280-19.943 129.142Q-20.022 129.004-20.278 129.004Q-20.514 129.004-20.714 129.118Q-20.914 129.233-21.033 129.432Q-21.153 129.632-21.153 129.865L-21.153 131.078L-20.780 131.078Q-20.599 131.099-20.565 131.280L-20.565 131.359Q-20.599 131.546-20.780 131.567L-22.083 131.567Q-22.264 131.546-22.301 131.359M-17.144 132.541Q-17.243 132.541-17.321 132.463Q-17.400 132.384-17.400 132.288Q-17.400 132.134-17.233 132.069Q-17.041 132.025-16.891 131.887Q-16.740 131.748-16.682 131.553Q-16.703 131.553-16.730 131.567L-16.785 131.567Q-16.987 131.567-17.132 131.425Q-17.277 131.283-17.277 131.078Q-17.277 130.873-17.134 130.733Q-16.990 130.593-16.785 130.593Q-16.600 130.593-16.457 130.699Q-16.313 130.805-16.235 130.974Q-16.156 131.143-16.156 131.328Q-16.156 131.745-16.417 132.085Q-16.679 132.425-17.086 132.534Q-17.106 132.541-17.144 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -143.165)\">\u003Cpath d=\"M-10.834 131.359L-10.834 131.294Q-10.807 131.147-10.718 131.106L-9.590 130.172Q-9.300 129.930-9.141 129.796Q-8.982 129.663-8.811 129.470Q-8.640 129.277-8.534 129.058Q-8.428 128.839-8.428 128.607Q-8.428 128.323-8.582 128.118Q-8.736 127.913-8.980 127.812Q-9.225 127.712-9.505 127.712Q-9.730 127.712-9.930 127.819Q-10.130 127.927-10.219 128.115Q-10.130 128.231-10.130 128.361Q-10.130 128.501-10.235 128.609Q-10.339 128.716-10.479 128.716Q-10.633 128.716-10.734 128.607Q-10.834 128.498-10.834 128.347Q-10.834 128.091-10.717 127.879Q-10.599 127.667-10.390 127.517Q-10.182 127.366-9.947 127.293Q-9.713 127.219-9.457 127.219Q-9.037 127.219-8.673 127.385Q-8.309 127.551-8.088 127.867Q-7.868 128.183-7.868 128.607Q-7.868 128.908-7.984 129.173Q-8.100 129.438-8.297 129.665Q-8.493 129.892-8.763 130.121Q-9.033 130.350-9.218 130.504L-9.925 131.078L-8.428 131.078L-8.428 130.952Q-8.384 130.767-8.209 130.747L-8.086 130.747Q-7.912 130.764-7.868 130.952L-7.868 131.359Q-7.912 131.546-8.086 131.567L-10.619 131.567Q-10.790 131.550-10.834 131.359M-5.636 131.635Q-6.015 131.635-6.306 131.427Q-6.596 131.218-6.789 130.878Q-6.982 130.538-7.076 130.155Q-7.170 129.773-7.170 129.424Q-7.170 129.082-7.075 128.694Q-6.979 128.306-6.789 127.973Q-6.600 127.640-6.307 127.430Q-6.015 127.219-5.636 127.219Q-5.150 127.219-4.800 127.568Q-4.450 127.917-4.277 128.429Q-4.104 128.942-4.104 129.424Q-4.104 129.909-4.277 130.424Q-4.450 130.938-4.800 131.287Q-5.150 131.635-5.636 131.635M-5.636 131.147Q-5.373 131.147-5.183 130.957Q-4.993 130.767-4.882 130.480Q-4.771 130.193-4.718 129.890Q-4.665 129.588-4.665 129.342Q-4.665 129.123-4.720 128.838Q-4.774 128.552-4.889 128.298Q-5.003 128.043-5.190 127.877Q-5.376 127.712-5.636 127.712Q-5.964 127.712-6.184 127.985Q-6.405 128.258-6.507 128.638Q-6.610 129.017-6.610 129.342Q-6.610 129.691-6.511 130.111Q-6.412 130.531-6.195 130.839Q-5.978 131.147-5.636 131.147M-1.538 130.391L-3.349 130.391Q-3.520 130.371-3.568 130.179L-3.568 129.971Q-3.568 129.906-3.530 129.844L-1.914 127.332Q-1.838 127.219-1.705 127.219L-1.305 127.219Q-1.209 127.219-1.141 127.288Q-1.073 127.356-1.073 127.452L-1.073 129.902L-0.492 129.902Q-0.321 129.923-0.276 130.104L-0.276 130.179Q-0.321 130.371-0.492 130.391L-1.073 130.391L-1.073 131.078L-0.570 131.078Q-0.389 131.099-0.355 131.280L-0.355 131.359Q-0.389 131.546-0.570 131.567L-2.040 131.567Q-2.221 131.546-2.259 131.359L-2.259 131.280Q-2.221 131.099-2.040 131.078L-1.538 131.078L-1.538 130.391M-1.538 127.633L-3 129.902L-1.538 129.902L-1.538 127.633M0.247 130.330Q0.247 130.080 0.383 129.858Q0.520 129.636 0.739 129.484Q0.958 129.332 1.207 129.256Q0.999 129.192 0.800 129.067Q0.602 128.942 0.477 128.759Q0.353 128.576 0.353 128.361Q0.353 128.012 0.568 127.754Q0.783 127.496 1.118 127.358Q1.453 127.219 1.795 127.219Q2.137 127.219 2.472 127.358Q2.807 127.496 3.022 127.758Q3.237 128.019 3.237 128.361Q3.237 128.576 3.113 128.757Q2.988 128.939 2.790 129.065Q2.591 129.192 2.383 129.256Q2.779 129.376 3.060 129.661Q3.340 129.947 3.340 130.330Q3.340 130.713 3.114 131.013Q2.889 131.314 2.530 131.475Q2.171 131.635 1.795 131.635Q1.419 131.635 1.060 131.476Q0.701 131.317 0.474 131.017Q0.247 130.716 0.247 130.330M0.807 130.330Q0.807 130.569 0.952 130.757Q1.098 130.945 1.327 131.046Q1.556 131.147 1.795 131.147Q2.034 131.147 2.262 131.046Q2.489 130.945 2.634 130.755Q2.779 130.566 2.779 130.330Q2.779 130.087 2.634 129.897Q2.489 129.708 2.262 129.605Q2.034 129.503 1.795 129.503Q1.556 129.503 1.327 129.605Q1.098 129.708 0.952 129.896Q0.807 130.084 0.807 130.330M0.913 128.361Q0.913 128.569 1.050 128.716Q1.187 128.863 1.393 128.937Q1.600 129.010 1.795 129.010Q1.986 129.010 2.195 128.937Q2.403 128.863 2.540 128.715Q2.677 128.566 2.677 128.361Q2.677 128.156 2.540 128.007Q2.403 127.859 2.195 127.785Q1.986 127.712 1.795 127.712Q1.600 127.712 1.393 127.785Q1.187 127.859 1.050 128.005Q0.913 128.152 0.913 128.361M4.564 132.148L4.488 132.148Q4.396 132.138 4.336 132.075Q4.276 132.011 4.276 131.929Q4.276 131.806 4.369 131.748Q4.663 131.560 4.898 131.307Q5.134 131.054 5.295 130.750Q5.456 130.446 5.534 130.114Q5.613 129.783 5.613 129.424Q5.613 128.952 5.469 128.522Q5.326 128.091 5.047 127.729Q4.769 127.366 4.382 127.113Q4.276 127.042 4.276 126.925Q4.276 126.840 4.336 126.780Q4.396 126.720 4.488 126.710L4.564 126.710Q4.611 126.710 4.642 126.731Q4.980 126.925 5.278 127.230Q5.575 127.534 5.768 127.879Q5.961 128.224 6.067 128.614Q6.173 129.004 6.173 129.424Q6.173 129.848 6.067 130.243Q5.961 130.637 5.765 130.984Q5.568 131.331 5.285 131.623Q5.001 131.916 4.649 132.128Q4.587 132.148 4.564 132.148\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(46.212 -191.534)\">\u003Cpath d=\"M-34.515 132.128Q-34.980 131.858-35.330 131.430Q-35.680 131.003-35.865 130.484Q-36.050 129.964-36.050 129.424Q-36.050 128.884-35.867 128.369Q-35.684 127.855-35.337 127.435Q-34.990 127.014-34.522 126.731Q-34.460 126.710-34.433 126.710L-34.354 126.710Q-34.269 126.720-34.211 126.778Q-34.153 126.837-34.153 126.925Q-34.153 127.052-34.241 127.107Q-34.635 127.359-34.920 127.723Q-35.205 128.088-35.347 128.518Q-35.489 128.949-35.489 129.424Q-35.489 129.779-35.405 130.118Q-35.322 130.456-35.166 130.750Q-35.010 131.044-34.783 131.292Q-34.556 131.540-34.252 131.741Q-34.153 131.810-34.153 131.929Q-34.153 132.015-34.211 132.076Q-34.269 132.138-34.354 132.148L-34.433 132.148Q-34.484 132.148-34.515 132.128M-33.377 131.359L-33.377 131.280Q-33.343 131.099-33.161 131.078L-32.908 131.078L-32.908 127.780L-33.161 127.780Q-33.343 127.759-33.377 127.571L-33.377 127.493Q-33.343 127.312-33.161 127.291L-31.446 127.291Q-31.210 127.291-30.999 127.375Q-30.789 127.459-30.622 127.607Q-30.454 127.756-30.359 127.956Q-30.263 128.156-30.263 128.388Q-30.263 128.710-30.473 128.963Q-30.683 129.215-31.005 129.328Q-30.759 129.383-30.555 129.535Q-30.352 129.687-30.234 129.911Q-30.116 130.135-30.116 130.384Q-30.116 130.699-30.275 130.971Q-30.434 131.242-30.709 131.405Q-30.984 131.567-31.299 131.567L-33.161 131.567Q-33.343 131.546-33.377 131.359M-32.348 129.585L-32.348 131.078L-31.446 131.078Q-31.247 131.078-31.070 130.988Q-30.892 130.897-30.782 130.740Q-30.673 130.583-30.673 130.384Q-30.673 130.183-30.762 130Q-30.851 129.817-31.010 129.701Q-31.169 129.585-31.367 129.585L-32.348 129.585M-32.348 127.780L-32.348 129.096L-31.593 129.096Q-31.292 129.096-31.056 128.891Q-30.820 128.686-30.820 128.388Q-30.820 128.224-30.906 128.084Q-30.991 127.944-31.136 127.862Q-31.281 127.780-31.446 127.780L-32.348 127.780M-28.304 132.541Q-28.404 132.541-28.482 132.463Q-28.561 132.384-28.561 132.288Q-28.561 132.134-28.393 132.069Q-28.202 132.025-28.051 131.887Q-27.901 131.748-27.843 131.553Q-27.864 131.553-27.891 131.567L-27.946 131.567Q-28.147 131.567-28.292 131.425Q-28.438 131.283-28.438 131.078Q-28.438 130.873-28.294 130.733Q-28.151 130.593-27.946 130.593Q-27.761 130.593-27.617 130.699Q-27.474 130.805-27.395 130.974Q-27.317 131.143-27.317 131.328Q-27.317 131.745-27.578 132.085Q-27.840 132.425-28.246 132.534Q-28.267 132.541-28.304 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -191.534)\">\u003Cpath d=\"M-22.301 131.359L-22.301 131.280Q-22.264 131.099-22.083 131.078L-21.714 131.078L-21.714 129.041L-22.083 129.041Q-22.264 129.021-22.301 128.829L-22.301 128.754Q-22.260 128.569-22.083 128.549L-21.368 128.549Q-21.197 128.569-21.153 128.754L-21.153 128.829L-21.160 128.850Q-20.962 128.692-20.722 128.604Q-20.483 128.515-20.227 128.515Q-19.923 128.515-19.714 128.638Q-19.506 128.761-19.405 128.986Q-19.304 129.212-19.304 129.523L-19.304 131.078L-18.931 131.078Q-18.750 131.099-18.716 131.280L-18.716 131.359Q-18.750 131.546-18.931 131.567L-20.152 131.567Q-20.322 131.546-20.367 131.359L-20.367 131.280Q-20.322 131.095-20.152 131.078L-19.864 131.078L-19.864 129.550Q-19.864 129.280-19.943 129.142Q-20.022 129.004-20.278 129.004Q-20.514 129.004-20.714 129.118Q-20.914 129.233-21.033 129.432Q-21.153 129.632-21.153 129.865L-21.153 131.078L-20.780 131.078Q-20.599 131.099-20.565 131.280L-20.565 131.359Q-20.599 131.546-20.780 131.567L-22.083 131.567Q-22.264 131.546-22.301 131.359M-17.144 132.541Q-17.243 132.541-17.321 132.463Q-17.400 132.384-17.400 132.288Q-17.400 132.134-17.233 132.069Q-17.041 132.025-16.891 131.887Q-16.740 131.748-16.682 131.553Q-16.703 131.553-16.730 131.567L-16.785 131.567Q-16.987 131.567-17.132 131.425Q-17.277 131.283-17.277 131.078Q-17.277 130.873-17.134 130.733Q-16.990 130.593-16.785 130.593Q-16.600 130.593-16.457 130.699Q-16.313 130.805-16.235 130.974Q-16.156 131.143-16.156 131.328Q-16.156 131.745-16.417 132.085Q-16.679 132.425-17.086 132.534Q-17.106 132.541-17.144 132.541\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(46.212 -191.534)\">\u003Cpath d=\"M-10.212 130.798Q-10.110 130.976-9.905 131.061Q-9.700 131.147-9.471 131.147Q-9.211 131.147-8.972 131.034Q-8.732 130.921-8.580 130.714Q-8.428 130.507-8.428 130.244Q-8.428 130.022-8.532 129.810Q-8.637 129.598-8.825 129.470Q-9.013 129.342-9.249 129.342Q-9.778 129.342-10.072 129.622Q-10.141 129.697-10.188 129.738Q-10.236 129.779-10.311 129.790L-10.400 129.790Q-10.575 129.769-10.619 129.578L-10.619 127.493Q-10.575 127.312-10.400 127.291L-8.336 127.291Q-8.165 127.308-8.121 127.493L-8.121 127.571Q-8.165 127.759-8.336 127.780L-10.059 127.780L-10.059 129.027Q-9.703 128.850-9.249 128.850Q-8.873 128.850-8.553 129.039Q-8.233 129.229-8.051 129.552Q-7.868 129.875-7.868 130.244Q-7.868 130.658-8.098 130.972Q-8.329 131.287-8.700 131.461Q-9.071 131.635-9.471 131.635Q-9.693 131.635-9.936 131.570Q-10.178 131.505-10.383 131.369Q-10.588 131.232-10.711 131.027Q-10.834 130.822-10.834 130.572Q-10.834 130.425-10.734 130.318Q-10.633 130.210-10.479 130.210Q-10.407 130.210-10.346 130.236Q-10.284 130.261-10.235 130.309Q-10.185 130.357-10.158 130.424Q-10.130 130.490-10.130 130.559Q-10.130 130.699-10.212 130.798M-6.743 131.359L-6.743 131.280Q-6.699 131.099-6.524 131.078L-5.810 131.078L-5.810 128.293Q-6.142 128.563-6.538 128.563Q-6.740 128.563-6.784 128.361L-6.784 128.282Q-6.740 128.094-6.569 128.074Q-6.282 128.074-6.060 127.865Q-5.837 127.657-5.714 127.353Q-5.653 127.240-5.516 127.219L-5.468 127.219Q-5.297 127.236-5.253 127.424L-5.253 131.078L-4.539 131.078Q-4.364 131.099-4.320 131.280L-4.320 131.359Q-4.364 131.546-4.539 131.567L-6.524 131.567Q-6.699 131.546-6.743 131.359M-3.404 131.359L-3.404 131.294Q-3.376 131.147-3.288 131.106L-2.160 130.172Q-1.869 129.930-1.710 129.796Q-1.551 129.663-1.380 129.470Q-1.209 129.277-1.103 129.058Q-0.998 128.839-0.998 128.607Q-0.998 128.323-1.151 128.118Q-1.305 127.913-1.550 127.812Q-1.794 127.712-2.074 127.712Q-2.300 127.712-2.500 127.819Q-2.700 127.927-2.789 128.115Q-2.700 128.231-2.700 128.361Q-2.700 128.501-2.804 128.609Q-2.908 128.716-3.048 128.716Q-3.202 128.716-3.303 128.607Q-3.404 128.498-3.404 128.347Q-3.404 128.091-3.286 127.879Q-3.168 127.667-2.959 127.517Q-2.751 127.366-2.517 127.293Q-2.283 127.219-2.026 127.219Q-1.606 127.219-1.242 127.385Q-0.878 127.551-0.657 127.867Q-0.437 128.183-0.437 128.607Q-0.437 128.908-0.553 129.173Q-0.669 129.438-0.866 129.665Q-1.062 129.892-1.332 130.121Q-1.603 130.350-1.787 130.504L-2.495 131.078L-0.998 131.078L-0.998 130.952Q-0.953 130.767-0.779 130.747L-0.656 130.747Q-0.481 130.764-0.437 130.952L-0.437 131.359Q-0.481 131.546-0.656 131.567L-3.188 131.567Q-3.359 131.550-3.404 131.359M0.848 132.148L0.773 132.148Q0.681 132.138 0.621 132.075Q0.561 132.011 0.561 131.929Q0.561 131.806 0.653 131.748Q0.947 131.560 1.183 131.307Q1.419 131.054 1.580 130.750Q1.740 130.446 1.819 130.114Q1.897 129.783 1.897 129.424Q1.897 128.952 1.754 128.522Q1.610 128.091 1.332 127.729Q1.053 127.366 0.667 127.113Q0.561 127.042 0.561 126.925Q0.561 126.840 0.621 126.780Q0.681 126.720 0.773 126.710L0.848 126.710Q0.896 126.710 0.927 126.731Q1.265 126.925 1.563 127.230Q1.860 127.534 2.053 127.879Q2.246 128.224 2.352 128.614Q2.458 129.004 2.458 129.424Q2.458 129.848 2.352 130.243Q2.246 130.637 2.050 130.984Q1.853 131.331 1.569 131.623Q1.286 131.916 0.934 132.128Q0.872 132.148 0.848 132.148\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">Shapes through one pre-norm encoder block (\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">512\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>, \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">8\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>, \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">64\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>, \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.9805em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2048\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>). The width \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> is the residual-stream invariant; only the attention scores (\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">×\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>) and FFN hidden (\u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> wide) inflate before collapsing back to \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:283.461px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 212.596 222.014\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-38.25 1.889)\">\u003Cpath d=\"M-1.990 136.506L-1.990 136.416Q-1.939 136.209-1.744 136.185L-0.705 136.185L-0.705 133.857L-1.677 133.857Q-1.877 133.834-1.927 133.615L-1.927 133.529Q-1.877 133.318-1.677 133.295L-0.310 133.295Q-0.115 133.314-0.064 133.529L-0.064 136.185L0.850 136.185Q1.045 136.209 1.096 136.416L1.096 136.506Q1.045 136.721 0.850 136.744L-1.744 136.744Q-1.939 136.721-1.990 136.506M-0.959 132.318L-0.959 132.264Q-0.959 132.092-0.822 131.971Q-0.685 131.849-0.509 131.849Q-0.337 131.849-0.201 131.971Q-0.064 132.092-0.064 132.264L-0.064 132.318Q-0.064 132.494-0.201 132.615Q-0.337 132.736-0.509 132.736Q-0.685 132.736-0.822 132.615Q-0.959 132.494-0.959 132.318M1.709 136.506L1.709 136.416Q1.752 136.209 1.959 136.185L2.381 136.185L2.381 133.857L1.959 133.857Q1.752 133.834 1.709 133.615L1.709 133.529Q1.756 133.318 1.959 133.295L2.776 133.295Q2.971 133.318 3.022 133.529L3.022 133.615L3.014 133.639Q3.241 133.459 3.514 133.357Q3.788 133.256 4.080 133.256Q4.428 133.256 4.666 133.396Q4.905 133.537 5.020 133.795Q5.135 134.053 5.135 134.408L5.135 136.185L5.561 136.185Q5.768 136.209 5.807 136.416L5.807 136.506Q5.768 136.721 5.561 136.744L4.166 136.744Q3.971 136.721 3.920 136.506L3.920 136.416Q3.971 136.205 4.166 136.185L4.495 136.185L4.495 134.439Q4.495 134.131 4.405 133.973Q4.315 133.814 4.022 133.814Q3.752 133.814 3.524 133.945Q3.295 134.076 3.159 134.305Q3.022 134.533 3.022 134.799L3.022 136.185L3.448 136.185Q3.655 136.209 3.694 136.416L3.694 136.506Q3.655 136.721 3.448 136.744L1.959 136.744Q1.752 136.721 1.709 136.506M5.955 138.287L5.955 138.201Q5.998 137.982 6.205 137.959L6.627 137.959L6.627 133.857L6.205 133.857Q5.998 133.834 5.955 133.615L5.955 133.529Q6.002 133.318 6.205 133.295L7.022 133.295Q7.217 133.314 7.268 133.529L7.268 133.599Q7.479 133.431 7.743 133.344Q8.006 133.256 8.276 133.256Q8.616 133.256 8.913 133.400Q9.209 133.545 9.424 133.797Q9.639 134.049 9.754 134.361Q9.870 134.674 9.870 135.017Q9.870 135.482 9.643 135.892Q9.416 136.303 9.030 136.543Q8.643 136.783 8.174 136.783Q7.655 136.783 7.268 136.416L7.268 137.959L7.694 137.959Q7.901 137.982 7.940 138.201L7.940 138.287Q7.901 138.498 7.694 138.521L6.205 138.521Q6.002 138.498 5.955 138.287M8.131 136.224Q8.440 136.224 8.690 136.055Q8.940 135.885 9.084 135.603Q9.229 135.322 9.229 135.017Q9.229 134.728 9.104 134.449Q8.979 134.170 8.747 133.992Q8.514 133.814 8.213 133.814Q7.893 133.814 7.631 134Q7.370 134.185 7.268 134.486L7.268 135.338Q7.358 135.705 7.579 135.965Q7.799 136.224 8.131 136.224M10.873 135.889L10.873 133.857L10.452 133.857Q10.245 133.834 10.202 133.615L10.202 133.529Q10.248 133.318 10.452 133.295L11.268 133.295Q11.463 133.318 11.514 133.529L11.514 135.857Q11.514 136.092 11.684 136.158Q11.854 136.224 12.139 136.224Q12.346 136.224 12.541 136.148Q12.737 136.072 12.862 135.922Q12.987 135.771 12.987 135.560L12.987 133.857L12.565 133.857Q12.354 133.834 12.315 133.615L12.315 133.529Q12.354 133.318 12.565 133.295L13.377 133.295Q13.577 133.318 13.627 133.529L13.627 136.185L14.053 136.185Q14.260 136.209 14.299 136.416L14.299 136.506Q14.260 136.721 14.053 136.744L13.237 136.744Q13.038 136.721 12.987 136.521Q12.584 136.783 12.077 136.783Q11.842 136.783 11.627 136.742Q11.413 136.701 11.247 136.599Q11.081 136.498 10.977 136.320Q10.873 136.142 10.873 135.889M15.577 135.639L15.577 133.857L14.827 133.857Q14.627 133.834 14.577 133.615L14.577 133.529Q14.627 133.318 14.827 133.295L15.577 133.295L15.577 132.545Q15.627 132.338 15.827 132.310L15.971 132.310Q16.166 132.338 16.217 132.545L16.217 133.295L17.577 133.295Q17.768 133.314 17.827 133.529L17.827 133.615Q17.772 133.834 17.577 133.857L16.217 133.857L16.217 135.607Q16.217 136.224 16.791 136.224Q17.041 136.224 17.206 136.039Q17.370 135.853 17.370 135.607Q17.370 135.514 17.442 135.443Q17.514 135.373 17.616 135.361L17.760 135.361Q17.959 135.385 18.010 135.592L18.010 135.639Q18.010 135.963 17.827 136.226Q17.643 136.490 17.350 136.637Q17.057 136.783 16.737 136.783Q16.225 136.783 15.901 136.473Q15.577 136.162 15.577 135.639\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-38.25 1.889)\">\u003Cpath d=\"M26.006 137.385Q25.475 137.076 25.075 136.588Q24.674 136.099 24.463 135.506Q24.252 134.912 24.252 134.295Q24.252 133.678 24.461 133.090Q24.670 132.502 25.067 132.021Q25.463 131.541 25.998 131.217Q26.069 131.193 26.100 131.193L26.190 131.193Q26.288 131.205 26.354 131.271Q26.420 131.338 26.420 131.439Q26.420 131.584 26.319 131.646Q25.870 131.935 25.543 132.351Q25.217 132.767 25.055 133.260Q24.893 133.752 24.893 134.295Q24.893 134.701 24.989 135.088Q25.084 135.474 25.262 135.810Q25.440 136.146 25.700 136.430Q25.959 136.713 26.307 136.943Q26.420 137.021 26.420 137.158Q26.420 137.256 26.354 137.326Q26.288 137.396 26.190 137.408L26.100 137.408Q26.041 137.408 26.006 137.385M30.651 135.256L28.209 135.256Q28.264 135.533 28.461 135.756Q28.659 135.978 28.936 136.101Q29.213 136.224 29.498 136.224Q29.971 136.224 30.194 135.935Q30.202 135.924 30.258 135.818Q30.315 135.713 30.364 135.670Q30.413 135.627 30.506 135.615L30.651 135.615Q30.842 135.635 30.901 135.849L30.901 135.904Q30.834 136.205 30.604 136.402Q30.373 136.599 30.061 136.691Q29.748 136.783 29.444 136.783Q28.959 136.783 28.520 136.555Q28.081 136.326 27.813 135.926Q27.545 135.525 27.545 135.033L27.545 134.974Q27.545 134.506 27.791 134.103Q28.038 133.701 28.446 133.467Q28.854 133.232 29.323 133.232Q29.827 133.232 30.180 133.455Q30.534 133.678 30.717 134.066Q30.901 134.455 30.901 134.959L30.901 135.017Q30.842 135.232 30.651 135.256M28.217 134.705L30.245 134.705Q30.198 134.295 29.959 134.043Q29.721 133.791 29.323 133.791Q28.928 133.791 28.622 134.053Q28.315 134.314 28.217 134.705M31.331 136.506L31.331 136.416Q31.381 136.205 31.577 136.185L31.776 136.185L31.776 133.857L31.577 133.857Q31.370 133.834 31.331 133.615L31.331 133.529Q31.381 133.314 31.577 133.295L32.057 133.295Q32.248 133.318 32.307 133.529Q32.627 133.256 33.041 133.256Q33.233 133.256 33.401 133.365Q33.569 133.474 33.643 133.646Q33.819 133.455 34.041 133.355Q34.264 133.256 34.506 133.256Q34.924 133.256 35.079 133.598Q35.233 133.939 35.233 134.408L35.233 136.185L35.432 136.185Q35.643 136.209 35.682 136.416L35.682 136.506Q35.631 136.721 35.432 136.744L34.616 136.744Q34.420 136.721 34.370 136.506L34.370 136.416Q34.420 136.209 34.616 136.185L34.706 136.185L34.706 134.439Q34.706 133.814 34.456 133.814Q34.123 133.814 33.946 134.125Q33.768 134.435 33.768 134.799L33.768 136.185L33.971 136.185Q34.178 136.209 34.217 136.416L34.217 136.506Q34.166 136.721 33.971 136.744L33.155 136.744Q32.956 136.721 32.905 136.506L32.905 136.416Q32.956 136.209 33.155 136.185L33.241 136.185L33.241 134.439Q33.241 133.814 32.995 133.814Q32.663 133.814 32.485 134.127Q32.307 134.439 32.307 134.799L32.307 136.185L32.506 136.185Q32.713 136.209 32.752 136.416L32.752 136.506Q32.702 136.724 32.506 136.744L31.577 136.744Q31.370 136.721 31.331 136.506M36.373 136.506L36.373 132.416L35.952 132.416Q35.745 132.392 35.702 132.178L35.702 132.088Q35.745 131.881 35.952 131.857L36.768 131.857Q36.963 131.881 37.014 132.088L37.014 133.599Q37.225 133.431 37.489 133.344Q37.752 133.256 38.022 133.256Q38.362 133.256 38.659 133.400Q38.956 133.545 39.170 133.797Q39.385 134.049 39.500 134.361Q39.616 134.674 39.616 135.017Q39.616 135.482 39.389 135.892Q39.163 136.303 38.776 136.543Q38.389 136.783 37.920 136.783Q37.401 136.783 37.014 136.416L37.014 136.506Q36.963 136.724 36.768 136.744L36.623 136.744Q36.432 136.721 36.373 136.506M37.877 136.224Q38.186 136.224 38.436 136.055Q38.686 135.885 38.831 135.603Q38.975 135.322 38.975 135.017Q38.975 134.728 38.850 134.449Q38.725 134.170 38.493 133.992Q38.260 133.814 37.959 133.814Q37.639 133.814 37.377 134Q37.116 134.185 37.014 134.486L37.014 135.338Q37.104 135.705 37.325 135.965Q37.545 136.224 37.877 136.224M43.389 135.256L40.948 135.256Q41.002 135.533 41.200 135.756Q41.397 135.978 41.674 136.101Q41.952 136.224 42.237 136.224Q42.709 136.224 42.932 135.935Q42.940 135.924 42.997 135.818Q43.053 135.713 43.102 135.670Q43.151 135.627 43.245 135.615L43.389 135.615Q43.581 135.635 43.639 135.849L43.639 135.904Q43.573 136.205 43.342 136.402Q43.112 136.599 42.799 136.691Q42.487 136.783 42.182 136.783Q41.698 136.783 41.258 136.555Q40.819 136.326 40.551 135.926Q40.284 135.525 40.284 135.033L40.284 134.974Q40.284 134.506 40.530 134.103Q40.776 133.701 41.184 133.467Q41.592 133.232 42.061 133.232Q42.565 133.232 42.918 133.455Q43.272 133.678 43.456 134.066Q43.639 134.455 43.639 134.959L43.639 135.017Q43.581 135.232 43.389 135.256M40.956 134.705L42.983 134.705Q42.936 134.295 42.698 134.043Q42.459 133.791 42.061 133.791Q41.666 133.791 41.360 134.053Q41.053 134.314 40.956 134.705M45.987 136.783Q45.522 136.783 45.157 136.533Q44.791 136.283 44.586 135.879Q44.381 135.474 44.381 135.017Q44.381 134.674 44.506 134.353Q44.631 134.033 44.864 133.783Q45.096 133.533 45.401 133.394Q45.706 133.256 46.061 133.256Q46.573 133.256 46.979 133.576L46.979 132.416L46.557 132.416Q46.346 132.392 46.307 132.178L46.307 132.088Q46.346 131.881 46.557 131.857L47.370 131.857Q47.569 131.881 47.620 132.088L47.620 136.185L48.045 136.185Q48.252 136.209 48.291 136.416L48.291 136.506Q48.252 136.721 48.045 136.744L47.229 136.744Q47.030 136.721 46.979 136.506L46.979 136.377Q46.784 136.568 46.522 136.676Q46.260 136.783 45.987 136.783M46.026 136.224Q46.385 136.224 46.637 135.955Q46.889 135.685 46.979 135.310L46.979 134.478Q46.920 134.291 46.793 134.140Q46.666 133.990 46.489 133.902Q46.311 133.814 46.116 133.814Q45.807 133.814 45.557 133.984Q45.307 134.154 45.163 134.439Q45.018 134.724 45.018 135.025Q45.018 135.474 45.303 135.849Q45.588 136.224 46.026 136.224M50.233 136.783Q49.768 136.783 49.403 136.533Q49.038 136.283 48.832 135.879Q48.627 135.474 48.627 135.017Q48.627 134.674 48.752 134.353Q48.877 134.033 49.110 133.783Q49.342 133.533 49.647 133.394Q49.952 133.256 50.307 133.256Q50.819 133.256 51.225 133.576L51.225 132.416L50.803 132.416Q50.592 132.392 50.553 132.178L50.553 132.088Q50.592 131.881 50.803 131.857L51.616 131.857Q51.815 131.881 51.866 132.088L51.866 136.185L52.291 136.185Q52.498 136.209 52.538 136.416L52.538 136.506Q52.498 136.721 52.291 136.744L51.475 136.744Q51.276 136.721 51.225 136.506L51.225 136.377Q51.030 136.568 50.768 136.676Q50.506 136.783 50.233 136.783M50.272 136.224Q50.631 136.224 50.883 135.955Q51.135 135.685 51.225 135.310L51.225 134.478Q51.166 134.291 51.039 134.140Q50.913 133.990 50.735 133.902Q50.557 133.814 50.362 133.814Q50.053 133.814 49.803 133.984Q49.553 134.154 49.409 134.439Q49.264 134.724 49.264 135.025Q49.264 135.474 49.549 135.849Q49.834 136.224 50.272 136.224M53.233 136.506L53.233 136.416Q53.284 136.209 53.479 136.185L54.518 136.185L54.518 133.857L53.545 133.857Q53.346 133.834 53.295 133.615L53.295 133.529Q53.346 133.318 53.545 133.295L54.913 133.295Q55.108 133.314 55.159 133.529L55.159 136.185L56.073 136.185Q56.268 136.209 56.319 136.416L56.319 136.506Q56.268 136.721 56.073 136.744L53.479 136.744Q53.284 136.721 53.233 136.506M54.264 132.318L54.264 132.264Q54.264 132.092 54.401 131.971Q54.538 131.849 54.713 131.849Q54.885 131.849 55.022 131.971Q55.159 132.092 55.159 132.264L55.159 132.318Q55.159 132.494 55.022 132.615Q54.885 132.736 54.713 132.736Q54.538 132.736 54.401 132.615Q54.264 132.494 54.264 132.318M56.932 136.506L56.932 136.416Q56.975 136.209 57.182 136.185L57.604 136.185L57.604 133.857L57.182 133.857Q56.975 133.834 56.932 133.615L56.932 133.529Q56.979 133.318 57.182 133.295L57.998 133.295Q58.194 133.318 58.245 133.529L58.245 133.615L58.237 133.639Q58.463 133.459 58.737 133.357Q59.010 133.256 59.303 133.256Q59.651 133.256 59.889 133.396Q60.127 133.537 60.243 133.795Q60.358 134.053 60.358 134.408L60.358 136.185L60.784 136.185Q60.991 136.209 61.030 136.416L61.030 136.506Q60.991 136.721 60.784 136.744L59.389 136.744Q59.194 136.721 59.143 136.506L59.143 136.416Q59.194 136.205 59.389 136.185L59.717 136.185L59.717 134.439Q59.717 134.131 59.627 133.973Q59.538 133.814 59.245 133.814Q58.975 133.814 58.747 133.945Q58.518 134.076 58.381 134.305Q58.245 134.533 58.245 134.799L58.245 136.185L58.670 136.185Q58.877 136.209 58.916 136.416L58.916 136.506Q58.877 136.721 58.670 136.744L57.182 136.744Q56.975 136.721 56.932 136.506M61.346 137.392Q61.346 137.092 61.495 136.830Q61.643 136.568 61.893 136.408Q61.709 136.154 61.709 135.834Q61.709 135.549 61.862 135.287Q61.612 134.963 61.612 134.545Q61.612 134.185 61.803 133.889Q61.995 133.592 62.313 133.424Q62.631 133.256 62.995 133.256Q63.202 133.256 63.405 133.316Q63.608 133.377 63.772 133.478Q64.155 133.217 64.627 133.217Q64.866 133.217 65.047 133.348Q65.229 133.478 65.229 133.705Q65.229 133.853 65.127 133.959Q65.026 134.064 64.870 134.064Q64.737 134.064 64.641 133.986Q64.545 133.908 64.514 133.783Q64.370 133.791 64.170 133.881Q64.373 134.193 64.373 134.545Q64.373 134.826 64.262 135.058Q64.151 135.291 63.956 135.469Q63.760 135.646 63.508 135.744Q63.256 135.842 62.995 135.842Q62.608 135.842 62.276 135.654Q62.264 135.654 62.254 135.726Q62.245 135.799 62.245 135.834Q62.245 135.955 62.311 136.062Q62.377 136.170 62.498 136.209Q62.514 136.205 62.528 136.203Q62.541 136.201 62.565 136.201Q62.581 136.201 62.612 136.209Q62.643 136.217 62.651 136.217L63.245 136.217Q64.026 136.217 64.567 136.459Q65.108 136.701 65.108 137.392Q65.108 137.693 64.928 137.920Q64.748 138.146 64.452 138.291Q64.155 138.435 63.834 138.502Q63.514 138.568 63.229 138.568Q62.838 138.568 62.397 138.445Q61.956 138.322 61.651 138.055Q61.346 137.787 61.346 137.392M61.885 137.385Q61.885 137.603 62.125 137.744Q62.366 137.885 62.690 137.951Q63.014 138.017 63.229 138.017Q63.444 138.017 63.768 137.951Q64.092 137.885 64.332 137.744Q64.573 137.603 64.573 137.385Q64.573 137.096 64.348 136.957Q64.123 136.818 63.842 136.785Q63.561 136.752 63.213 136.752L62.596 136.752Q62.413 136.752 62.250 136.832Q62.088 136.912 61.987 137.058Q61.885 137.205 61.885 137.385M62.995 135.287Q63.295 135.287 63.514 135.068Q63.733 134.849 63.733 134.545Q63.733 134.389 63.678 134.258Q63.623 134.127 63.518 134.021Q63.413 133.916 63.282 133.861Q63.151 133.806 62.995 133.806Q62.690 133.806 62.471 134.025Q62.252 134.244 62.252 134.545Q62.252 134.842 62.475 135.064Q62.698 135.287 62.995 135.287M65.940 136.545L65.940 135.631Q65.967 135.424 66.178 135.400L66.346 135.400Q66.510 135.424 66.569 135.584Q66.772 136.224 67.498 136.224Q67.706 136.224 67.934 136.189Q68.163 136.154 68.331 136.039Q68.498 135.924 68.498 135.721Q68.498 135.510 68.276 135.396Q68.053 135.283 67.780 135.240L67.081 135.127Q65.940 134.916 65.940 134.193Q65.940 133.904 66.084 133.715Q66.229 133.525 66.469 133.418Q66.709 133.310 66.965 133.271Q67.221 133.232 67.498 133.232Q67.748 133.232 67.942 133.262Q68.135 133.291 68.299 133.369Q68.377 133.252 68.506 133.232L68.584 133.232Q68.682 133.244 68.745 133.306Q68.807 133.369 68.819 133.463L68.819 134.170Q68.807 134.264 68.745 134.330Q68.682 134.396 68.584 134.408L68.416 134.408Q68.323 134.396 68.256 134.330Q68.190 134.264 68.178 134.170Q68.178 133.791 67.483 133.791Q67.135 133.791 66.817 133.873Q66.498 133.955 66.498 134.201Q66.498 134.467 67.170 134.576L67.873 134.697Q68.358 134.779 68.707 135.027Q69.057 135.275 69.057 135.721Q69.057 136.111 68.821 136.353Q68.584 136.596 68.235 136.689Q67.885 136.783 67.498 136.783Q66.920 136.783 66.522 136.529Q66.452 136.654 66.403 136.711Q66.354 136.767 66.248 136.783L66.178 136.783Q65.963 136.760 65.940 136.545M70.639 137.408L70.553 137.408Q70.448 137.396 70.379 137.324Q70.311 137.252 70.311 137.158Q70.311 137.017 70.416 136.951Q70.752 136.736 71.022 136.447Q71.291 136.158 71.475 135.810Q71.659 135.463 71.748 135.084Q71.838 134.705 71.838 134.295Q71.838 133.756 71.674 133.264Q71.510 132.771 71.192 132.357Q70.873 131.943 70.432 131.654Q70.311 131.572 70.311 131.439Q70.311 131.342 70.379 131.273Q70.448 131.205 70.553 131.193L70.639 131.193Q70.694 131.193 70.729 131.217Q71.116 131.439 71.456 131.787Q71.795 132.135 72.016 132.529Q72.237 132.924 72.358 133.369Q72.479 133.814 72.479 134.295Q72.479 134.779 72.358 135.230Q72.237 135.681 72.012 136.078Q71.788 136.474 71.463 136.808Q71.139 137.142 70.737 137.385Q70.666 137.408 70.639 137.408\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-65.203 106.869H59.989V81.26H-65.203Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-53.126 -40.235)\">\u003Cpath d=\"M-2.662 136.506L-2.662 136.416Q-2.611 136.205-2.416 136.185L-2.216 136.185L-2.216 133.857L-2.416 133.857Q-2.623 133.834-2.662 133.615L-2.662 133.529Q-2.611 133.314-2.416 133.295L-1.935 133.295Q-1.744 133.318-1.685 133.529Q-1.365 133.256-0.951 133.256Q-0.759 133.256-0.591 133.365Q-0.423 133.474-0.349 133.646Q-0.173 133.455 0.049 133.355Q0.272 133.256 0.514 133.256Q0.932 133.256 1.086 133.598Q1.241 133.939 1.241 134.408L1.241 136.185L1.440 136.185Q1.651 136.209 1.690 136.416L1.690 136.506Q1.639 136.721 1.440 136.744L0.623 136.744Q0.428 136.721 0.377 136.506L0.377 136.416Q0.428 136.209 0.623 136.185L0.713 136.185L0.713 134.439Q0.713 133.814 0.463 133.814Q0.131 133.814-0.046 134.125Q-0.224 134.435-0.224 134.799L-0.224 136.185L-0.021 136.185Q0.186 136.209 0.225 136.416L0.225 136.506Q0.174 136.721-0.021 136.744L-0.837 136.744Q-1.037 136.721-1.087 136.506L-1.087 136.416Q-1.037 136.209-0.837 136.185L-0.752 136.185L-0.752 134.439Q-0.752 133.814-0.998 133.814Q-1.330 133.814-1.507 134.127Q-1.685 134.439-1.685 134.799L-1.685 136.185L-1.486 136.185Q-1.279 136.209-1.240 136.416L-1.240 136.506Q-1.291 136.724-1.486 136.744L-2.416 136.744Q-2.623 136.721-2.662 136.506M2.381 135.889L2.381 133.857L1.959 133.857Q1.752 133.834 1.709 133.615L1.709 133.529Q1.756 133.318 1.959 133.295L2.776 133.295Q2.971 133.318 3.022 133.529L3.022 135.857Q3.022 136.092 3.192 136.158Q3.362 136.224 3.647 136.224Q3.854 136.224 4.049 136.148Q4.245 136.072 4.370 135.922Q4.495 135.771 4.495 135.560L4.495 133.857L4.073 133.857Q3.862 133.834 3.823 133.615L3.823 133.529Q3.862 133.318 4.073 133.295L4.885 133.295Q5.084 133.318 5.135 133.529L5.135 136.185L5.561 136.185Q5.768 136.209 5.807 136.416L5.807 136.506Q5.768 136.721 5.561 136.744L4.745 136.744Q4.545 136.721 4.495 136.521Q4.092 136.783 3.584 136.783Q3.350 136.783 3.135 136.742Q2.920 136.701 2.754 136.599Q2.588 136.498 2.485 136.320Q2.381 136.142 2.381 135.889M6.334 136.506L6.334 136.416Q6.385 136.209 6.580 136.185L7.686 136.185L7.686 132.416L6.580 132.416Q6.385 132.392 6.334 132.178L6.334 132.088Q6.385 131.881 6.580 131.857L8.077 131.857Q8.268 131.881 8.327 132.088L8.327 136.185L9.428 136.185Q9.627 136.209 9.678 136.416L9.678 136.506Q9.627 136.721 9.428 136.744L6.580 136.744Q6.385 136.721 6.334 136.506M11.331 135.639L11.331 133.857L10.581 133.857Q10.381 133.834 10.331 133.615L10.331 133.529Q10.381 133.318 10.581 133.295L11.331 133.295L11.331 132.545Q11.381 132.338 11.581 132.310L11.725 132.310Q11.920 132.338 11.971 132.545L11.971 133.295L13.331 133.295Q13.522 133.314 13.581 133.529L13.581 133.615Q13.526 133.834 13.331 133.857L11.971 133.857L11.971 135.607Q11.971 136.224 12.545 136.224Q12.795 136.224 12.959 136.039Q13.123 135.853 13.123 135.607Q13.123 135.514 13.196 135.443Q13.268 135.373 13.370 135.361L13.514 135.361Q13.713 135.385 13.764 135.592L13.764 135.639Q13.764 135.963 13.581 136.226Q13.397 136.490 13.104 136.637Q12.811 136.783 12.491 136.783Q11.979 136.783 11.655 136.473Q11.331 136.162 11.331 135.639M14.995 136.506L14.995 136.416Q15.045 136.209 15.241 136.185L16.280 136.185L16.280 133.857L15.307 133.857Q15.108 133.834 15.057 133.615L15.057 133.529Q15.108 133.318 15.307 133.295L16.674 133.295Q16.870 133.314 16.920 133.529L16.920 136.185L17.834 136.185Q18.030 136.209 18.081 136.416L18.081 136.506Q18.030 136.721 17.834 136.744L15.241 136.744Q15.045 136.721 14.995 136.506M16.026 132.318L16.026 132.264Q16.026 132.092 16.163 131.971Q16.299 131.849 16.475 131.849Q16.647 131.849 16.784 131.971Q16.920 132.092 16.920 132.264L16.920 132.318Q16.920 132.494 16.784 132.615Q16.647 132.736 16.475 132.736Q16.299 132.736 16.163 132.615Q16.026 132.494 16.026 132.318M22.120 134.607L19.377 134.607Q19.252 134.596 19.166 134.510Q19.081 134.424 19.081 134.295Q19.081 134.166 19.166 134.084Q19.252 134.002 19.377 133.990L22.120 133.990Q22.245 134.002 22.327 134.084Q22.409 134.166 22.409 134.295Q22.409 134.424 22.327 134.510Q22.245 134.596 22.120 134.607M22.940 136.506L22.940 136.416Q22.983 136.209 23.190 136.185L23.612 136.185L23.612 132.416L23.190 132.416Q22.983 132.392 22.940 132.178L22.940 132.088Q22.983 131.881 23.190 131.857L24.006 131.857Q24.202 131.881 24.252 132.088L24.252 133.639Q24.713 133.256 25.311 133.256Q25.659 133.256 25.897 133.396Q26.135 133.537 26.250 133.795Q26.366 134.053 26.366 134.408L26.366 136.185L26.791 136.185Q26.998 136.209 27.038 136.416L27.038 136.506Q26.998 136.721 26.791 136.744L25.397 136.744Q25.202 136.721 25.151 136.506L25.151 136.416Q25.202 136.205 25.397 136.185L25.725 136.185L25.725 134.439Q25.725 134.131 25.635 133.973Q25.545 133.814 25.252 133.814Q24.983 133.814 24.754 133.945Q24.526 134.076 24.389 134.305Q24.252 134.533 24.252 134.799L24.252 136.185L24.678 136.185Q24.885 136.209 24.924 136.416L24.924 136.506Q24.885 136.721 24.678 136.744L23.190 136.744Q22.983 136.721 22.940 136.506M30.627 135.256L28.186 135.256Q28.241 135.533 28.438 135.756Q28.635 135.978 28.913 136.101Q29.190 136.224 29.475 136.224Q29.948 136.224 30.170 135.935Q30.178 135.924 30.235 135.818Q30.291 135.713 30.340 135.670Q30.389 135.627 30.483 135.615L30.627 135.615Q30.819 135.635 30.877 135.849L30.877 135.904Q30.811 136.205 30.581 136.402Q30.350 136.599 30.038 136.691Q29.725 136.783 29.420 136.783Q28.936 136.783 28.497 136.555Q28.057 136.326 27.789 135.926Q27.522 135.525 27.522 135.033L27.522 134.974Q27.522 134.506 27.768 134.103Q28.014 133.701 28.422 133.467Q28.831 133.232 29.299 133.232Q29.803 133.232 30.157 133.455Q30.510 133.678 30.694 134.066Q30.877 134.455 30.877 134.959L30.877 135.017Q30.819 135.232 30.627 135.256M28.194 134.705L30.221 134.705Q30.174 134.295 29.936 134.043Q29.698 133.791 29.299 133.791Q28.905 133.791 28.598 134.053Q28.291 134.314 28.194 134.705M31.768 135.631Q31.768 135.185 32.182 134.928Q32.596 134.670 33.137 134.570Q33.678 134.471 34.186 134.463Q34.186 134.248 34.051 134.096Q33.916 133.943 33.709 133.867Q33.502 133.791 33.291 133.791Q32.948 133.791 32.788 133.814L32.788 133.873Q32.788 134.041 32.668 134.156Q32.549 134.271 32.385 134.271Q32.209 134.271 32.094 134.148Q31.979 134.025 31.979 133.857Q31.979 133.451 32.360 133.342Q32.741 133.232 33.299 133.232Q33.569 133.232 33.836 133.310Q34.104 133.389 34.329 133.539Q34.553 133.689 34.690 133.910Q34.827 134.131 34.827 134.408L34.827 136.127Q34.827 136.185 35.354 136.185Q35.549 136.205 35.600 136.416L35.600 136.506Q35.549 136.721 35.354 136.744L35.209 136.744Q34.866 136.744 34.637 136.697Q34.409 136.650 34.264 136.463Q33.803 136.783 33.096 136.783Q32.760 136.783 32.456 136.642Q32.151 136.502 31.959 136.240Q31.768 135.978 31.768 135.631M32.409 135.639Q32.409 135.912 32.651 136.068Q32.893 136.224 33.178 136.224Q33.397 136.224 33.629 136.166Q33.862 136.107 34.024 135.969Q34.186 135.830 34.186 135.607L34.186 135.017Q33.905 135.017 33.489 135.074Q33.073 135.131 32.741 135.269Q32.409 135.408 32.409 135.639M37.471 136.783Q37.006 136.783 36.641 136.533Q36.276 136.283 36.071 135.879Q35.866 135.474 35.866 135.017Q35.866 134.674 35.991 134.353Q36.116 134.033 36.348 133.783Q36.581 133.533 36.885 133.394Q37.190 133.256 37.545 133.256Q38.057 133.256 38.463 133.576L38.463 132.416L38.041 132.416Q37.831 132.392 37.791 132.178L37.791 132.088Q37.831 131.881 38.041 131.857L38.854 131.857Q39.053 131.881 39.104 132.088L39.104 136.185L39.530 136.185Q39.737 136.209 39.776 136.416L39.776 136.506Q39.737 136.721 39.530 136.744L38.713 136.744Q38.514 136.721 38.463 136.506L38.463 136.377Q38.268 136.568 38.006 136.676Q37.745 136.783 37.471 136.783M37.510 136.224Q37.870 136.224 38.122 135.955Q38.373 135.685 38.463 135.310L38.463 134.478Q38.405 134.291 38.278 134.140Q38.151 133.990 37.973 133.902Q37.795 133.814 37.600 133.814Q37.291 133.814 37.041 133.984Q36.791 134.154 36.647 134.439Q36.502 134.724 36.502 135.025Q36.502 135.474 36.788 135.849Q37.073 136.224 37.510 136.224\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-53.126 -40.235)\">\u003Cpath d=\"M44.729 136.545L44.729 135.631Q44.756 135.424 44.967 135.400L45.135 135.400Q45.299 135.424 45.358 135.584Q45.561 136.224 46.288 136.224Q46.495 136.224 46.723 136.189Q46.952 136.154 47.120 136.039Q47.288 135.924 47.288 135.721Q47.288 135.510 47.065 135.396Q46.842 135.283 46.569 135.240L45.870 135.127Q44.729 134.916 44.729 134.193Q44.729 133.904 44.873 133.715Q45.018 133.525 45.258 133.418Q45.498 133.310 45.754 133.271Q46.010 133.232 46.288 133.232Q46.538 133.232 46.731 133.262Q46.924 133.291 47.088 133.369Q47.166 133.252 47.295 133.232L47.373 133.232Q47.471 133.244 47.534 133.306Q47.596 133.369 47.608 133.463L47.608 134.170Q47.596 134.264 47.534 134.330Q47.471 134.396 47.373 134.408L47.206 134.408Q47.112 134.396 47.045 134.330Q46.979 134.264 46.967 134.170Q46.967 133.791 46.272 133.791Q45.924 133.791 45.606 133.873Q45.288 133.955 45.288 134.201Q45.288 134.467 45.959 134.576L46.663 134.697Q47.147 134.779 47.497 135.027Q47.846 135.275 47.846 135.721Q47.846 136.111 47.610 136.353Q47.373 136.596 47.024 136.689Q46.674 136.783 46.288 136.783Q45.709 136.783 45.311 136.529Q45.241 136.654 45.192 136.711Q45.143 136.767 45.038 136.783L44.967 136.783Q44.752 136.760 44.729 136.545M51.901 135.256L49.459 135.256Q49.514 135.533 49.711 135.756Q49.909 135.978 50.186 136.101Q50.463 136.224 50.748 136.224Q51.221 136.224 51.444 135.935Q51.452 135.924 51.508 135.818Q51.565 135.713 51.614 135.670Q51.663 135.627 51.756 135.615L51.901 135.615Q52.092 135.635 52.151 135.849L52.151 135.904Q52.084 136.205 51.854 136.402Q51.623 136.599 51.311 136.691Q50.998 136.783 50.694 136.783Q50.209 136.783 49.770 136.555Q49.331 136.326 49.063 135.926Q48.795 135.525 48.795 135.033L48.795 134.974Q48.795 134.506 49.041 134.103Q49.288 133.701 49.696 133.467Q50.104 133.232 50.573 133.232Q51.077 133.232 51.430 133.455Q51.784 133.678 51.967 134.066Q52.151 134.455 52.151 134.959L52.151 135.017Q52.092 135.232 51.901 135.256M49.467 134.705L51.495 134.705Q51.448 134.295 51.209 134.043Q50.971 133.791 50.573 133.791Q50.178 133.791 49.872 134.053Q49.565 134.314 49.467 134.705M53.084 136.506L53.084 136.416Q53.135 136.209 53.331 136.185L54.436 136.185L54.436 132.416L53.331 132.416Q53.135 132.392 53.084 132.178L53.084 132.088Q53.135 131.881 53.331 131.857L54.827 131.857Q55.018 131.881 55.077 132.088L55.077 136.185L56.178 136.185Q56.377 136.209 56.428 136.416L56.428 136.506Q56.377 136.721 56.178 136.744L53.331 136.744Q53.135 136.721 53.084 136.506M57.202 136.506L57.202 136.416Q57.252 136.209 57.448 136.185L58.331 136.185L58.331 133.857L57.475 133.857Q57.276 133.834 57.225 133.615L57.225 133.529Q57.276 133.318 57.475 133.295L58.331 133.295L58.331 132.842Q58.331 132.377 58.737 132.096Q59.143 131.814 59.623 131.814Q59.936 131.814 60.180 131.935Q60.424 132.056 60.424 132.338Q60.424 132.502 60.315 132.619Q60.206 132.736 60.041 132.736Q59.893 132.736 59.772 132.631Q59.651 132.525 59.651 132.377L59.569 132.377Q59.416 132.377 59.280 132.437Q59.143 132.498 59.057 132.613Q58.971 132.728 58.971 132.873L58.971 133.295L60.002 133.295Q60.198 133.314 60.248 133.529L60.248 133.615Q60.198 133.834 60.002 133.857L58.971 133.857L58.971 136.185L59.850 136.185Q60.045 136.209 60.096 136.416L60.096 136.506Q60.045 136.721 59.850 136.744L57.448 136.744Q57.252 136.721 57.202 136.506M64.623 134.607L61.881 134.607Q61.756 134.596 61.670 134.510Q61.584 134.424 61.584 134.295Q61.584 134.166 61.670 134.084Q61.756 134.002 61.881 133.990L64.623 133.990Q64.748 134.002 64.831 134.084Q64.913 134.166 64.913 134.295Q64.913 134.424 64.831 134.510Q64.748 134.596 64.623 134.607M65.780 135.631Q65.780 135.185 66.194 134.928Q66.608 134.670 67.149 134.570Q67.690 134.471 68.198 134.463Q68.198 134.248 68.063 134.096Q67.928 133.943 67.721 133.867Q67.514 133.791 67.303 133.791Q66.959 133.791 66.799 133.814L66.799 133.873Q66.799 134.041 66.680 134.156Q66.561 134.271 66.397 134.271Q66.221 134.271 66.106 134.148Q65.991 134.025 65.991 133.857Q65.991 133.451 66.372 133.342Q66.752 133.232 67.311 133.232Q67.581 133.232 67.848 133.310Q68.116 133.389 68.340 133.539Q68.565 133.689 68.702 133.910Q68.838 134.131 68.838 134.408L68.838 136.127Q68.838 136.185 69.366 136.185Q69.561 136.205 69.612 136.416L69.612 136.506Q69.561 136.721 69.366 136.744L69.221 136.744Q68.877 136.744 68.649 136.697Q68.420 136.650 68.276 136.463Q67.815 136.783 67.108 136.783Q66.772 136.783 66.467 136.642Q66.163 136.502 65.971 136.240Q65.780 135.978 65.780 135.631M66.420 135.639Q66.420 135.912 66.663 136.068Q66.905 136.224 67.190 136.224Q67.409 136.224 67.641 136.166Q67.873 136.107 68.036 135.969Q68.198 135.830 68.198 135.607L68.198 135.017Q67.916 135.017 67.500 135.074Q67.084 135.131 66.752 135.269Q66.420 135.408 66.420 135.639M70.819 135.639L70.819 133.857L70.069 133.857Q69.870 133.834 69.819 133.615L69.819 133.529Q69.870 133.318 70.069 133.295L70.819 133.295L70.819 132.545Q70.870 132.338 71.069 132.310L71.213 132.310Q71.409 132.338 71.459 132.545L71.459 133.295L72.819 133.295Q73.010 133.314 73.069 133.529L73.069 133.615Q73.014 133.834 72.819 133.857L71.459 133.857L71.459 135.607Q71.459 136.224 72.034 136.224Q72.284 136.224 72.448 136.039Q72.612 135.853 72.612 135.607Q72.612 135.514 72.684 135.443Q72.756 135.373 72.858 135.361L73.002 135.361Q73.202 135.385 73.252 135.592L73.252 135.639Q73.252 135.963 73.069 136.226Q72.885 136.490 72.592 136.637Q72.299 136.783 71.979 136.783Q71.467 136.783 71.143 136.473Q70.819 136.162 70.819 135.639M75.065 135.639L75.065 133.857L74.315 133.857Q74.116 133.834 74.065 133.615L74.065 133.529Q74.116 133.318 74.315 133.295L75.065 133.295L75.065 132.545Q75.116 132.338 75.315 132.310L75.459 132.310Q75.655 132.338 75.706 132.545L75.706 133.295L77.065 133.295Q77.256 133.314 77.315 133.529L77.315 133.615Q77.260 133.834 77.065 133.857L75.706 133.857L75.706 135.607Q75.706 136.224 76.280 136.224Q76.530 136.224 76.694 136.039Q76.858 135.853 76.858 135.607Q76.858 135.514 76.930 135.443Q77.002 135.373 77.104 135.361L77.248 135.361Q77.448 135.385 77.498 135.592L77.498 135.639Q77.498 135.963 77.315 136.226Q77.131 136.490 76.838 136.637Q76.545 136.783 76.225 136.783Q75.713 136.783 75.389 136.473Q75.065 136.162 75.065 135.639M81.623 135.256L79.182 135.256Q79.237 135.533 79.434 135.756Q79.631 135.978 79.909 136.101Q80.186 136.224 80.471 136.224Q80.944 136.224 81.166 135.935Q81.174 135.924 81.231 135.818Q81.288 135.713 81.336 135.670Q81.385 135.627 81.479 135.615L81.623 135.615Q81.815 135.635 81.873 135.849L81.873 135.904Q81.807 136.205 81.577 136.402Q81.346 136.599 81.034 136.691Q80.721 136.783 80.416 136.783Q79.932 136.783 79.493 136.555Q79.053 136.326 78.786 135.926Q78.518 135.525 78.518 135.033L78.518 134.974Q78.518 134.506 78.764 134.103Q79.010 133.701 79.418 133.467Q79.827 133.232 80.295 133.232Q80.799 133.232 81.153 133.455Q81.506 133.678 81.690 134.066Q81.873 134.455 81.873 134.959L81.873 135.017Q81.815 135.232 81.623 135.256M79.190 134.705L81.217 134.705Q81.170 134.295 80.932 134.043Q80.694 133.791 80.295 133.791Q79.901 133.791 79.594 134.053Q79.288 134.314 79.190 134.705M82.428 136.506L82.428 136.416Q82.471 136.209 82.678 136.185L83.100 136.185L83.100 133.857L82.678 133.857Q82.471 133.834 82.428 133.615L82.428 133.529Q82.475 133.318 82.678 133.295L83.495 133.295Q83.690 133.318 83.741 133.529L83.741 133.615L83.733 133.639Q83.959 133.459 84.233 133.357Q84.506 133.256 84.799 133.256Q85.147 133.256 85.385 133.396Q85.623 133.537 85.739 133.795Q85.854 134.053 85.854 134.408L85.854 136.185L86.280 136.185Q86.487 136.209 86.526 136.416L86.526 136.506Q86.487 136.721 86.280 136.744L84.885 136.744Q84.690 136.721 84.639 136.506L84.639 136.416Q84.690 136.205 84.885 136.185L85.213 136.185L85.213 134.439Q85.213 134.131 85.123 133.973Q85.034 133.814 84.741 133.814Q84.471 133.814 84.243 133.945Q84.014 134.076 83.877 134.305Q83.741 134.533 83.741 134.799L83.741 136.185L84.166 136.185Q84.373 136.209 84.413 136.416L84.413 136.506Q84.373 136.721 84.166 136.744L82.678 136.744Q82.471 136.721 82.428 136.506M87.803 135.639L87.803 133.857L87.053 133.857Q86.854 133.834 86.803 133.615L86.803 133.529Q86.854 133.318 87.053 133.295L87.803 133.295L87.803 132.545Q87.854 132.338 88.053 132.310L88.198 132.310Q88.393 132.338 88.444 132.545L88.444 133.295L89.803 133.295Q89.995 133.314 90.053 133.529L90.053 133.615Q89.998 133.834 89.803 133.857L88.444 133.857L88.444 135.607Q88.444 136.224 89.018 136.224Q89.268 136.224 89.432 136.039Q89.596 135.853 89.596 135.607Q89.596 135.514 89.668 135.443Q89.741 135.373 89.842 135.361L89.987 135.361Q90.186 135.385 90.237 135.592L90.237 135.639Q90.237 135.963 90.053 136.226Q89.870 136.490 89.577 136.637Q89.284 136.783 88.963 136.783Q88.452 136.783 88.127 136.473Q87.803 136.162 87.803 135.639M91.467 136.506L91.467 136.416Q91.518 136.209 91.713 136.185L92.752 136.185L92.752 133.857L91.780 133.857Q91.581 133.834 91.530 133.615L91.530 133.529Q91.581 133.318 91.780 133.295L93.147 133.295Q93.342 133.314 93.393 133.529L93.393 136.185L94.307 136.185Q94.502 136.209 94.553 136.416L94.553 136.506Q94.502 136.721 94.307 136.744L91.713 136.744Q91.518 136.721 91.467 136.506M92.498 132.318L92.498 132.264Q92.498 132.092 92.635 131.971Q92.772 131.849 92.948 131.849Q93.120 131.849 93.256 131.971Q93.393 132.092 93.393 132.264L93.393 132.318Q93.393 132.494 93.256 132.615Q93.120 132.736 92.948 132.736Q92.772 132.736 92.635 132.615Q92.498 132.494 92.498 132.318M97.217 136.783Q96.745 136.783 96.360 136.539Q95.975 136.295 95.752 135.885Q95.530 135.474 95.530 135.017Q95.530 134.674 95.655 134.351Q95.780 134.029 96.010 133.775Q96.241 133.521 96.547 133.377Q96.854 133.232 97.217 133.232Q97.581 133.232 97.893 133.379Q98.206 133.525 98.428 133.771Q98.651 134.017 98.778 134.338Q98.905 134.658 98.905 135.017Q98.905 135.474 98.680 135.887Q98.456 136.299 98.071 136.541Q97.686 136.783 97.217 136.783M97.217 136.224Q97.682 136.224 97.973 135.830Q98.264 135.435 98.264 134.951Q98.264 134.658 98.129 134.390Q97.995 134.123 97.754 133.957Q97.514 133.791 97.217 133.791Q96.913 133.791 96.674 133.957Q96.436 134.123 96.301 134.390Q96.166 134.658 96.166 134.951Q96.166 135.431 96.459 135.828Q96.752 136.224 97.217 136.224M99.413 136.506L99.413 136.416Q99.456 136.209 99.663 136.185L100.084 136.185L100.084 133.857L99.663 133.857Q99.456 133.834 99.413 133.615L99.413 133.529Q99.459 133.318 99.663 133.295L100.479 133.295Q100.674 133.318 100.725 133.529L100.725 133.615L100.717 133.639Q100.944 133.459 101.217 133.357Q101.491 133.256 101.784 133.256Q102.131 133.256 102.370 133.396Q102.608 133.537 102.723 133.795Q102.838 134.053 102.838 134.408L102.838 136.185L103.264 136.185Q103.471 136.209 103.510 136.416L103.510 136.506Q103.471 136.721 103.264 136.744L101.870 136.744Q101.674 136.721 101.623 136.506L101.623 136.416Q101.674 136.205 101.870 136.185L102.198 136.185L102.198 134.439Q102.198 134.131 102.108 133.973Q102.018 133.814 101.725 133.814Q101.456 133.814 101.227 133.945Q100.998 134.076 100.862 134.305Q100.725 134.533 100.725 134.799L100.725 136.185L101.151 136.185Q101.358 136.209 101.397 136.416L101.397 136.506Q101.358 136.721 101.151 136.744L99.663 136.744Q99.456 136.721 99.413 136.506\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M-65.203 64.19H59.989V44.273H-65.203Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-21.25 -80.068)\">\u003Cpath d=\"M-2.201 135.631Q-2.201 135.185-1.787 134.928Q-1.373 134.670-0.832 134.570Q-0.291 134.471 0.217 134.463Q0.217 134.248 0.082 134.096Q-0.052 133.943-0.259 133.867Q-0.466 133.791-0.677 133.791Q-1.021 133.791-1.181 133.814L-1.181 133.873Q-1.181 134.041-1.300 134.156Q-1.420 134.271-1.584 134.271Q-1.759 134.271-1.875 134.148Q-1.990 134.025-1.990 133.857Q-1.990 133.451-1.609 133.342Q-1.228 133.232-0.670 133.232Q-0.400 133.232-0.132 133.310Q0.135 133.389 0.360 133.539Q0.584 133.689 0.721 133.910Q0.858 134.131 0.858 134.408L0.858 136.127Q0.858 136.185 1.385 136.185Q1.580 136.205 1.631 136.416L1.631 136.506Q1.580 136.721 1.385 136.744L1.241 136.744Q0.897 136.744 0.668 136.697Q0.440 136.650 0.295 136.463Q-0.166 136.783-0.873 136.783Q-1.209 136.783-1.513 136.642Q-1.818 136.502-2.009 136.240Q-2.201 135.978-2.201 135.631M-1.560 135.639Q-1.560 135.912-1.318 136.068Q-1.076 136.224-0.791 136.224Q-0.572 136.224-0.339 136.166Q-0.107 136.107 0.055 135.969Q0.217 135.830 0.217 135.607L0.217 135.017Q-0.064 135.017-0.480 135.074Q-0.896 135.131-1.228 135.269Q-1.560 135.408-1.560 135.639M3.502 136.783Q3.038 136.783 2.672 136.533Q2.307 136.283 2.102 135.879Q1.897 135.474 1.897 135.017Q1.897 134.674 2.022 134.353Q2.147 134.033 2.379 133.783Q2.612 133.533 2.916 133.394Q3.221 133.256 3.577 133.256Q4.088 133.256 4.495 133.576L4.495 132.416L4.073 132.416Q3.862 132.392 3.823 132.178L3.823 132.088Q3.862 131.881 4.073 131.857L4.885 131.857Q5.084 131.881 5.135 132.088L5.135 136.185L5.561 136.185Q5.768 136.209 5.807 136.416L5.807 136.506Q5.768 136.721 5.561 136.744L4.745 136.744Q4.545 136.721 4.495 136.506L4.495 136.377Q4.299 136.568 4.038 136.676Q3.776 136.783 3.502 136.783M3.541 136.224Q3.901 136.224 4.153 135.955Q4.405 135.685 4.495 135.310L4.495 134.478Q4.436 134.291 4.309 134.140Q4.182 133.990 4.004 133.902Q3.827 133.814 3.631 133.814Q3.323 133.814 3.073 133.984Q2.823 134.154 2.678 134.439Q2.534 134.724 2.534 135.025Q2.534 135.474 2.819 135.849Q3.104 136.224 3.541 136.224M7.748 136.783Q7.284 136.783 6.918 136.533Q6.553 136.283 6.348 135.879Q6.143 135.474 6.143 135.017Q6.143 134.674 6.268 134.353Q6.393 134.033 6.625 133.783Q6.858 133.533 7.163 133.394Q7.467 133.256 7.823 133.256Q8.334 133.256 8.741 133.576L8.741 132.416L8.319 132.416Q8.108 132.392 8.069 132.178L8.069 132.088Q8.108 131.881 8.319 131.857L9.131 131.857Q9.331 131.881 9.381 132.088L9.381 136.185L9.807 136.185Q10.014 136.209 10.053 136.416L10.053 136.506Q10.014 136.721 9.807 136.744L8.991 136.744Q8.791 136.721 8.741 136.506L8.741 136.377Q8.545 136.568 8.284 136.676Q8.022 136.783 7.748 136.783M7.788 136.224Q8.147 136.224 8.399 135.955Q8.651 135.685 8.741 135.310L8.741 134.478Q8.682 134.291 8.555 134.140Q8.428 133.990 8.250 133.902Q8.073 133.814 7.877 133.814Q7.569 133.814 7.319 133.984Q7.069 134.154 6.924 134.439Q6.780 134.724 6.780 135.025Q6.780 135.474 7.065 135.849Q7.350 136.224 7.788 136.224\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -80.068)\">\u003Cpath d=\"M15.608 136.822Q15.311 136.822 15.086 136.650Q14.862 136.478 14.739 136.203Q14.616 135.928 14.616 135.646L14.616 135.592Q14.616 135.334 14.707 135.098Q14.799 134.861 14.959 134.705L15.416 134.248Q15.194 133.611 15.194 132.959L15.194 132.904Q15.194 132.639 15.301 132.375Q15.409 132.111 15.614 131.943Q15.819 131.775 16.096 131.775Q16.373 131.775 16.553 131.947Q16.733 132.119 16.811 132.381Q16.889 132.642 16.889 132.904L16.889 132.959Q16.889 133.228 16.762 133.484Q16.635 133.740 16.469 133.939Q16.303 134.139 16.041 134.400Q16.221 134.810 16.584 135.377Q16.799 134.974 17.112 134.135L17.225 133.842Q17.084 133.806 17.041 133.615L17.041 133.529Q17.092 133.318 17.288 133.295L18.112 133.295Q18.311 133.314 18.362 133.529L18.362 133.615Q18.311 133.834 18.112 133.857L17.784 133.857L17.592 134.361Q17.209 135.385 16.928 135.857Q17.100 136.045 17.245 136.154Q17.389 136.264 17.569 136.264Q17.690 136.264 17.745 136.127Q17.799 135.990 17.799 135.842Q17.862 135.607 18.065 135.607Q18.268 135.607 18.331 135.842L18.331 135.896Q18.331 136.260 18.122 136.541Q17.913 136.822 17.569 136.822Q17.092 136.822 16.616 136.303Q16.159 136.822 15.608 136.822M15.608 136.264Q15.959 136.264 16.272 135.873Q15.858 135.232 15.651 134.806Q15.538 134.912 15.467 134.992Q15.397 135.072 15.348 135.154Q15.299 135.236 15.278 135.348Q15.256 135.459 15.256 135.592Q15.256 135.810 15.340 136.037Q15.424 136.264 15.608 136.264M15.834 133.814Q16.061 133.568 16.211 133.353Q16.362 133.139 16.362 132.928Q16.362 132.740 16.301 132.539Q16.241 132.338 16.096 132.338Q15.913 132.338 15.817 132.535Q15.721 132.732 15.721 132.943Q15.721 133.381 15.834 133.814\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -80.068)\">\u003Cpath d=\"M22.963 136.506L22.963 136.416Q23.006 136.209 23.213 136.185L23.635 136.185L23.635 133.857L23.213 133.857Q23.006 133.834 22.963 133.615L22.963 133.529Q23.010 133.318 23.213 133.295L24.030 133.295Q24.225 133.318 24.276 133.529L24.276 133.615L24.268 133.639Q24.495 133.459 24.768 133.357Q25.041 133.256 25.334 133.256Q25.682 133.256 25.920 133.396Q26.159 133.537 26.274 133.795Q26.389 134.053 26.389 134.408L26.389 136.185L26.815 136.185Q27.022 136.209 27.061 136.416L27.061 136.506Q27.022 136.721 26.815 136.744L25.420 136.744Q25.225 136.721 25.174 136.506L25.174 136.416Q25.225 136.205 25.420 136.185L25.748 136.185L25.748 134.439Q25.748 134.131 25.659 133.973Q25.569 133.814 25.276 133.814Q25.006 133.814 24.778 133.945Q24.549 134.076 24.413 134.305Q24.276 134.533 24.276 134.799L24.276 136.185L24.702 136.185Q24.909 136.209 24.948 136.416L24.948 136.506Q24.909 136.721 24.702 136.744L23.213 136.744Q23.006 136.721 22.963 136.506M29.260 136.783Q28.788 136.783 28.403 136.539Q28.018 136.295 27.795 135.885Q27.573 135.474 27.573 135.017Q27.573 134.674 27.698 134.351Q27.823 134.029 28.053 133.775Q28.284 133.521 28.590 133.377Q28.897 133.232 29.260 133.232Q29.623 133.232 29.936 133.379Q30.248 133.525 30.471 133.771Q30.694 134.017 30.821 134.338Q30.948 134.658 30.948 135.017Q30.948 135.474 30.723 135.887Q30.498 136.299 30.114 136.541Q29.729 136.783 29.260 136.783M29.260 136.224Q29.725 136.224 30.016 135.830Q30.307 135.435 30.307 134.951Q30.307 134.658 30.172 134.390Q30.038 134.123 29.797 133.957Q29.557 133.791 29.260 133.791Q28.956 133.791 28.717 133.957Q28.479 134.123 28.344 134.390Q28.209 134.658 28.209 134.951Q28.209 135.431 28.502 135.828Q28.795 136.224 29.260 136.224M31.608 136.506L31.608 136.416Q31.666 136.209 31.858 136.185L32.569 136.185L32.569 133.857L31.858 133.857Q31.663 133.834 31.608 133.615L31.608 133.529Q31.666 133.318 31.858 133.295L32.959 133.295Q33.159 133.314 33.209 133.529L33.209 133.857Q33.471 133.572 33.827 133.414Q34.182 133.256 34.569 133.256Q34.862 133.256 35.096 133.390Q35.331 133.525 35.331 133.791Q35.331 133.959 35.221 134.076Q35.112 134.193 34.944 134.193Q34.791 134.193 34.676 134.082Q34.561 133.971 34.561 133.814Q34.186 133.814 33.872 134.015Q33.557 134.217 33.383 134.551Q33.209 134.885 33.209 135.264L33.209 136.185L34.155 136.185Q34.362 136.209 34.401 136.416L34.401 136.506Q34.362 136.721 34.155 136.744L31.858 136.744Q31.666 136.721 31.608 136.506M35.577 136.506L35.577 136.416Q35.627 136.205 35.823 136.185L36.022 136.185L36.022 133.857L35.823 133.857Q35.616 133.834 35.577 133.615L35.577 133.529Q35.627 133.314 35.823 133.295L36.303 133.295Q36.495 133.318 36.553 133.529Q36.873 133.256 37.288 133.256Q37.479 133.256 37.647 133.365Q37.815 133.474 37.889 133.646Q38.065 133.455 38.288 133.355Q38.510 133.256 38.752 133.256Q39.170 133.256 39.325 133.598Q39.479 133.939 39.479 134.408L39.479 136.185L39.678 136.185Q39.889 136.209 39.928 136.416L39.928 136.506Q39.877 136.721 39.678 136.744L38.862 136.744Q38.666 136.721 38.616 136.506L38.616 136.416Q38.666 136.209 38.862 136.185L38.952 136.185L38.952 134.439Q38.952 133.814 38.702 133.814Q38.370 133.814 38.192 134.125Q38.014 134.435 38.014 134.799L38.014 136.185L38.217 136.185Q38.424 136.209 38.463 136.416L38.463 136.506Q38.413 136.721 38.217 136.744L37.401 136.744Q37.202 136.721 37.151 136.506L37.151 136.416Q37.202 136.209 37.401 136.185L37.487 136.185L37.487 134.439Q37.487 133.814 37.241 133.814Q36.909 133.814 36.731 134.127Q36.553 134.439 36.553 134.799L36.553 136.185L36.752 136.185Q36.959 136.209 36.998 136.416L36.998 136.506Q36.948 136.724 36.752 136.744L35.823 136.744Q35.616 136.721 35.577 136.506\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-65.203 24.356H59.989V-1.25H-65.203Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-38.25 -122.747)\">\u003Cpath d=\"M-2.287 136.506L-2.287 136.416Q-2.236 136.209-2.041 136.185L-1.158 136.185L-1.158 133.857L-2.013 133.857Q-2.212 133.834-2.263 133.615L-2.263 133.529Q-2.212 133.318-2.013 133.295L-1.158 133.295L-1.158 132.842Q-1.158 132.377-0.752 132.096Q-0.345 131.814 0.135 131.814Q0.448 131.814 0.692 131.935Q0.936 132.056 0.936 132.338Q0.936 132.502 0.827 132.619Q0.717 132.736 0.553 132.736Q0.405 132.736 0.284 132.631Q0.163 132.525 0.163 132.377L0.080 132.377Q-0.072 132.377-0.209 132.437Q-0.345 132.498-0.431 132.613Q-0.517 132.728-0.517 132.873L-0.517 133.295L0.514 133.295Q0.709 133.314 0.760 133.529L0.760 133.615Q0.709 133.834 0.514 133.857L-0.517 133.857L-0.517 136.185L0.362 136.185Q0.557 136.209 0.608 136.416L0.608 136.506Q0.557 136.721 0.362 136.744L-2.041 136.744Q-2.236 136.721-2.287 136.506M5.151 135.256L2.709 135.256Q2.764 135.533 2.961 135.756Q3.159 135.978 3.436 136.101Q3.713 136.224 3.998 136.224Q4.471 136.224 4.694 135.935Q4.702 135.924 4.758 135.818Q4.815 135.713 4.864 135.670Q4.913 135.627 5.006 135.615L5.151 135.615Q5.342 135.635 5.401 135.849L5.401 135.904Q5.334 136.205 5.104 136.402Q4.873 136.599 4.561 136.691Q4.248 136.783 3.944 136.783Q3.459 136.783 3.020 136.555Q2.580 136.326 2.313 135.926Q2.045 135.525 2.045 135.033L2.045 134.974Q2.045 134.506 2.291 134.103Q2.538 133.701 2.946 133.467Q3.354 133.232 3.823 133.232Q4.327 133.232 4.680 133.455Q5.034 133.678 5.217 134.066Q5.401 134.455 5.401 134.959L5.401 135.017Q5.342 135.232 5.151 135.256M2.717 134.705L4.745 134.705Q4.698 134.295 4.459 134.043Q4.221 133.791 3.823 133.791Q3.428 133.791 3.122 134.053Q2.815 134.314 2.717 134.705M9.397 135.256L6.955 135.256Q7.010 135.533 7.207 135.756Q7.405 135.978 7.682 136.101Q7.959 136.224 8.245 136.224Q8.717 136.224 8.940 135.935Q8.948 135.924 9.004 135.818Q9.061 135.713 9.110 135.670Q9.159 135.627 9.252 135.615L9.397 135.615Q9.588 135.635 9.647 135.849L9.647 135.904Q9.581 136.205 9.350 136.402Q9.120 136.599 8.807 136.691Q8.495 136.783 8.190 136.783Q7.705 136.783 7.266 136.555Q6.827 136.326 6.559 135.926Q6.291 135.525 6.291 135.033L6.291 134.974Q6.291 134.506 6.538 134.103Q6.784 133.701 7.192 133.467Q7.600 133.232 8.069 133.232Q8.573 133.232 8.926 133.455Q9.280 133.678 9.463 134.066Q9.647 134.455 9.647 134.959L9.647 135.017Q9.588 135.232 9.397 135.256M6.963 134.705L8.991 134.705Q8.944 134.295 8.706 134.043Q8.467 133.791 8.069 133.791Q7.674 133.791 7.368 134.053Q7.061 134.314 6.963 134.705M11.995 136.783Q11.530 136.783 11.164 136.533Q10.799 136.283 10.594 135.879Q10.389 135.474 10.389 135.017Q10.389 134.674 10.514 134.353Q10.639 134.033 10.872 133.783Q11.104 133.533 11.409 133.394Q11.713 133.256 12.069 133.256Q12.581 133.256 12.987 133.576L12.987 132.416L12.565 132.416Q12.354 132.392 12.315 132.178L12.315 132.088Q12.354 131.881 12.565 131.857L13.377 131.857Q13.577 131.881 13.627 132.088L13.627 136.185L14.053 136.185Q14.260 136.209 14.299 136.416L14.299 136.506Q14.260 136.721 14.053 136.744L13.237 136.744Q13.038 136.721 12.987 136.506L12.987 136.377Q12.791 136.568 12.530 136.676Q12.268 136.783 11.995 136.783M12.034 136.224Q12.393 136.224 12.645 135.955Q12.897 135.685 12.987 135.310L12.987 134.478Q12.928 134.291 12.801 134.140Q12.674 133.990 12.497 133.902Q12.319 133.814 12.123 133.814Q11.815 133.814 11.565 133.984Q11.315 134.154 11.170 134.439Q11.026 134.724 11.026 135.025Q11.026 135.474 11.311 135.849Q11.596 136.224 12.034 136.224M17.873 134.607L15.131 134.607Q15.006 134.596 14.920 134.510Q14.834 134.424 14.834 134.295Q14.834 134.166 14.920 134.084Q15.006 134.002 15.131 133.990L17.873 133.990Q17.998 134.002 18.081 134.084Q18.163 134.166 18.163 134.295Q18.163 134.424 18.081 134.510Q17.998 134.596 17.873 134.607M18.944 136.506L18.944 136.416Q18.995 136.209 19.190 136.185L20.073 136.185L20.073 133.857L19.217 133.857Q19.018 133.834 18.967 133.615L18.967 133.529Q19.018 133.318 19.217 133.295L20.073 133.295L20.073 132.842Q20.073 132.377 20.479 132.096Q20.885 131.814 21.366 131.814Q21.678 131.814 21.922 131.935Q22.166 132.056 22.166 132.338Q22.166 132.502 22.057 132.619Q21.948 132.736 21.784 132.736Q21.635 132.736 21.514 132.631Q21.393 132.525 21.393 132.377L21.311 132.377Q21.159 132.377 21.022 132.437Q20.885 132.498 20.799 132.613Q20.713 132.728 20.713 132.873L20.713 133.295L21.745 133.295Q21.940 133.314 21.991 133.529L21.991 133.615Q21.940 133.834 21.745 133.857L20.713 133.857L20.713 136.185L21.592 136.185Q21.788 136.209 21.838 136.416L21.838 136.506Q21.788 136.721 21.592 136.744L19.190 136.744Q18.995 136.721 18.944 136.506M24.991 136.783Q24.518 136.783 24.133 136.539Q23.748 136.295 23.526 135.885Q23.303 135.474 23.303 135.017Q23.303 134.674 23.428 134.351Q23.553 134.029 23.784 133.775Q24.014 133.521 24.321 133.377Q24.627 133.232 24.991 133.232Q25.354 133.232 25.666 133.379Q25.979 133.525 26.202 133.771Q26.424 134.017 26.551 134.338Q26.678 134.658 26.678 135.017Q26.678 135.474 26.454 135.887Q26.229 136.299 25.844 136.541Q25.459 136.783 24.991 136.783M24.991 136.224Q25.456 136.224 25.747 135.830Q26.038 135.435 26.038 134.951Q26.038 134.658 25.903 134.390Q25.768 134.123 25.528 133.957Q25.288 133.791 24.991 133.791Q24.686 133.791 24.448 133.957Q24.209 134.123 24.075 134.390Q23.940 134.658 23.940 134.951Q23.940 135.431 24.233 135.828Q24.526 136.224 24.991 136.224M27.338 136.506L27.338 136.416Q27.397 136.209 27.588 136.185L28.299 136.185L28.299 133.857L27.588 133.857Q27.393 133.834 27.338 133.615L27.338 133.529Q27.397 133.318 27.588 133.295L28.690 133.295Q28.889 133.314 28.940 133.529L28.940 133.857Q29.202 133.572 29.557 133.414Q29.913 133.256 30.299 133.256Q30.592 133.256 30.827 133.390Q31.061 133.525 31.061 133.791Q31.061 133.959 30.952 134.076Q30.842 134.193 30.674 134.193Q30.522 134.193 30.407 134.082Q30.291 133.971 30.291 133.814Q29.916 133.814 29.602 134.015Q29.288 134.217 29.114 134.551Q28.940 134.885 28.940 135.264L28.940 136.185L29.885 136.185Q30.092 136.209 30.131 136.416L30.131 136.506Q30.092 136.721 29.885 136.744L27.588 136.744Q27.397 136.721 27.338 136.506M32.370 136.521L31.905 133.857L31.745 133.857Q31.538 133.834 31.498 133.615L31.498 133.529Q31.538 133.318 31.745 133.295L32.913 133.295Q33.123 133.318 33.163 133.529L33.163 133.615Q33.123 133.834 32.913 133.857L32.440 133.857Q32.553 134.502 32.631 134.947Q32.709 135.392 32.760 135.711Q32.811 136.029 32.811 136.103Q32.819 135.931 33.104 134.935Q33.143 134.822 33.241 134.748Q33.338 134.674 33.459 134.674L33.538 134.674Q33.659 134.674 33.756 134.748Q33.854 134.822 33.889 134.935Q33.998 135.318 34.081 135.642Q34.163 135.967 34.163 136.103Q34.174 135.814 34.522 133.857L34.049 133.857Q33.842 133.834 33.803 133.615L33.803 133.529Q33.842 133.318 34.049 133.295L35.225 133.295Q35.416 133.318 35.475 133.529L35.475 133.615Q35.420 133.834 35.225 133.857L35.057 133.857L34.592 136.521Q34.569 136.639 34.481 136.711Q34.393 136.783 34.272 136.783L34.131 136.783Q34.010 136.783 33.914 136.711Q33.819 136.639 33.776 136.521Q33.729 136.342 33.657 136.086Q33.584 135.830 33.541 135.621Q33.498 135.412 33.498 135.310Q33.491 135.592 33.209 136.521Q33.182 136.631 33.084 136.707Q32.987 136.783 32.866 136.783L32.690 136.783Q32.569 136.783 32.481 136.711Q32.393 136.639 32.370 136.521M36.014 135.631Q36.014 135.185 36.428 134.928Q36.842 134.670 37.383 134.570Q37.924 134.471 38.432 134.463Q38.432 134.248 38.297 134.096Q38.163 133.943 37.956 133.867Q37.748 133.791 37.538 133.791Q37.194 133.791 37.034 133.814L37.034 133.873Q37.034 134.041 36.914 134.156Q36.795 134.271 36.631 134.271Q36.456 134.271 36.340 134.148Q36.225 134.025 36.225 133.857Q36.225 133.451 36.606 133.342Q36.987 133.232 37.545 133.232Q37.815 133.232 38.082 133.310Q38.350 133.389 38.575 133.539Q38.799 133.689 38.936 133.910Q39.073 134.131 39.073 134.408L39.073 136.127Q39.073 136.185 39.600 136.185Q39.795 136.205 39.846 136.416L39.846 136.506Q39.795 136.721 39.600 136.744L39.456 136.744Q39.112 136.744 38.883 136.697Q38.655 136.650 38.510 136.463Q38.049 136.783 37.342 136.783Q37.006 136.783 36.702 136.642Q36.397 136.502 36.206 136.240Q36.014 135.978 36.014 135.631M36.655 135.639Q36.655 135.912 36.897 136.068Q37.139 136.224 37.424 136.224Q37.643 136.224 37.875 136.166Q38.108 136.107 38.270 135.969Q38.432 135.830 38.432 135.607L38.432 135.017Q38.151 135.017 37.735 135.074Q37.319 135.131 36.987 135.269Q36.655 135.408 36.655 135.639M40.077 136.506L40.077 136.416Q40.135 136.209 40.327 136.185L41.038 136.185L41.038 133.857L40.327 133.857Q40.131 133.834 40.077 133.615L40.077 133.529Q40.135 133.318 40.327 133.295L41.428 133.295Q41.627 133.314 41.678 133.529L41.678 133.857Q41.940 133.572 42.295 133.414Q42.651 133.256 43.038 133.256Q43.331 133.256 43.565 133.390Q43.799 133.525 43.799 133.791Q43.799 133.959 43.690 134.076Q43.581 134.193 43.413 134.193Q43.260 134.193 43.145 134.082Q43.030 133.971 43.030 133.814Q42.655 133.814 42.340 134.015Q42.026 134.217 41.852 134.551Q41.678 134.885 41.678 135.264L41.678 136.185L42.623 136.185Q42.831 136.209 42.870 136.416L42.870 136.506Q42.831 136.721 42.623 136.744L40.327 136.744Q40.135 136.721 40.077 136.506M45.963 136.783Q45.498 136.783 45.133 136.533Q44.768 136.283 44.563 135.879Q44.358 135.474 44.358 135.017Q44.358 134.674 44.483 134.353Q44.608 134.033 44.840 133.783Q45.073 133.533 45.377 133.394Q45.682 133.256 46.038 133.256Q46.549 133.256 46.956 133.576L46.956 132.416L46.534 132.416Q46.323 132.392 46.284 132.178L46.284 132.088Q46.323 131.881 46.534 131.857L47.346 131.857Q47.545 131.881 47.596 132.088L47.596 136.185L48.022 136.185Q48.229 136.209 48.268 136.416L48.268 136.506Q48.229 136.721 48.022 136.744L47.206 136.744Q47.006 136.721 46.956 136.506L46.956 136.377Q46.760 136.568 46.498 136.676Q46.237 136.783 45.963 136.783M46.002 136.224Q46.362 136.224 46.614 135.955Q46.866 135.685 46.956 135.310L46.956 134.478Q46.897 134.291 46.770 134.140Q46.643 133.990 46.465 133.902Q46.288 133.814 46.092 133.814Q45.784 133.814 45.534 133.984Q45.284 134.154 45.139 134.439Q44.995 134.724 44.995 135.025Q44.995 135.474 45.280 135.849Q45.565 136.224 46.002 136.224\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-38.25 -122.747)\">\u003Cpath d=\"M55.756 137.385Q55.225 137.076 54.825 136.588Q54.424 136.099 54.213 135.506Q54.002 134.912 54.002 134.295Q54.002 133.678 54.211 133.090Q54.420 132.502 54.817 132.021Q55.213 131.541 55.748 131.217Q55.819 131.193 55.850 131.193L55.940 131.193Q56.038 131.205 56.104 131.271Q56.170 131.338 56.170 131.439Q56.170 131.584 56.069 131.646Q55.620 131.935 55.293 132.351Q54.967 132.767 54.805 133.260Q54.643 133.752 54.643 134.295Q54.643 134.701 54.739 135.088Q54.834 135.474 55.012 135.810Q55.190 136.146 55.450 136.430Q55.709 136.713 56.057 136.943Q56.170 137.021 56.170 137.158Q56.170 137.256 56.104 137.326Q56.038 137.396 55.940 137.408L55.850 137.408Q55.791 137.408 55.756 137.385M57.096 136.506L57.096 136.416Q57.135 136.209 57.346 136.185L57.682 136.185L57.682 132.416L57.346 132.416Q57.135 132.392 57.096 132.178L57.096 132.088Q57.135 131.881 57.346 131.857L60.600 131.857Q60.799 131.881 60.850 132.088L60.850 132.928Q60.803 133.142 60.600 133.170L60.456 133.170Q60.260 133.142 60.209 132.928L60.209 132.416L58.323 132.416L58.323 134.017L59.331 134.017L59.331 133.799Q59.381 133.592 59.577 133.568L59.721 133.568Q59.916 133.588 59.967 133.799L59.967 134.783Q59.916 135.002 59.721 135.025L59.577 135.025Q59.381 135.006 59.331 134.783L59.331 134.576L58.323 134.576L58.323 136.185L58.811 136.185Q59.006 136.209 59.057 136.416L59.057 136.506Q59.006 136.721 58.811 136.744L57.346 136.744Q57.135 136.721 57.096 136.506M61.342 136.506L61.342 136.416Q61.381 136.209 61.592 136.185L61.928 136.185L61.928 132.416L61.592 132.416Q61.381 132.392 61.342 132.178L61.342 132.088Q61.381 131.881 61.592 131.857L64.846 131.857Q65.045 131.881 65.096 132.088L65.096 132.928Q65.049 133.142 64.846 133.170L64.702 133.170Q64.506 133.142 64.456 132.928L64.456 132.416L62.569 132.416L62.569 134.017L63.577 134.017L63.577 133.799Q63.627 133.592 63.823 133.568L63.967 133.568Q64.163 133.588 64.213 133.799L64.213 134.783Q64.163 135.002 63.967 135.025L63.823 135.025Q63.627 135.006 63.577 134.783L63.577 134.576L62.569 134.576L62.569 136.185L63.057 136.185Q63.252 136.209 63.303 136.416L63.303 136.506Q63.252 136.721 63.057 136.744L61.592 136.744Q61.381 136.721 61.342 136.506M65.581 136.506L65.581 136.416Q65.631 136.209 65.831 136.185L66.100 136.185L66.100 132.416L65.831 132.416Q65.631 132.392 65.581 132.178L65.581 132.088Q65.631 131.881 65.831 131.857L66.612 131.857Q66.741 131.857 66.846 131.931Q66.952 132.006 66.991 132.119Q67.268 132.908 67.428 133.357Q67.588 133.806 67.842 134.525Q68.096 135.244 68.235 135.654Q68.373 136.064 68.373 136.103L68.373 132.416L68.100 132.416Q67.905 132.392 67.854 132.178L67.854 132.088Q67.905 131.881 68.100 131.857L69.174 131.857Q69.370 131.881 69.420 132.088L69.420 132.178Q69.370 132.392 69.174 132.416L68.901 132.416L68.901 136.506Q68.850 136.721 68.655 136.744L68.389 136.744Q68.264 136.744 68.161 136.670Q68.057 136.596 68.014 136.478Q67.717 135.631 67.344 134.582Q66.971 133.533 66.801 133.045Q66.631 132.556 66.627 132.498L66.627 136.185L66.901 136.185Q67.092 136.209 67.151 136.416L67.151 136.506Q67.092 136.721 66.901 136.744L65.831 136.744Q65.631 136.721 65.581 136.506M70.666 137.408L70.581 137.408Q70.475 137.396 70.407 137.324Q70.338 137.252 70.338 137.158Q70.338 137.017 70.444 136.951Q70.780 136.736 71.049 136.447Q71.319 136.158 71.502 135.810Q71.686 135.463 71.776 135.084Q71.866 134.705 71.866 134.295Q71.866 133.756 71.702 133.264Q71.538 132.771 71.219 132.357Q70.901 131.943 70.459 131.654Q70.338 131.572 70.338 131.439Q70.338 131.342 70.407 131.273Q70.475 131.205 70.581 131.193L70.666 131.193Q70.721 131.193 70.756 131.217Q71.143 131.439 71.483 131.787Q71.823 132.135 72.043 132.529Q72.264 132.924 72.385 133.369Q72.506 133.814 72.506 134.295Q72.506 134.779 72.385 135.230Q72.264 135.681 72.039 136.078Q71.815 136.474 71.491 136.808Q71.166 137.142 70.764 137.385Q70.694 137.408 70.666 137.408\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M-65.203-18.323H59.989V-38.24H-65.203Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-21.25 -162.582)\">\u003Cpath d=\"M-2.201 135.631Q-2.201 135.185-1.787 134.928Q-1.373 134.670-0.832 134.570Q-0.291 134.471 0.217 134.463Q0.217 134.248 0.082 134.096Q-0.052 133.943-0.259 133.867Q-0.466 133.791-0.677 133.791Q-1.021 133.791-1.181 133.814L-1.181 133.873Q-1.181 134.041-1.300 134.156Q-1.420 134.271-1.584 134.271Q-1.759 134.271-1.875 134.148Q-1.990 134.025-1.990 133.857Q-1.990 133.451-1.609 133.342Q-1.228 133.232-0.670 133.232Q-0.400 133.232-0.132 133.310Q0.135 133.389 0.360 133.539Q0.584 133.689 0.721 133.910Q0.858 134.131 0.858 134.408L0.858 136.127Q0.858 136.185 1.385 136.185Q1.580 136.205 1.631 136.416L1.631 136.506Q1.580 136.721 1.385 136.744L1.241 136.744Q0.897 136.744 0.668 136.697Q0.440 136.650 0.295 136.463Q-0.166 136.783-0.873 136.783Q-1.209 136.783-1.513 136.642Q-1.818 136.502-2.009 136.240Q-2.201 135.978-2.201 135.631M-1.560 135.639Q-1.560 135.912-1.318 136.068Q-1.076 136.224-0.791 136.224Q-0.572 136.224-0.339 136.166Q-0.107 136.107 0.055 135.969Q0.217 135.830 0.217 135.607L0.217 135.017Q-0.064 135.017-0.480 135.074Q-0.896 135.131-1.228 135.269Q-1.560 135.408-1.560 135.639M3.502 136.783Q3.038 136.783 2.672 136.533Q2.307 136.283 2.102 135.879Q1.897 135.474 1.897 135.017Q1.897 134.674 2.022 134.353Q2.147 134.033 2.379 133.783Q2.612 133.533 2.916 133.394Q3.221 133.256 3.577 133.256Q4.088 133.256 4.495 133.576L4.495 132.416L4.073 132.416Q3.862 132.392 3.823 132.178L3.823 132.088Q3.862 131.881 4.073 131.857L4.885 131.857Q5.084 131.881 5.135 132.088L5.135 136.185L5.561 136.185Q5.768 136.209 5.807 136.416L5.807 136.506Q5.768 136.721 5.561 136.744L4.745 136.744Q4.545 136.721 4.495 136.506L4.495 136.377Q4.299 136.568 4.038 136.676Q3.776 136.783 3.502 136.783M3.541 136.224Q3.901 136.224 4.153 135.955Q4.405 135.685 4.495 135.310L4.495 134.478Q4.436 134.291 4.309 134.140Q4.182 133.990 4.004 133.902Q3.827 133.814 3.631 133.814Q3.323 133.814 3.073 133.984Q2.823 134.154 2.678 134.439Q2.534 134.724 2.534 135.025Q2.534 135.474 2.819 135.849Q3.104 136.224 3.541 136.224M7.748 136.783Q7.284 136.783 6.918 136.533Q6.553 136.283 6.348 135.879Q6.143 135.474 6.143 135.017Q6.143 134.674 6.268 134.353Q6.393 134.033 6.625 133.783Q6.858 133.533 7.163 133.394Q7.467 133.256 7.823 133.256Q8.334 133.256 8.741 133.576L8.741 132.416L8.319 132.416Q8.108 132.392 8.069 132.178L8.069 132.088Q8.108 131.881 8.319 131.857L9.131 131.857Q9.331 131.881 9.381 132.088L9.381 136.185L9.807 136.185Q10.014 136.209 10.053 136.416L10.053 136.506Q10.014 136.721 9.807 136.744L8.991 136.744Q8.791 136.721 8.741 136.506L8.741 136.377Q8.545 136.568 8.284 136.676Q8.022 136.783 7.748 136.783M7.788 136.224Q8.147 136.224 8.399 135.955Q8.651 135.685 8.741 135.310L8.741 134.478Q8.682 134.291 8.555 134.140Q8.428 133.990 8.250 133.902Q8.073 133.814 7.877 133.814Q7.569 133.814 7.319 133.984Q7.069 134.154 6.924 134.439Q6.780 134.724 6.780 135.025Q6.780 135.474 7.065 135.849Q7.350 136.224 7.788 136.224\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -162.582)\">\u003Cpath d=\"M15.608 136.822Q15.311 136.822 15.086 136.650Q14.862 136.478 14.739 136.203Q14.616 135.928 14.616 135.646L14.616 135.592Q14.616 135.334 14.707 135.098Q14.799 134.861 14.959 134.705L15.416 134.248Q15.194 133.611 15.194 132.959L15.194 132.904Q15.194 132.639 15.301 132.375Q15.409 132.111 15.614 131.943Q15.819 131.775 16.096 131.775Q16.373 131.775 16.553 131.947Q16.733 132.119 16.811 132.381Q16.889 132.642 16.889 132.904L16.889 132.959Q16.889 133.228 16.762 133.484Q16.635 133.740 16.469 133.939Q16.303 134.139 16.041 134.400Q16.221 134.810 16.584 135.377Q16.799 134.974 17.112 134.135L17.225 133.842Q17.084 133.806 17.041 133.615L17.041 133.529Q17.092 133.318 17.288 133.295L18.112 133.295Q18.311 133.314 18.362 133.529L18.362 133.615Q18.311 133.834 18.112 133.857L17.784 133.857L17.592 134.361Q17.209 135.385 16.928 135.857Q17.100 136.045 17.245 136.154Q17.389 136.264 17.569 136.264Q17.690 136.264 17.745 136.127Q17.799 135.990 17.799 135.842Q17.862 135.607 18.065 135.607Q18.268 135.607 18.331 135.842L18.331 135.896Q18.331 136.260 18.122 136.541Q17.913 136.822 17.569 136.822Q17.092 136.822 16.616 136.303Q16.159 136.822 15.608 136.822M15.608 136.264Q15.959 136.264 16.272 135.873Q15.858 135.232 15.651 134.806Q15.538 134.912 15.467 134.992Q15.397 135.072 15.348 135.154Q15.299 135.236 15.278 135.348Q15.256 135.459 15.256 135.592Q15.256 135.810 15.340 136.037Q15.424 136.264 15.608 136.264M15.834 133.814Q16.061 133.568 16.211 133.353Q16.362 133.139 16.362 132.928Q16.362 132.740 16.301 132.539Q16.241 132.338 16.096 132.338Q15.913 132.338 15.817 132.535Q15.721 132.732 15.721 132.943Q15.721 133.381 15.834 133.814\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-21.25 -162.582)\">\u003Cpath d=\"M22.963 136.506L22.963 136.416Q23.006 136.209 23.213 136.185L23.635 136.185L23.635 133.857L23.213 133.857Q23.006 133.834 22.963 133.615L22.963 133.529Q23.010 133.318 23.213 133.295L24.030 133.295Q24.225 133.318 24.276 133.529L24.276 133.615L24.268 133.639Q24.495 133.459 24.768 133.357Q25.041 133.256 25.334 133.256Q25.682 133.256 25.920 133.396Q26.159 133.537 26.274 133.795Q26.389 134.053 26.389 134.408L26.389 136.185L26.815 136.185Q27.022 136.209 27.061 136.416L27.061 136.506Q27.022 136.721 26.815 136.744L25.420 136.744Q25.225 136.721 25.174 136.506L25.174 136.416Q25.225 136.205 25.420 136.185L25.748 136.185L25.748 134.439Q25.748 134.131 25.659 133.973Q25.569 133.814 25.276 133.814Q25.006 133.814 24.778 133.945Q24.549 134.076 24.413 134.305Q24.276 134.533 24.276 134.799L24.276 136.185L24.702 136.185Q24.909 136.209 24.948 136.416L24.948 136.506Q24.909 136.721 24.702 136.744L23.213 136.744Q23.006 136.721 22.963 136.506M29.260 136.783Q28.788 136.783 28.403 136.539Q28.018 136.295 27.795 135.885Q27.573 135.474 27.573 135.017Q27.573 134.674 27.698 134.351Q27.823 134.029 28.053 133.775Q28.284 133.521 28.590 133.377Q28.897 133.232 29.260 133.232Q29.623 133.232 29.936 133.379Q30.248 133.525 30.471 133.771Q30.694 134.017 30.821 134.338Q30.948 134.658 30.948 135.017Q30.948 135.474 30.723 135.887Q30.498 136.299 30.114 136.541Q29.729 136.783 29.260 136.783M29.260 136.224Q29.725 136.224 30.016 135.830Q30.307 135.435 30.307 134.951Q30.307 134.658 30.172 134.390Q30.038 134.123 29.797 133.957Q29.557 133.791 29.260 133.791Q28.956 133.791 28.717 133.957Q28.479 134.123 28.344 134.390Q28.209 134.658 28.209 134.951Q28.209 135.431 28.502 135.828Q28.795 136.224 29.260 136.224M31.608 136.506L31.608 136.416Q31.666 136.209 31.858 136.185L32.569 136.185L32.569 133.857L31.858 133.857Q31.663 133.834 31.608 133.615L31.608 133.529Q31.666 133.318 31.858 133.295L32.959 133.295Q33.159 133.314 33.209 133.529L33.209 133.857Q33.471 133.572 33.827 133.414Q34.182 133.256 34.569 133.256Q34.862 133.256 35.096 133.390Q35.331 133.525 35.331 133.791Q35.331 133.959 35.221 134.076Q35.112 134.193 34.944 134.193Q34.791 134.193 34.676 134.082Q34.561 133.971 34.561 133.814Q34.186 133.814 33.872 134.015Q33.557 134.217 33.383 134.551Q33.209 134.885 33.209 135.264L33.209 136.185L34.155 136.185Q34.362 136.209 34.401 136.416L34.401 136.506Q34.362 136.721 34.155 136.744L31.858 136.744Q31.666 136.721 31.608 136.506M35.577 136.506L35.577 136.416Q35.627 136.205 35.823 136.185L36.022 136.185L36.022 133.857L35.823 133.857Q35.616 133.834 35.577 133.615L35.577 133.529Q35.627 133.314 35.823 133.295L36.303 133.295Q36.495 133.318 36.553 133.529Q36.873 133.256 37.288 133.256Q37.479 133.256 37.647 133.365Q37.815 133.474 37.889 133.646Q38.065 133.455 38.288 133.355Q38.510 133.256 38.752 133.256Q39.170 133.256 39.325 133.598Q39.479 133.939 39.479 134.408L39.479 136.185L39.678 136.185Q39.889 136.209 39.928 136.416L39.928 136.506Q39.877 136.721 39.678 136.744L38.862 136.744Q38.666 136.721 38.616 136.506L38.616 136.416Q38.666 136.209 38.862 136.185L38.952 136.185L38.952 134.439Q38.952 133.814 38.702 133.814Q38.370 133.814 38.192 134.125Q38.014 134.435 38.014 134.799L38.014 136.185L38.217 136.185Q38.424 136.209 38.463 136.416L38.463 136.506Q38.413 136.721 38.217 136.744L37.401 136.744Q37.202 136.721 37.151 136.506L37.151 136.416Q37.202 136.209 37.401 136.185L37.487 136.185L37.487 134.439Q37.487 133.814 37.241 133.814Q36.909 133.814 36.731 134.127Q36.553 134.439 36.553 134.799L36.553 136.185L36.752 136.185Q36.959 136.209 36.998 136.416L36.998 136.506Q36.948 136.724 36.752 136.744L35.823 136.744Q35.616 136.721 35.577 136.506\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-46.75 -200.126)\">\u003Cpath d=\"M-0.486 136.783Q-0.959 136.783-1.343 136.539Q-1.728 136.295-1.951 135.885Q-2.173 135.474-2.173 135.017Q-2.173 134.674-2.048 134.351Q-1.923 134.029-1.693 133.775Q-1.462 133.521-1.156 133.377Q-0.849 133.232-0.486 133.232Q-0.123 133.232 0.190 133.379Q0.502 133.525 0.725 133.771Q0.948 134.017 1.075 134.338Q1.202 134.658 1.202 135.017Q1.202 135.474 0.977 135.887Q0.752 136.299 0.368 136.541Q-0.017 136.783-0.486 136.783M-0.486 136.224Q-0.021 136.224 0.270 135.830Q0.561 135.435 0.561 134.951Q0.561 134.658 0.426 134.390Q0.291 134.123 0.051 133.957Q-0.189 133.791-0.486 133.791Q-0.791 133.791-1.029 133.957Q-1.267 134.123-1.402 134.390Q-1.537 134.658-1.537 134.951Q-1.537 135.431-1.244 135.828Q-0.951 136.224-0.486 136.224M2.381 135.889L2.381 133.857L1.959 133.857Q1.752 133.834 1.709 133.615L1.709 133.529Q1.756 133.318 1.959 133.295L2.776 133.295Q2.971 133.318 3.022 133.529L3.022 135.857Q3.022 136.092 3.192 136.158Q3.362 136.224 3.647 136.224Q3.854 136.224 4.049 136.148Q4.245 136.072 4.370 135.922Q4.495 135.771 4.495 135.560L4.495 133.857L4.073 133.857Q3.862 133.834 3.823 133.615L3.823 133.529Q3.862 133.318 4.073 133.295L4.885 133.295Q5.084 133.318 5.135 133.529L5.135 136.185L5.561 136.185Q5.768 136.209 5.807 136.416L5.807 136.506Q5.768 136.721 5.561 136.744L4.745 136.744Q4.545 136.721 4.495 136.521Q4.092 136.783 3.584 136.783Q3.350 136.783 3.135 136.742Q2.920 136.701 2.754 136.599Q2.588 136.498 2.485 136.320Q2.381 136.142 2.381 135.889M7.084 135.639L7.084 133.857L6.334 133.857Q6.135 133.834 6.084 133.615L6.084 133.529Q6.135 133.318 6.334 133.295L7.084 133.295L7.084 132.545Q7.135 132.338 7.334 132.310L7.479 132.310Q7.674 132.338 7.725 132.545L7.725 133.295L9.084 133.295Q9.276 133.314 9.334 133.529L9.334 133.615Q9.280 133.834 9.084 133.857L7.725 133.857L7.725 135.607Q7.725 136.224 8.299 136.224Q8.549 136.224 8.713 136.039Q8.877 135.853 8.877 135.607Q8.877 135.514 8.950 135.443Q9.022 135.373 9.123 135.361L9.268 135.361Q9.467 135.385 9.518 135.592L9.518 135.639Q9.518 135.963 9.334 136.226Q9.151 136.490 8.858 136.637Q8.565 136.783 8.245 136.783Q7.733 136.783 7.409 136.473Q7.084 136.162 7.084 135.639M10.202 138.287L10.202 138.201Q10.245 137.982 10.452 137.959L10.873 137.959L10.873 133.857L10.452 133.857Q10.245 133.834 10.202 133.615L10.202 133.529Q10.248 133.318 10.452 133.295L11.268 133.295Q11.463 133.314 11.514 133.529L11.514 133.599Q11.725 133.431 11.989 133.344Q12.252 133.256 12.522 133.256Q12.862 133.256 13.159 133.400Q13.456 133.545 13.670 133.797Q13.885 134.049 14 134.361Q14.116 134.674 14.116 135.017Q14.116 135.482 13.889 135.892Q13.663 136.303 13.276 136.543Q12.889 136.783 12.420 136.783Q11.901 136.783 11.514 136.416L11.514 137.959L11.940 137.959Q12.147 137.982 12.186 138.201L12.186 138.287Q12.147 138.498 11.940 138.521L10.452 138.521Q10.248 138.498 10.202 138.287M12.377 136.224Q12.686 136.224 12.936 136.055Q13.186 135.885 13.331 135.603Q13.475 135.322 13.475 135.017Q13.475 134.728 13.350 134.449Q13.225 134.170 12.993 133.992Q12.760 133.814 12.459 133.814Q12.139 133.814 11.877 134Q11.616 134.185 11.514 134.486L11.514 135.338Q11.604 135.705 11.825 135.965Q12.045 136.224 12.377 136.224M15.120 135.889L15.120 133.857L14.698 133.857Q14.491 133.834 14.448 133.615L14.448 133.529Q14.495 133.318 14.698 133.295L15.514 133.295Q15.709 133.318 15.760 133.529L15.760 135.857Q15.760 136.092 15.930 136.158Q16.100 136.224 16.385 136.224Q16.592 136.224 16.788 136.148Q16.983 136.072 17.108 135.922Q17.233 135.771 17.233 135.560L17.233 133.857L16.811 133.857Q16.600 133.834 16.561 133.615L16.561 133.529Q16.600 133.318 16.811 133.295L17.623 133.295Q17.823 133.318 17.873 133.529L17.873 136.185L18.299 136.185Q18.506 136.209 18.545 136.416L18.545 136.506Q18.506 136.721 18.299 136.744L17.483 136.744Q17.284 136.721 17.233 136.521Q16.831 136.783 16.323 136.783Q16.088 136.783 15.873 136.742Q15.659 136.701 15.493 136.599Q15.327 136.498 15.223 136.320Q15.120 136.142 15.120 135.889M19.823 135.639L19.823 133.857L19.073 133.857Q18.873 133.834 18.823 133.615L18.823 133.529Q18.873 133.318 19.073 133.295L19.823 133.295L19.823 132.545Q19.873 132.338 20.073 132.310L20.217 132.310Q20.413 132.338 20.463 132.545L20.463 133.295L21.823 133.295Q22.014 133.314 22.073 133.529L22.073 133.615Q22.018 133.834 21.823 133.857L20.463 133.857L20.463 135.607Q20.463 136.224 21.038 136.224Q21.288 136.224 21.452 136.039Q21.616 135.853 21.616 135.607Q21.616 135.514 21.688 135.443Q21.760 135.373 21.862 135.361L22.006 135.361Q22.206 135.385 22.256 135.592L22.256 135.639Q22.256 135.963 22.073 136.226Q21.889 136.490 21.596 136.637Q21.303 136.783 20.983 136.783Q20.471 136.783 20.147 136.473Q19.823 136.162 19.823 135.639\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-46.75 -200.126)\">\u003Cpath d=\"M30.256 137.385Q29.725 137.076 29.325 136.588Q28.924 136.099 28.713 135.506Q28.502 134.912 28.502 134.295Q28.502 133.678 28.711 133.090Q28.920 132.502 29.317 132.021Q29.713 131.541 30.248 131.217Q30.319 131.193 30.350 131.193L30.440 131.193Q30.538 131.205 30.604 131.271Q30.670 131.338 30.670 131.439Q30.670 131.584 30.569 131.646Q30.120 131.935 29.793 132.351Q29.467 132.767 29.305 133.260Q29.143 133.752 29.143 134.295Q29.143 134.701 29.239 135.088Q29.334 135.474 29.512 135.810Q29.690 136.146 29.950 136.430Q30.209 136.713 30.557 136.943Q30.670 137.021 30.670 137.158Q30.670 137.256 30.604 137.326Q30.538 137.396 30.440 137.408L30.350 137.408Q30.291 137.408 30.256 137.385M32.588 135.639L32.588 133.857L31.838 133.857Q31.639 133.834 31.588 133.615L31.588 133.529Q31.639 133.318 31.838 133.295L32.588 133.295L32.588 132.545Q32.639 132.338 32.838 132.310L32.983 132.310Q33.178 132.338 33.229 132.545L33.229 133.295L34.588 133.295Q34.780 133.314 34.838 133.529L34.838 133.615Q34.784 133.834 34.588 133.857L33.229 133.857L33.229 135.607Q33.229 136.224 33.803 136.224Q34.053 136.224 34.217 136.039Q34.381 135.853 34.381 135.607Q34.381 135.514 34.454 135.443Q34.526 135.373 34.627 135.361L34.772 135.361Q34.971 135.385 35.022 135.592L35.022 135.639Q35.022 135.963 34.838 136.226Q34.655 136.490 34.362 136.637Q34.069 136.783 33.748 136.783Q33.237 136.783 32.913 136.473Q32.588 136.162 32.588 135.639M37.756 136.783Q37.284 136.783 36.899 136.539Q36.514 136.295 36.291 135.885Q36.069 135.474 36.069 135.017Q36.069 134.674 36.194 134.351Q36.319 134.029 36.549 133.775Q36.780 133.521 37.086 133.377Q37.393 133.232 37.756 133.232Q38.120 133.232 38.432 133.379Q38.745 133.525 38.967 133.771Q39.190 134.017 39.317 134.338Q39.444 134.658 39.444 135.017Q39.444 135.474 39.219 135.887Q38.995 136.299 38.610 136.541Q38.225 136.783 37.756 136.783M37.756 136.224Q38.221 136.224 38.512 135.830Q38.803 135.435 38.803 134.951Q38.803 134.658 38.668 134.390Q38.534 134.123 38.293 133.957Q38.053 133.791 37.756 133.791Q37.452 133.791 37.213 133.957Q36.975 134.123 36.840 134.390Q36.706 134.658 36.706 134.951Q36.706 135.431 36.998 135.828Q37.291 136.224 37.756 136.224\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-46.75 -200.126)\">\u003Cpath d=\"M44.213 136.506L44.213 136.416Q44.256 136.209 44.463 136.185L44.885 136.185L44.885 133.857L44.463 133.857Q44.256 133.834 44.213 133.615L44.213 133.529Q44.260 133.318 44.463 133.295L45.280 133.295Q45.475 133.318 45.526 133.529L45.526 133.615L45.518 133.639Q45.745 133.459 46.018 133.357Q46.291 133.256 46.584 133.256Q46.932 133.256 47.170 133.396Q47.409 133.537 47.524 133.795Q47.639 134.053 47.639 134.408L47.639 136.185L48.065 136.185Q48.272 136.209 48.311 136.416L48.311 136.506Q48.272 136.721 48.065 136.744L46.670 136.744Q46.475 136.721 46.424 136.506L46.424 136.416Q46.475 136.205 46.670 136.185L46.998 136.185L46.998 134.439Q46.998 134.131 46.909 133.973Q46.819 133.814 46.526 133.814Q46.256 133.814 46.028 133.945Q45.799 134.076 45.663 134.305Q45.526 134.533 45.526 134.799L45.526 136.185L45.952 136.185Q46.159 136.209 46.198 136.416L46.198 136.506Q46.159 136.721 45.952 136.744L44.463 136.744Q44.256 136.721 44.213 136.506M51.901 135.256L49.459 135.256Q49.514 135.533 49.711 135.756Q49.909 135.978 50.186 136.101Q50.463 136.224 50.748 136.224Q51.221 136.224 51.444 135.935Q51.452 135.924 51.508 135.818Q51.565 135.713 51.614 135.670Q51.663 135.627 51.756 135.615L51.901 135.615Q52.092 135.635 52.151 135.849L52.151 135.904Q52.084 136.205 51.854 136.402Q51.623 136.599 51.311 136.691Q50.998 136.783 50.694 136.783Q50.209 136.783 49.770 136.555Q49.331 136.326 49.063 135.926Q48.795 135.525 48.795 135.033L48.795 134.974Q48.795 134.506 49.041 134.103Q49.288 133.701 49.696 133.467Q50.104 133.232 50.573 133.232Q51.077 133.232 51.430 133.455Q51.784 133.678 51.967 134.066Q52.151 134.455 52.151 134.959L52.151 135.017Q52.092 135.232 51.901 135.256M49.467 134.705L51.495 134.705Q51.448 134.295 51.209 134.043Q50.971 133.791 50.573 133.791Q50.178 133.791 49.872 134.053Q49.565 134.314 49.467 134.705M52.893 136.506L52.893 136.416Q52.932 136.209 53.139 136.185L53.545 136.185L54.475 134.967L53.604 133.857L53.186 133.857Q52.991 133.838 52.940 133.615L52.940 133.529Q52.991 133.318 53.186 133.295L54.346 133.295Q54.545 133.318 54.596 133.529L54.596 133.615Q54.545 133.834 54.346 133.857L54.237 133.857L54.733 134.514L55.209 133.857L55.092 133.857Q54.893 133.834 54.842 133.615L54.842 133.529Q54.893 133.318 55.092 133.295L56.252 133.295Q56.448 133.314 56.498 133.529L56.498 133.615Q56.448 133.834 56.252 133.857L55.842 133.857L54.995 134.967L55.956 136.185L56.362 136.185Q56.561 136.209 56.612 136.416L56.612 136.506Q56.573 136.721 56.362 136.744L55.209 136.744Q55.002 136.721 54.963 136.506L54.963 136.416Q55.002 136.209 55.209 136.185L55.338 136.185L54.733 135.330L54.147 136.185L54.291 136.185Q54.498 136.209 54.538 136.416L54.538 136.506Q54.498 136.721 54.291 136.744L53.139 136.744Q52.944 136.724 52.893 136.506M58.081 135.639L58.081 133.857L57.331 133.857Q57.131 133.834 57.081 133.615L57.081 133.529Q57.131 133.318 57.331 133.295L58.081 133.295L58.081 132.545Q58.131 132.338 58.331 132.310L58.475 132.310Q58.670 132.338 58.721 132.545L58.721 133.295L60.081 133.295Q60.272 133.314 60.331 133.529L60.331 133.615Q60.276 133.834 60.081 133.857L58.721 133.857L58.721 135.607Q58.721 136.224 59.295 136.224Q59.545 136.224 59.709 136.039Q59.873 135.853 59.873 135.607Q59.873 135.514 59.946 135.443Q60.018 135.373 60.120 135.361L60.264 135.361Q60.463 135.385 60.514 135.592L60.514 135.639Q60.514 135.963 60.331 136.226Q60.147 136.490 59.854 136.637Q59.561 136.783 59.241 136.783Q58.729 136.783 58.405 136.473Q58.081 136.162 58.081 135.639\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-46.75 -200.126)\">\u003Cpath d=\"M65.843 136.506L65.843 136.416Q65.894 136.209 66.089 136.185L67.195 136.185L67.195 132.416L66.089 132.416Q65.894 132.392 65.843 132.178L65.843 132.088Q65.894 131.881 66.089 131.857L67.585 131.857Q67.777 131.881 67.835 132.088L67.835 136.185L68.937 136.185Q69.136 136.209 69.187 136.416L69.187 136.506Q69.136 136.721 68.937 136.744L66.089 136.744Q65.894 136.721 65.843 136.506M70.046 135.631Q70.046 135.185 70.460 134.928Q70.874 134.670 71.415 134.570Q71.957 134.471 72.464 134.463Q72.464 134.248 72.330 134.096Q72.195 133.943 71.988 133.867Q71.781 133.791 71.570 133.791Q71.226 133.791 71.066 133.814L71.066 133.873Q71.066 134.041 70.947 134.156Q70.828 134.271 70.664 134.271Q70.488 134.271 70.373 134.148Q70.257 134.025 70.257 133.857Q70.257 133.451 70.638 133.342Q71.019 133.232 71.578 133.232Q71.847 133.232 72.115 133.310Q72.382 133.389 72.607 133.539Q72.832 133.689 72.968 133.910Q73.105 134.131 73.105 134.408L73.105 136.127Q73.105 136.185 73.632 136.185Q73.828 136.205 73.878 136.416L73.878 136.506Q73.828 136.721 73.632 136.744L73.488 136.744Q73.144 136.744 72.915 136.697Q72.687 136.650 72.542 136.463Q72.082 136.783 71.374 136.783Q71.039 136.783 70.734 136.642Q70.429 136.502 70.238 136.240Q70.046 135.978 70.046 135.631M70.687 135.639Q70.687 135.912 70.929 136.068Q71.171 136.224 71.457 136.224Q71.675 136.224 71.908 136.166Q72.140 136.107 72.302 135.969Q72.464 135.830 72.464 135.607L72.464 135.017Q72.183 135.017 71.767 135.074Q71.351 135.131 71.019 135.269Q70.687 135.408 70.687 135.639M74.230 137.865Q74.230 137.756 74.281 137.664Q74.332 137.572 74.423 137.521Q74.515 137.471 74.621 137.471Q74.730 137.471 74.822 137.521Q74.914 137.572 74.964 137.664Q75.015 137.756 75.015 137.865L74.871 137.865Q74.871 138.002 74.894 138.002Q75.152 138.002 75.339 137.810Q75.527 137.619 75.613 137.353L75.824 136.744L74.687 133.857L74.359 133.857Q74.164 133.834 74.109 133.615L74.109 133.529Q74.167 133.318 74.359 133.295L75.519 133.295Q75.714 133.318 75.765 133.529L75.765 133.615Q75.714 133.834 75.519 133.857L75.253 133.857Q75.589 134.705 75.833 135.359Q76.078 136.014 76.078 136.103L76.085 136.103Q76.085 136.045 76.177 135.752Q76.269 135.459 76.462 134.875Q76.656 134.291 76.796 133.857L76.519 133.857Q76.308 133.834 76.269 133.615L76.269 133.529Q76.320 133.314 76.519 133.295L77.671 133.295Q77.878 133.318 77.917 133.529L77.917 133.615Q77.878 133.834 77.671 133.857L77.351 133.857L76.175 137.353Q76.007 137.853 75.681 138.207Q75.355 138.560 74.894 138.560Q74.621 138.560 74.425 138.349Q74.230 138.139 74.230 137.865M81.644 135.256L79.203 135.256Q79.257 135.533 79.455 135.756Q79.652 135.978 79.929 136.101Q80.207 136.224 80.492 136.224Q80.964 136.224 81.187 135.935Q81.195 135.924 81.251 135.818Q81.308 135.713 81.357 135.670Q81.406 135.627 81.499 135.615L81.644 135.615Q81.835 135.635 81.894 135.849L81.894 135.904Q81.828 136.205 81.597 136.402Q81.367 136.599 81.054 136.691Q80.742 136.783 80.437 136.783Q79.953 136.783 79.513 136.555Q79.074 136.326 78.806 135.926Q78.539 135.525 78.539 135.033L78.539 134.974Q78.539 134.506 78.785 134.103Q79.031 133.701 79.439 133.467Q79.847 133.232 80.316 133.232Q80.820 133.232 81.173 133.455Q81.527 133.678 81.710 134.066Q81.894 134.455 81.894 134.959L81.894 135.017Q81.835 135.232 81.644 135.256M79.210 134.705L81.238 134.705Q81.191 134.295 80.953 134.043Q80.714 133.791 80.316 133.791Q79.921 133.791 79.615 134.053Q79.308 134.314 79.210 134.705M82.601 136.506L82.601 136.416Q82.660 136.209 82.851 136.185L83.562 136.185L83.562 133.857L82.851 133.857Q82.656 133.834 82.601 133.615L82.601 133.529Q82.660 133.318 82.851 133.295L83.953 133.295Q84.152 133.314 84.203 133.529L84.203 133.857Q84.464 133.572 84.820 133.414Q85.175 133.256 85.562 133.256Q85.855 133.256 86.089 133.390Q86.324 133.525 86.324 133.791Q86.324 133.959 86.214 134.076Q86.105 134.193 85.937 134.193Q85.785 134.193 85.669 134.082Q85.554 133.971 85.554 133.814Q85.179 133.814 84.865 134.015Q84.550 134.217 84.376 134.551Q84.203 134.885 84.203 135.264L84.203 136.185L85.148 136.185Q85.355 136.209 85.394 136.416L85.394 136.506Q85.355 136.721 85.148 136.744L82.851 136.744Q82.660 136.721 82.601 136.506M87.664 137.408L87.578 137.408Q87.472 137.396 87.404 137.324Q87.335 137.252 87.335 137.158Q87.335 137.017 87.441 136.951Q87.777 136.736 88.046 136.447Q88.316 136.158 88.499 135.810Q88.683 135.463 88.773 135.084Q88.863 134.705 88.863 134.295Q88.863 133.756 88.699 133.264Q88.535 132.771 88.216 132.357Q87.898 131.943 87.457 131.654Q87.335 131.572 87.335 131.439Q87.335 131.342 87.404 131.273Q87.472 131.205 87.578 131.193L87.664 131.193Q87.718 131.193 87.753 131.217Q88.140 131.439 88.480 131.787Q88.820 132.135 89.040 132.529Q89.261 132.924 89.382 133.369Q89.503 133.814 89.503 134.295Q89.503 134.779 89.382 135.230Q89.261 135.681 89.037 136.078Q88.812 136.474 88.488 136.808Q88.164 137.142 87.761 137.385Q87.691 137.408 87.664 137.408\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-2.607 129.545v-19.676\"\u002F>\u003Cpath stroke=\"none\" d=\"m-2.607 107.269-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-2.607 80.861V66.99\"\u002F>\u003Cpath stroke=\"none\" d=\"m-2.607 64.39-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-2.607 44.073V27.356\"\u002F>\u003Cpath stroke=\"none\" d=\"m-2.607 24.756-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-2.607-1.651v-13.872\"\u002F>\u003Cpath stroke=\"none\" d=\"m-2.607-18.123-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-2.607-38.44v-17.03\"\u002F>\u003Cpath stroke=\"none\" d=\"m-2.607-58.07-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M68.525 129.631c39.833-21.34 39.833-55.483 2.325-74.237\"\u002F>\u003Cpath stroke=\"none\" d=\"m68.525 54.232 2.79 3.72-.465-2.558 2.325-1.162\"\u002F>\u003Cg transform=\"translate(104.74 -42.569)\">\u003Cpath d=\"M-0.361 136.744L-2.341 136.744L-2.341 136.447Q-2.072 136.447-1.904 136.402Q-1.736 136.357-1.736 136.185L-1.736 134.049Q-1.736 133.834-1.798 133.738Q-1.861 133.642-1.978 133.621Q-2.095 133.599-2.341 133.599L-2.341 133.303L-1.173 133.217L-1.173 134.002Q-1.095 133.791-0.943 133.605Q-0.791 133.420-0.591 133.318Q-0.392 133.217-0.166 133.217Q0.080 133.217 0.272 133.361Q0.463 133.506 0.463 133.736Q0.463 133.892 0.358 134.002Q0.252 134.111 0.096 134.111Q-0.060 134.111-0.170 134.002Q-0.279 133.892-0.279 133.736Q-0.279 133.576-0.173 133.471Q-0.498 133.471-0.712 133.699Q-0.927 133.928-1.023 134.267Q-1.119 134.607-1.119 134.912L-1.119 136.185Q-1.119 136.353-0.892 136.400Q-0.666 136.447-0.361 136.447L-0.361 136.744M0.944 134.990Q0.944 134.510 1.176 134.094Q1.409 133.678 1.819 133.428Q2.229 133.178 2.705 133.178Q3.436 133.178 3.834 133.619Q4.233 134.060 4.233 134.791Q4.233 134.896 4.139 134.920L1.690 134.920L1.690 134.990Q1.690 135.400 1.811 135.756Q1.932 136.111 2.204 136.328Q2.475 136.545 2.905 136.545Q3.268 136.545 3.565 136.316Q3.862 136.088 3.963 135.736Q3.971 135.689 4.057 135.674L4.139 135.674Q4.233 135.701 4.233 135.783Q4.233 135.791 4.225 135.822Q4.163 136.049 4.024 136.232Q3.885 136.416 3.694 136.549Q3.502 136.681 3.284 136.752Q3.065 136.822 2.827 136.822Q2.455 136.822 2.118 136.685Q1.780 136.549 1.512 136.297Q1.245 136.045 1.094 135.705Q0.944 135.365 0.944 134.990M1.698 134.681L3.659 134.681Q3.659 134.377 3.557 134.086Q3.455 133.795 3.239 133.613Q3.022 133.431 2.705 133.431Q2.405 133.431 2.174 133.619Q1.944 133.806 1.821 134.098Q1.698 134.389 1.698 134.681M4.764 136.736L4.764 135.514Q4.764 135.486 4.795 135.455Q4.827 135.424 4.850 135.424L4.955 135.424Q5.026 135.424 5.041 135.486Q5.104 135.806 5.243 136.047Q5.381 136.287 5.614 136.428Q5.846 136.568 6.155 136.568Q6.393 136.568 6.602 136.508Q6.811 136.447 6.948 136.299Q7.084 136.150 7.084 135.904Q7.084 135.650 6.873 135.484Q6.663 135.318 6.393 135.264L5.772 135.150Q5.366 135.072 5.065 134.816Q4.764 134.560 4.764 134.185Q4.764 133.818 4.965 133.596Q5.166 133.373 5.491 133.275Q5.815 133.178 6.155 133.178Q6.620 133.178 6.916 133.385L7.139 133.201Q7.163 133.178 7.194 133.178L7.245 133.178Q7.276 133.178 7.303 133.205Q7.330 133.232 7.330 133.264L7.330 134.248Q7.330 134.279 7.305 134.308Q7.280 134.338 7.245 134.338L7.139 134.338Q7.104 134.338 7.077 134.310Q7.049 134.283 7.049 134.248Q7.049 133.849 6.797 133.629Q6.545 133.408 6.147 133.408Q5.791 133.408 5.508 133.531Q5.225 133.654 5.225 133.959Q5.225 134.178 5.426 134.310Q5.627 134.443 5.873 134.486L6.498 134.599Q6.928 134.689 7.237 134.986Q7.545 135.283 7.545 135.697Q7.545 136.267 7.147 136.545Q6.748 136.822 6.155 136.822Q5.604 136.822 5.252 136.486L4.955 136.799Q4.932 136.822 4.897 136.822L4.850 136.822Q4.827 136.822 4.795 136.791Q4.764 136.760 4.764 136.736M9.932 136.744L8.155 136.744L8.155 136.447Q8.428 136.447 8.596 136.400Q8.764 136.353 8.764 136.185L8.764 134.049Q8.764 133.834 8.707 133.738Q8.651 133.642 8.538 133.621Q8.424 133.599 8.178 133.599L8.178 133.303L9.377 133.217L9.377 136.185Q9.377 136.353 9.524 136.400Q9.670 136.447 9.932 136.447L9.932 136.744M8.491 131.822Q8.491 131.631 8.625 131.500Q8.760 131.369 8.956 131.369Q9.077 131.369 9.180 131.431Q9.284 131.494 9.346 131.598Q9.409 131.701 9.409 131.822Q9.409 132.017 9.278 132.152Q9.147 132.287 8.956 132.287Q8.756 132.287 8.623 132.154Q8.491 132.021 8.491 131.822M12.248 136.822Q11.768 136.822 11.360 136.578Q10.952 136.334 10.713 135.920Q10.475 135.506 10.475 135.017Q10.475 134.525 10.733 134.109Q10.991 133.693 11.422 133.455Q11.854 133.217 12.346 133.217Q12.967 133.217 13.416 133.654L13.416 132.025Q13.416 131.810 13.354 131.715Q13.291 131.619 13.174 131.598Q13.057 131.576 12.811 131.576L12.811 131.279L14.034 131.193L14.034 136.002Q14.034 136.213 14.096 136.308Q14.159 136.404 14.276 136.426Q14.393 136.447 14.643 136.447L14.643 136.744L13.393 136.822L13.393 136.338Q12.928 136.822 12.248 136.822M12.315 136.568Q12.655 136.568 12.948 136.377Q13.241 136.185 13.393 135.889L13.393 134.056Q13.245 133.783 12.983 133.627Q12.721 133.471 12.409 133.471Q11.784 133.471 11.500 133.918Q11.217 134.365 11.217 135.025Q11.217 135.670 11.469 136.119Q11.721 136.568 12.315 136.568M15.834 135.791L15.834 134.049Q15.834 133.834 15.772 133.738Q15.709 133.642 15.590 133.621Q15.471 133.599 15.225 133.599L15.225 133.303L16.471 133.217L16.471 135.767L16.471 135.791Q16.471 136.103 16.526 136.265Q16.581 136.428 16.731 136.498Q16.881 136.568 17.202 136.568Q17.631 136.568 17.905 136.230Q18.178 135.892 18.178 135.447L18.178 134.049Q18.178 133.834 18.116 133.738Q18.053 133.642 17.934 133.621Q17.815 133.599 17.569 133.599L17.569 133.303L18.815 133.217L18.815 136.002Q18.815 136.213 18.877 136.308Q18.940 136.404 19.059 136.426Q19.178 136.447 19.424 136.447L19.424 136.744L18.202 136.822L18.202 136.201Q18.034 136.490 17.752 136.656Q17.471 136.822 17.151 136.822Q15.834 136.822 15.834 135.791M19.967 135.912Q19.967 135.428 20.370 135.133Q20.772 134.838 21.323 134.719Q21.873 134.599 22.366 134.599L22.366 134.310Q22.366 134.084 22.250 133.877Q22.135 133.670 21.938 133.551Q21.741 133.431 21.510 133.431Q21.084 133.431 20.799 133.537Q20.870 133.564 20.916 133.619Q20.963 133.674 20.989 133.744Q21.014 133.814 21.014 133.889Q21.014 133.994 20.963 134.086Q20.913 134.178 20.821 134.228Q20.729 134.279 20.623 134.279Q20.518 134.279 20.426 134.228Q20.334 134.178 20.284 134.086Q20.233 133.994 20.233 133.889Q20.233 133.471 20.622 133.324Q21.010 133.178 21.510 133.178Q21.842 133.178 22.196 133.308Q22.549 133.439 22.778 133.693Q23.006 133.947 23.006 134.295L23.006 136.096Q23.006 136.228 23.079 136.338Q23.151 136.447 23.280 136.447Q23.405 136.447 23.473 136.342Q23.541 136.236 23.541 136.096L23.541 135.584L23.823 135.584L23.823 136.096Q23.823 136.299 23.706 136.457Q23.588 136.615 23.407 136.699Q23.225 136.783 23.022 136.783Q22.791 136.783 22.639 136.611Q22.487 136.439 22.456 136.209Q22.295 136.490 21.987 136.656Q21.678 136.822 21.327 136.822Q20.815 136.822 20.391 136.599Q19.967 136.377 19.967 135.912M20.655 135.912Q20.655 136.197 20.881 136.383Q21.108 136.568 21.401 136.568Q21.647 136.568 21.872 136.451Q22.096 136.334 22.231 136.131Q22.366 135.928 22.366 135.674L22.366 134.842Q22.100 134.842 21.815 134.896Q21.530 134.951 21.258 135.080Q20.987 135.209 20.821 135.416Q20.655 135.623 20.655 135.912M26.030 136.744L24.198 136.744L24.198 136.447Q24.471 136.447 24.639 136.400Q24.807 136.353 24.807 136.185L24.807 132.025Q24.807 131.810 24.745 131.715Q24.682 131.619 24.563 131.598Q24.444 131.576 24.198 131.576L24.198 131.279L25.420 131.193L25.420 136.185Q25.420 136.353 25.588 136.400Q25.756 136.447 26.030 136.447\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M68.525 47.118c39.833-21.34 39.833-55.483 2.325-74.237\"\u002F>\u003Cpath stroke=\"none\" d=\"m68.525-28.282 2.79 3.72-.465-2.557 2.325-1.163\"\u002F>\u003Cg transform=\"translate(104.74 -125.082)\">\u003Cpath d=\"M-0.361 136.744L-2.341 136.744L-2.341 136.447Q-2.072 136.447-1.904 136.402Q-1.736 136.357-1.736 136.185L-1.736 134.049Q-1.736 133.834-1.798 133.738Q-1.861 133.642-1.978 133.621Q-2.095 133.599-2.341 133.599L-2.341 133.303L-1.173 133.217L-1.173 134.002Q-1.095 133.791-0.943 133.605Q-0.791 133.420-0.591 133.318Q-0.392 133.217-0.166 133.217Q0.080 133.217 0.272 133.361Q0.463 133.506 0.463 133.736Q0.463 133.892 0.358 134.002Q0.252 134.111 0.096 134.111Q-0.060 134.111-0.170 134.002Q-0.279 133.892-0.279 133.736Q-0.279 133.576-0.173 133.471Q-0.498 133.471-0.712 133.699Q-0.927 133.928-1.023 134.267Q-1.119 134.607-1.119 134.912L-1.119 136.185Q-1.119 136.353-0.892 136.400Q-0.666 136.447-0.361 136.447L-0.361 136.744M0.944 134.990Q0.944 134.510 1.176 134.094Q1.409 133.678 1.819 133.428Q2.229 133.178 2.705 133.178Q3.436 133.178 3.834 133.619Q4.233 134.060 4.233 134.791Q4.233 134.896 4.139 134.920L1.690 134.920L1.690 134.990Q1.690 135.400 1.811 135.756Q1.932 136.111 2.204 136.328Q2.475 136.545 2.905 136.545Q3.268 136.545 3.565 136.316Q3.862 136.088 3.963 135.736Q3.971 135.689 4.057 135.674L4.139 135.674Q4.233 135.701 4.233 135.783Q4.233 135.791 4.225 135.822Q4.163 136.049 4.024 136.232Q3.885 136.416 3.694 136.549Q3.502 136.681 3.284 136.752Q3.065 136.822 2.827 136.822Q2.455 136.822 2.118 136.685Q1.780 136.549 1.512 136.297Q1.245 136.045 1.094 135.705Q0.944 135.365 0.944 134.990M1.698 134.681L3.659 134.681Q3.659 134.377 3.557 134.086Q3.455 133.795 3.239 133.613Q3.022 133.431 2.705 133.431Q2.405 133.431 2.174 133.619Q1.944 133.806 1.821 134.098Q1.698 134.389 1.698 134.681M4.764 136.736L4.764 135.514Q4.764 135.486 4.795 135.455Q4.827 135.424 4.850 135.424L4.955 135.424Q5.026 135.424 5.041 135.486Q5.104 135.806 5.243 136.047Q5.381 136.287 5.614 136.428Q5.846 136.568 6.155 136.568Q6.393 136.568 6.602 136.508Q6.811 136.447 6.948 136.299Q7.084 136.150 7.084 135.904Q7.084 135.650 6.873 135.484Q6.663 135.318 6.393 135.264L5.772 135.150Q5.366 135.072 5.065 134.816Q4.764 134.560 4.764 134.185Q4.764 133.818 4.965 133.596Q5.166 133.373 5.491 133.275Q5.815 133.178 6.155 133.178Q6.620 133.178 6.916 133.385L7.139 133.201Q7.163 133.178 7.194 133.178L7.245 133.178Q7.276 133.178 7.303 133.205Q7.330 133.232 7.330 133.264L7.330 134.248Q7.330 134.279 7.305 134.308Q7.280 134.338 7.245 134.338L7.139 134.338Q7.104 134.338 7.077 134.310Q7.049 134.283 7.049 134.248Q7.049 133.849 6.797 133.629Q6.545 133.408 6.147 133.408Q5.791 133.408 5.508 133.531Q5.225 133.654 5.225 133.959Q5.225 134.178 5.426 134.310Q5.627 134.443 5.873 134.486L6.498 134.599Q6.928 134.689 7.237 134.986Q7.545 135.283 7.545 135.697Q7.545 136.267 7.147 136.545Q6.748 136.822 6.155 136.822Q5.604 136.822 5.252 136.486L4.955 136.799Q4.932 136.822 4.897 136.822L4.850 136.822Q4.827 136.822 4.795 136.791Q4.764 136.760 4.764 136.736M9.932 136.744L8.155 136.744L8.155 136.447Q8.428 136.447 8.596 136.400Q8.764 136.353 8.764 136.185L8.764 134.049Q8.764 133.834 8.707 133.738Q8.651 133.642 8.538 133.621Q8.424 133.599 8.178 133.599L8.178 133.303L9.377 133.217L9.377 136.185Q9.377 136.353 9.524 136.400Q9.670 136.447 9.932 136.447L9.932 136.744M8.491 131.822Q8.491 131.631 8.625 131.500Q8.760 131.369 8.956 131.369Q9.077 131.369 9.180 131.431Q9.284 131.494 9.346 131.598Q9.409 131.701 9.409 131.822Q9.409 132.017 9.278 132.152Q9.147 132.287 8.956 132.287Q8.756 132.287 8.623 132.154Q8.491 132.021 8.491 131.822M12.248 136.822Q11.768 136.822 11.360 136.578Q10.952 136.334 10.713 135.920Q10.475 135.506 10.475 135.017Q10.475 134.525 10.733 134.109Q10.991 133.693 11.422 133.455Q11.854 133.217 12.346 133.217Q12.967 133.217 13.416 133.654L13.416 132.025Q13.416 131.810 13.354 131.715Q13.291 131.619 13.174 131.598Q13.057 131.576 12.811 131.576L12.811 131.279L14.034 131.193L14.034 136.002Q14.034 136.213 14.096 136.308Q14.159 136.404 14.276 136.426Q14.393 136.447 14.643 136.447L14.643 136.744L13.393 136.822L13.393 136.338Q12.928 136.822 12.248 136.822M12.315 136.568Q12.655 136.568 12.948 136.377Q13.241 136.185 13.393 135.889L13.393 134.056Q13.245 133.783 12.983 133.627Q12.721 133.471 12.409 133.471Q11.784 133.471 11.500 133.918Q11.217 134.365 11.217 135.025Q11.217 135.670 11.469 136.119Q11.721 136.568 12.315 136.568M15.834 135.791L15.834 134.049Q15.834 133.834 15.772 133.738Q15.709 133.642 15.590 133.621Q15.471 133.599 15.225 133.599L15.225 133.303L16.471 133.217L16.471 135.767L16.471 135.791Q16.471 136.103 16.526 136.265Q16.581 136.428 16.731 136.498Q16.881 136.568 17.202 136.568Q17.631 136.568 17.905 136.230Q18.178 135.892 18.178 135.447L18.178 134.049Q18.178 133.834 18.116 133.738Q18.053 133.642 17.934 133.621Q17.815 133.599 17.569 133.599L17.569 133.303L18.815 133.217L18.815 136.002Q18.815 136.213 18.877 136.308Q18.940 136.404 19.059 136.426Q19.178 136.447 19.424 136.447L19.424 136.744L18.202 136.822L18.202 136.201Q18.034 136.490 17.752 136.656Q17.471 136.822 17.151 136.822Q15.834 136.822 15.834 135.791M19.967 135.912Q19.967 135.428 20.370 135.133Q20.772 134.838 21.323 134.719Q21.873 134.599 22.366 134.599L22.366 134.310Q22.366 134.084 22.250 133.877Q22.135 133.670 21.938 133.551Q21.741 133.431 21.510 133.431Q21.084 133.431 20.799 133.537Q20.870 133.564 20.916 133.619Q20.963 133.674 20.989 133.744Q21.014 133.814 21.014 133.889Q21.014 133.994 20.963 134.086Q20.913 134.178 20.821 134.228Q20.729 134.279 20.623 134.279Q20.518 134.279 20.426 134.228Q20.334 134.178 20.284 134.086Q20.233 133.994 20.233 133.889Q20.233 133.471 20.622 133.324Q21.010 133.178 21.510 133.178Q21.842 133.178 22.196 133.308Q22.549 133.439 22.778 133.693Q23.006 133.947 23.006 134.295L23.006 136.096Q23.006 136.228 23.079 136.338Q23.151 136.447 23.280 136.447Q23.405 136.447 23.473 136.342Q23.541 136.236 23.541 136.096L23.541 135.584L23.823 135.584L23.823 136.096Q23.823 136.299 23.706 136.457Q23.588 136.615 23.407 136.699Q23.225 136.783 23.022 136.783Q22.791 136.783 22.639 136.611Q22.487 136.439 22.456 136.209Q22.295 136.490 21.987 136.656Q21.678 136.822 21.327 136.822Q20.815 136.822 20.391 136.599Q19.967 136.377 19.967 135.912M20.655 135.912Q20.655 136.197 20.881 136.383Q21.108 136.568 21.401 136.568Q21.647 136.568 21.872 136.451Q22.096 136.334 22.231 136.131Q22.366 135.928 22.366 135.674L22.366 134.842Q22.100 134.842 21.815 134.896Q21.530 134.951 21.258 135.080Q20.987 135.209 20.821 135.416Q20.655 135.623 20.655 135.912M26.030 136.744L24.198 136.744L24.198 136.447Q24.471 136.447 24.639 136.400Q24.807 136.353 24.807 136.185L24.807 132.025Q24.807 131.810 24.745 131.715Q24.682 131.619 24.563 131.598Q24.444 131.576 24.198 131.576L24.198 131.279L25.420 131.193L25.420 136.185Q25.420 136.353 25.588 136.400Q25.756 136.447 26.030 136.447\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">One encoder layer: multi-head self-attention then a position-wise FFN, each wrapped in add-and-norm. The blue arcs are the residual connections around each sublayer.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:518.995px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 389.246 302.667\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cpath fill=\"none\" d=\"M-58.737 158.756V42.1H46.54v116.656ZM46.54 42.1\" style=\"stroke-dasharray:3.0,3.0\"\u002F>\u003Cpath fill=\"none\" d=\"M-48.778 224.197H36.58v-17.071h-85.358Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(-24.172 2.139)\">\u003Cpath d=\"M-5.586 215.488L-5.586 214.688Q-5.562 214.507-5.378 214.486L-5.231 214.486Q-5.087 214.507-5.036 214.647Q-4.858 215.207-4.223 215.207Q-4.041 215.207-3.841 215.177Q-3.641 215.146-3.495 215.045Q-3.348 214.944-3.348 214.766Q-3.348 214.582-3.542 214.483Q-3.737 214.384-3.976 214.346L-4.588 214.247Q-5.586 214.062-5.586 213.430Q-5.586 213.177-5.460 213.011Q-5.333 212.846-5.123 212.752Q-4.913 212.658-4.689 212.623Q-4.465 212.589-4.223 212.589Q-4.004 212.589-3.835 212.615Q-3.665 212.641-3.522 212.709Q-3.453 212.606-3.341 212.589L-3.272 212.589Q-3.187 212.600-3.132 212.654Q-3.078 212.709-3.067 212.791L-3.067 213.410Q-3.078 213.492-3.132 213.550Q-3.187 213.608-3.272 213.618L-3.419 213.618Q-3.501 213.608-3.559 213.550Q-3.618 213.492-3.628 213.410Q-3.628 213.078-4.236 213.078Q-4.540 213.078-4.819 213.150Q-5.098 213.222-5.098 213.437Q-5.098 213.669-4.510 213.765L-3.894 213.871Q-3.471 213.943-3.165 214.160Q-2.859 214.377-2.859 214.766Q-2.859 215.108-3.066 215.320Q-3.272 215.532-3.578 215.614Q-3.884 215.696-4.223 215.696Q-4.728 215.696-5.077 215.474Q-5.139 215.583-5.181 215.633Q-5.224 215.683-5.316 215.696L-5.378 215.696Q-5.566 215.676-5.586 215.488M-0.528 215.696Q-0.941 215.696-1.278 215.483Q-1.615 215.269-1.809 214.910Q-2.004 214.551-2.004 214.151Q-2.004 213.850-1.895 213.568Q-1.786 213.287-1.584 213.064Q-1.382 212.842-1.114 212.716Q-0.846 212.589-0.528 212.589Q-0.210 212.589 0.064 212.717Q0.337 212.846 0.532 213.061Q0.727 213.276 0.838 213.557Q0.949 213.837 0.949 214.151Q0.949 214.551 0.752 214.912Q0.556 215.272 0.219 215.484Q-0.118 215.696-0.528 215.696M-0.528 215.207Q-0.121 215.207 0.134 214.862Q0.388 214.517 0.388 214.093Q0.388 213.837 0.270 213.603Q0.152 213.369-0.058 213.223Q-0.268 213.078-0.528 213.078Q-0.794 213.078-1.003 213.223Q-1.211 213.369-1.329 213.603Q-1.447 213.837-1.447 214.093Q-1.447 214.514-1.191 214.860Q-0.934 215.207-0.528 215.207M1.981 214.913L1.981 213.136L1.612 213.136Q1.431 213.116 1.393 212.924L1.393 212.849Q1.434 212.664 1.612 212.644L2.326 212.644Q2.497 212.664 2.542 212.849L2.542 214.886Q2.542 215.091 2.690 215.149Q2.839 215.207 3.088 215.207Q3.270 215.207 3.441 215.141Q3.611 215.074 3.721 214.943Q3.830 214.811 3.830 214.626L3.830 213.136L3.461 213.136Q3.276 213.116 3.242 212.924L3.242 212.849Q3.276 212.664 3.461 212.644L4.172 212.644Q4.346 212.664 4.391 212.849L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L4.049 215.662Q3.875 215.641 3.830 215.467Q3.478 215.696 3.034 215.696Q2.829 215.696 2.641 215.660Q2.453 215.624 2.307 215.536Q2.162 215.447 2.072 215.291Q1.981 215.136 1.981 214.913M5.242 215.454L5.242 215.375Q5.293 215.194 5.461 215.173L6.083 215.173L6.083 213.136L5.461 213.136Q5.290 213.116 5.242 212.924L5.242 212.849Q5.293 212.664 5.461 212.644L6.424 212.644Q6.599 212.661 6.643 212.849L6.643 213.136Q6.872 212.887 7.183 212.748Q7.494 212.610 7.833 212.610Q8.089 212.610 8.294 212.728Q8.499 212.846 8.499 213.078Q8.499 213.225 8.403 213.328Q8.308 213.430 8.161 213.430Q8.027 213.430 7.927 213.333Q7.826 213.235 7.826 213.099Q7.498 213.099 7.223 213.275Q6.947 213.451 6.795 213.743Q6.643 214.035 6.643 214.367L6.643 215.173L7.470 215.173Q7.651 215.194 7.686 215.375L7.686 215.454Q7.651 215.641 7.470 215.662L5.461 215.662Q5.293 215.641 5.242 215.454M9.251 214.151Q9.251 213.731 9.465 213.369Q9.678 213.006 10.042 212.798Q10.406 212.589 10.827 212.589Q11.312 212.589 11.644 212.685Q11.975 212.781 11.975 213.136Q11.975 213.283 11.876 213.391Q11.777 213.498 11.627 213.498Q11.476 213.498 11.372 213.398Q11.268 213.297 11.268 213.150L11.268 213.099Q11.128 213.078 10.834 213.078Q10.547 213.078 10.312 213.227Q10.078 213.375 9.945 213.623Q9.812 213.871 9.812 214.151Q9.812 214.432 9.962 214.678Q10.112 214.924 10.362 215.066Q10.611 215.207 10.899 215.207Q11.172 215.207 11.283 215.117Q11.394 215.026 11.497 214.860Q11.599 214.695 11.702 214.681L11.849 214.681Q11.941 214.691 11.997 214.751Q12.054 214.811 12.054 214.900Q12.054 214.941 12.037 214.975Q11.941 215.231 11.763 215.389Q11.586 215.546 11.345 215.621Q11.104 215.696 10.827 215.696Q10.403 215.696 10.039 215.488Q9.675 215.279 9.463 214.927Q9.251 214.575 9.251 214.151M15.550 214.360L13.414 214.360Q13.462 214.602 13.635 214.797Q13.807 214.992 14.050 215.100Q14.293 215.207 14.542 215.207Q14.956 215.207 15.151 214.954Q15.157 214.944 15.207 214.852Q15.256 214.760 15.299 214.722Q15.342 214.684 15.424 214.674L15.550 214.674Q15.718 214.691 15.769 214.879L15.769 214.927Q15.711 215.190 15.509 215.363Q15.308 215.536 15.034 215.616Q14.761 215.696 14.494 215.696Q14.070 215.696 13.686 215.496Q13.301 215.296 13.067 214.946Q12.833 214.596 12.833 214.165L12.833 214.114Q12.833 213.704 13.048 213.351Q13.264 212.999 13.621 212.794Q13.978 212.589 14.388 212.589Q14.829 212.589 15.139 212.784Q15.448 212.979 15.609 213.319Q15.769 213.659 15.769 214.100L15.769 214.151Q15.718 214.339 15.550 214.360M13.421 213.878L15.195 213.878Q15.154 213.519 14.945 213.298Q14.737 213.078 14.388 213.078Q14.043 213.078 13.775 213.307Q13.506 213.536 13.421 213.878\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-24.172 2.139)\">\u003Cpath d=\"M20.982 214.695L20.982 213.136L20.326 213.136Q20.152 213.116 20.107 212.924L20.107 212.849Q20.152 212.664 20.326 212.644L20.982 212.644L20.982 211.988Q21.027 211.807 21.201 211.783L21.328 211.783Q21.498 211.807 21.543 211.988L21.543 212.644L22.732 212.644Q22.900 212.661 22.951 212.849L22.951 212.924Q22.903 213.116 22.732 213.136L21.543 213.136L21.543 214.667Q21.543 215.207 22.045 215.207Q22.264 215.207 22.408 215.045Q22.551 214.883 22.551 214.667Q22.551 214.585 22.614 214.524Q22.678 214.462 22.766 214.452L22.893 214.452Q23.067 214.473 23.112 214.654L23.112 214.695Q23.112 214.978 22.951 215.209Q22.790 215.440 22.534 215.568Q22.278 215.696 21.997 215.696Q21.550 215.696 21.266 215.424Q20.982 215.153 20.982 214.695M25.504 215.696Q25.091 215.696 24.754 215.483Q24.417 215.269 24.223 214.910Q24.028 214.551 24.028 214.151Q24.028 213.850 24.137 213.568Q24.246 213.287 24.448 213.064Q24.650 212.842 24.918 212.716Q25.186 212.589 25.504 212.589Q25.822 212.589 26.096 212.717Q26.369 212.846 26.564 213.061Q26.759 213.276 26.870 213.557Q26.981 213.837 26.981 214.151Q26.981 214.551 26.784 214.912Q26.588 215.272 26.251 215.484Q25.914 215.696 25.504 215.696M25.504 215.207Q25.911 215.207 26.166 214.862Q26.420 214.517 26.420 214.093Q26.420 213.837 26.302 213.603Q26.184 213.369 25.974 213.223Q25.764 213.078 25.504 213.078Q25.238 213.078 25.029 213.223Q24.821 213.369 24.703 213.603Q24.585 213.837 24.585 214.093Q24.585 214.514 24.841 214.860Q25.098 215.207 25.504 215.207M27.490 215.454L27.490 215.375Q27.535 215.194 27.705 215.173L28.112 215.173L28.112 211.875L27.705 211.875Q27.535 211.854 27.490 211.666L27.490 211.588Q27.535 211.407 27.705 211.386L28.358 211.386Q28.529 211.403 28.574 211.588L28.574 214.059L29.575 213.136L29.315 213.136Q29.134 213.116 29.100 212.924L29.100 212.849Q29.134 212.664 29.315 212.644L30.583 212.644Q30.761 212.664 30.802 212.849L30.802 212.924Q30.765 213.116 30.583 213.136L30.262 213.136L29.435 213.891L30.443 215.173L30.737 215.173Q30.918 215.194 30.956 215.375L30.956 215.454Q30.918 215.641 30.737 215.662L29.715 215.662Q29.544 215.641 29.500 215.454L29.500 215.375Q29.544 215.194 29.715 215.173L29.855 215.173L29.100 214.206L28.574 214.688L28.574 215.173L28.980 215.173Q29.148 215.194 29.199 215.375L29.199 215.454Q29.148 215.641 28.980 215.662L27.705 215.662Q27.535 215.641 27.490 215.454M34.152 214.360L32.016 214.360Q32.063 214.602 32.236 214.797Q32.409 214.992 32.651 215.100Q32.894 215.207 33.143 215.207Q33.557 215.207 33.752 214.954Q33.759 214.944 33.808 214.852Q33.858 214.760 33.901 214.722Q33.943 214.684 34.025 214.674L34.152 214.674Q34.319 214.691 34.370 214.879L34.370 214.927Q34.312 215.190 34.111 215.363Q33.909 215.536 33.636 215.616Q33.362 215.696 33.096 215.696Q32.672 215.696 32.287 215.496Q31.903 215.296 31.669 214.946Q31.434 214.596 31.434 214.165L31.434 214.114Q31.434 213.704 31.650 213.351Q31.865 212.999 32.222 212.794Q32.579 212.589 32.990 212.589Q33.431 212.589 33.740 212.784Q34.049 212.979 34.210 213.319Q34.370 213.659 34.370 214.100L34.370 214.151Q34.319 214.339 34.152 214.360M32.022 213.878L33.796 213.878Q33.755 213.519 33.547 213.298Q33.338 213.078 32.990 213.078Q32.644 213.078 32.376 213.307Q32.108 213.536 32.022 213.878M34.856 215.454L34.856 215.375Q34.893 215.194 35.075 215.173L35.444 215.173L35.444 213.136L35.075 213.136Q34.893 213.116 34.856 212.924L34.856 212.849Q34.897 212.664 35.075 212.644L35.789 212.644Q35.960 212.664 36.004 212.849L36.004 212.924L35.997 212.945Q36.196 212.787 36.435 212.699Q36.674 212.610 36.931 212.610Q37.235 212.610 37.443 212.733Q37.652 212.856 37.753 213.081Q37.853 213.307 37.853 213.618L37.853 215.173L38.226 215.173Q38.407 215.194 38.441 215.375L38.441 215.454Q38.407 215.641 38.226 215.662L37.006 215.662Q36.835 215.641 36.790 215.454L36.790 215.375Q36.835 215.190 37.006 215.173L37.293 215.173L37.293 213.645Q37.293 213.375 37.214 213.237Q37.136 213.099 36.879 213.099Q36.643 213.099 36.443 213.213Q36.244 213.328 36.124 213.527Q36.004 213.727 36.004 213.960L36.004 215.173L36.377 215.173Q36.558 215.194 36.592 215.375L36.592 215.454Q36.558 215.641 36.377 215.662L35.075 215.662Q34.893 215.641 34.856 215.454M39.022 215.488L39.022 214.688Q39.046 214.507 39.231 214.486L39.378 214.486Q39.521 214.507 39.573 214.647Q39.750 215.207 40.386 215.207Q40.567 215.207 40.767 215.177Q40.967 215.146 41.114 215.045Q41.261 214.944 41.261 214.766Q41.261 214.582 41.066 214.483Q40.871 214.384 40.632 214.346L40.020 214.247Q39.022 214.062 39.022 213.430Q39.022 213.177 39.149 213.011Q39.275 212.846 39.485 212.752Q39.696 212.658 39.920 212.623Q40.143 212.589 40.386 212.589Q40.605 212.589 40.774 212.615Q40.943 212.641 41.087 212.709Q41.155 212.606 41.268 212.589L41.336 212.589Q41.422 212.600 41.476 212.654Q41.531 212.709 41.541 212.791L41.541 213.410Q41.531 213.492 41.476 213.550Q41.422 213.608 41.336 213.618L41.189 213.618Q41.107 213.608 41.049 213.550Q40.991 213.492 40.981 213.410Q40.981 213.078 40.372 213.078Q40.068 213.078 39.790 213.150Q39.511 213.222 39.511 213.437Q39.511 213.669 40.099 213.765L40.714 213.871Q41.138 213.943 41.444 214.160Q41.750 214.377 41.750 214.766Q41.750 215.108 41.543 215.320Q41.336 215.532 41.030 215.614Q40.725 215.696 40.386 215.696Q39.880 215.696 39.532 215.474Q39.470 215.583 39.427 215.633Q39.385 215.683 39.292 215.696L39.231 215.696Q39.043 215.676 39.022 215.488\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M-50.339 195.745h88.48v-17.072h-88.48Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(-40.907 -27.092)\">\u003Cpath d=\"M-3.026 214.360L-5.162 214.360Q-5.115 214.602-4.942 214.797Q-4.769 214.992-4.527 215.100Q-4.284 215.207-4.035 215.207Q-3.621 215.207-3.426 214.954Q-3.419 214.944-3.370 214.852Q-3.320 214.760-3.277 214.722Q-3.235 214.684-3.153 214.674L-3.026 214.674Q-2.859 214.691-2.807 214.879L-2.807 214.927Q-2.866 215.190-3.067 215.363Q-3.269 215.536-3.542 215.616Q-3.816 215.696-4.082 215.696Q-4.506 215.696-4.891 215.496Q-5.275 215.296-5.509 214.946Q-5.744 214.596-5.744 214.165L-5.744 214.114Q-5.744 213.704-5.528 213.351Q-5.313 212.999-4.956 212.794Q-4.599 212.589-4.188 212.589Q-3.747 212.589-3.438 212.784Q-3.129 212.979-2.968 213.319Q-2.807 213.659-2.807 214.100L-2.807 214.151Q-2.859 214.339-3.026 214.360M-5.156 213.878L-3.382 213.878Q-3.423 213.519-3.631 213.298Q-3.840 213.078-4.188 213.078Q-4.534 213.078-4.802 213.307Q-5.070 213.536-5.156 213.878M-2.432 215.454L-2.432 215.375Q-2.387 215.190-2.216 215.173L-2.042 215.173L-2.042 213.136L-2.216 213.136Q-2.397 213.116-2.432 212.924L-2.432 212.849Q-2.387 212.661-2.216 212.644L-1.796 212.644Q-1.628 212.664-1.577 212.849Q-1.297 212.610-0.934 212.610Q-0.767 212.610-0.620 212.705Q-0.473 212.801-0.408 212.952Q-0.254 212.784-0.059 212.697Q0.135 212.610 0.347 212.610Q0.713 212.610 0.848 212.909Q0.983 213.208 0.983 213.618L0.983 215.173L1.157 215.173Q1.342 215.194 1.376 215.375L1.376 215.454Q1.332 215.641 1.157 215.662L0.443 215.662Q0.272 215.641 0.228 215.454L0.228 215.375Q0.272 215.194 0.443 215.173L0.522 215.173L0.522 213.645Q0.522 213.099 0.303 213.099Q0.012 213.099-0.143 213.370Q-0.299 213.642-0.299 213.960L-0.299 215.173L-0.121 215.173Q0.060 215.194 0.094 215.375L0.094 215.454Q0.050 215.641-0.121 215.662L-0.835 215.662Q-1.010 215.641-1.054 215.454L-1.054 215.375Q-1.010 215.194-0.835 215.173L-0.760 215.173L-0.760 213.645Q-0.760 213.099-0.975 213.099Q-1.266 213.099-1.422 213.372Q-1.577 213.645-1.577 213.960L-1.577 215.173L-1.403 215.173Q-1.222 215.194-1.187 215.375L-1.187 215.454Q-1.232 215.645-1.403 215.662L-2.216 215.662Q-2.397 215.641-2.432 215.454M1.981 215.454L1.981 211.875L1.612 211.875Q1.431 211.854 1.393 211.666L1.393 211.588Q1.431 211.407 1.612 211.386L2.326 211.386Q2.497 211.407 2.542 211.588L2.542 212.911Q2.726 212.764 2.957 212.687Q3.188 212.610 3.423 212.610Q3.721 212.610 3.981 212.736Q4.240 212.863 4.428 213.083Q4.616 213.304 4.717 213.577Q4.818 213.850 4.818 214.151Q4.818 214.558 4.620 214.917Q4.422 215.276 4.083 215.486Q3.745 215.696 3.335 215.696Q2.880 215.696 2.542 215.375L2.542 215.454Q2.497 215.645 2.326 215.662L2.200 215.662Q2.032 215.641 1.981 215.454M3.297 215.207Q3.567 215.207 3.786 215.059Q4.005 214.910 4.131 214.664Q4.257 214.418 4.257 214.151Q4.257 213.898 4.148 213.654Q4.039 213.410 3.835 213.254Q3.632 213.099 3.369 213.099Q3.088 213.099 2.859 213.261Q2.630 213.423 2.542 213.686L2.542 214.432Q2.620 214.753 2.813 214.980Q3.006 215.207 3.297 215.207M8.120 214.360L5.984 214.360Q6.031 214.602 6.204 214.797Q6.377 214.992 6.619 215.100Q6.862 215.207 7.111 215.207Q7.525 215.207 7.720 214.954Q7.727 214.944 7.776 214.852Q7.826 214.760 7.869 214.722Q7.911 214.684 7.993 214.674L8.120 214.674Q8.287 214.691 8.338 214.879L8.338 214.927Q8.280 215.190 8.079 215.363Q7.877 215.536 7.604 215.616Q7.330 215.696 7.064 215.696Q6.640 215.696 6.255 215.496Q5.871 215.296 5.637 214.946Q5.402 214.596 5.402 214.165L5.402 214.114Q5.402 213.704 5.618 213.351Q5.833 212.999 6.190 212.794Q6.547 212.589 6.958 212.589Q7.399 212.589 7.708 212.784Q8.017 212.979 8.178 213.319Q8.338 213.659 8.338 214.100L8.338 214.151Q8.287 214.339 8.120 214.360M5.990 213.878L7.764 213.878Q7.723 213.519 7.515 213.298Q7.306 213.078 6.958 213.078Q6.612 213.078 6.344 213.307Q6.076 213.536 5.990 213.878M10.393 215.696Q9.986 215.696 9.666 215.477Q9.347 215.259 9.167 214.905Q8.988 214.551 8.988 214.151Q8.988 213.850 9.097 213.570Q9.207 213.290 9.410 213.071Q9.613 212.852 9.880 212.731Q10.147 212.610 10.458 212.610Q10.905 212.610 11.261 212.890L11.261 211.875L10.892 211.875Q10.707 211.854 10.673 211.666L10.673 211.588Q10.707 211.407 10.892 211.386L11.603 211.386Q11.777 211.407 11.821 211.588L11.821 215.173L12.194 215.173Q12.375 215.194 12.409 215.375L12.409 215.454Q12.375 215.641 12.194 215.662L11.480 215.662Q11.305 215.641 11.261 215.454L11.261 215.341Q11.090 215.508 10.861 215.602Q10.632 215.696 10.393 215.696M10.427 215.207Q10.741 215.207 10.962 214.972Q11.182 214.736 11.261 214.408L11.261 213.680Q11.210 213.516 11.099 213.384Q10.987 213.252 10.832 213.175Q10.676 213.099 10.505 213.099Q10.235 213.099 10.017 213.247Q9.798 213.396 9.672 213.645Q9.545 213.895 9.545 214.158Q9.545 214.551 9.795 214.879Q10.044 215.207 10.427 215.207M14.108 215.696Q13.701 215.696 13.382 215.477Q13.062 215.259 12.883 214.905Q12.703 214.551 12.703 214.151Q12.703 213.850 12.813 213.570Q12.922 213.290 13.125 213.071Q13.329 212.852 13.595 212.731Q13.862 212.610 14.173 212.610Q14.621 212.610 14.976 212.890L14.976 211.875L14.607 211.875Q14.422 211.854 14.388 211.666L14.388 211.588Q14.422 211.407 14.607 211.386L15.318 211.386Q15.492 211.407 15.537 211.588L15.537 215.173L15.909 215.173Q16.090 215.194 16.125 215.375L16.125 215.454Q16.090 215.641 15.909 215.662L15.195 215.662Q15.021 215.641 14.976 215.454L14.976 215.341Q14.805 215.508 14.576 215.602Q14.347 215.696 14.108 215.696M14.142 215.207Q14.457 215.207 14.677 214.972Q14.898 214.736 14.976 214.408L14.976 213.680Q14.925 213.516 14.814 213.384Q14.703 213.252 14.547 213.175Q14.392 213.099 14.221 213.099Q13.951 213.099 13.732 213.247Q13.513 213.396 13.387 213.645Q13.260 213.895 13.260 214.158Q13.260 214.551 13.510 214.879Q13.759 215.207 14.142 215.207M16.733 215.454L16.733 215.375Q16.777 215.194 16.948 215.173L17.858 215.173L17.858 213.136L17.006 213.136Q16.832 213.116 16.788 212.924L16.788 212.849Q16.832 212.664 17.006 212.644L18.203 212.644Q18.374 212.661 18.418 212.849L18.418 215.173L19.218 215.173Q19.389 215.194 19.433 215.375L19.433 215.454Q19.389 215.641 19.218 215.662L16.948 215.662Q16.777 215.641 16.733 215.454M17.635 211.789L17.635 211.742Q17.635 211.591 17.755 211.485Q17.875 211.379 18.028 211.379Q18.179 211.379 18.298 211.485Q18.418 211.591 18.418 211.742L18.418 211.789Q18.418 211.943 18.298 212.049Q18.179 212.155 18.028 212.155Q17.875 212.155 17.755 212.049Q17.635 211.943 17.635 211.789M19.970 215.454L19.970 215.375Q20.007 215.194 20.189 215.173L20.558 215.173L20.558 213.136L20.189 213.136Q20.007 213.116 19.970 212.924L19.970 212.849Q20.011 212.664 20.189 212.644L20.903 212.644Q21.074 212.664 21.118 212.849L21.118 212.924L21.111 212.945Q21.310 212.787 21.549 212.699Q21.788 212.610 22.045 212.610Q22.349 212.610 22.557 212.733Q22.766 212.856 22.867 213.081Q22.967 213.307 22.967 213.618L22.967 215.173L23.340 215.173Q23.521 215.194 23.555 215.375L23.555 215.454Q23.521 215.641 23.340 215.662L22.120 215.662Q21.949 215.641 21.904 215.454L21.904 215.375Q21.949 215.190 22.120 215.173L22.407 215.173L22.407 213.645Q22.407 213.375 22.328 213.237Q22.250 213.099 21.993 213.099Q21.757 213.099 21.557 213.213Q21.358 213.328 21.238 213.527Q21.118 213.727 21.118 213.960L21.118 215.173L21.491 215.173Q21.672 215.194 21.706 215.375L21.706 215.454Q21.672 215.641 21.491 215.662L20.189 215.662Q20.007 215.641 19.970 215.454M23.832 216.229Q23.832 215.966 23.962 215.737Q24.092 215.508 24.311 215.368Q24.150 215.146 24.150 214.866Q24.150 214.616 24.283 214.387Q24.065 214.103 24.065 213.738Q24.065 213.423 24.232 213.163Q24.400 212.904 24.678 212.757Q24.957 212.610 25.275 212.610Q25.456 212.610 25.633 212.663Q25.811 212.716 25.955 212.805Q26.290 212.576 26.703 212.576Q26.912 212.576 27.071 212.690Q27.230 212.805 27.230 213.003Q27.230 213.133 27.141 213.225Q27.052 213.317 26.915 213.317Q26.799 213.317 26.715 213.249Q26.631 213.181 26.604 213.071Q26.478 213.078 26.303 213.157Q26.481 213.430 26.481 213.738Q26.481 213.984 26.384 214.187Q26.286 214.391 26.115 214.546Q25.944 214.702 25.724 214.787Q25.504 214.872 25.275 214.872Q24.936 214.872 24.646 214.708Q24.635 214.708 24.627 214.772Q24.618 214.835 24.618 214.866Q24.618 214.972 24.676 215.066Q24.734 215.160 24.840 215.194Q24.854 215.190 24.866 215.189Q24.878 215.187 24.899 215.187Q24.912 215.187 24.940 215.194Q24.967 215.201 24.974 215.201L25.493 215.201Q26.177 215.201 26.650 215.412Q27.124 215.624 27.124 216.229Q27.124 216.493 26.966 216.691Q26.809 216.889 26.549 217.016Q26.290 217.142 26.009 217.200Q25.729 217.258 25.480 217.258Q25.138 217.258 24.752 217.151Q24.365 217.043 24.099 216.809Q23.832 216.575 23.832 216.229M24.304 216.223Q24.304 216.414 24.514 216.537Q24.724 216.660 25.008 216.718Q25.292 216.776 25.480 216.776Q25.668 216.776 25.951 216.718Q26.235 216.660 26.445 216.537Q26.655 216.414 26.655 216.223Q26.655 215.970 26.459 215.848Q26.262 215.727 26.016 215.698Q25.770 215.669 25.466 215.669L24.926 215.669Q24.765 215.669 24.623 215.739Q24.482 215.809 24.393 215.937Q24.304 216.065 24.304 216.223M25.275 214.387Q25.538 214.387 25.729 214.196Q25.921 214.004 25.921 213.738Q25.921 213.601 25.873 213.486Q25.825 213.372 25.733 213.280Q25.640 213.187 25.526 213.140Q25.411 213.092 25.275 213.092Q25.008 213.092 24.817 213.283Q24.625 213.475 24.625 213.738Q24.625 213.997 24.820 214.192Q25.015 214.387 25.275 214.387\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.907 -27.092)\">\u003Cpath d=\"M32.678 214.855L32.678 213.792L31.615 213.792Q31.506 213.782 31.431 213.707Q31.356 213.632 31.356 213.519Q31.356 213.406 31.431 213.334Q31.506 213.263 31.615 213.252L32.678 213.252L32.678 212.183Q32.689 212.073 32.764 212.001Q32.839 211.930 32.952 211.930Q33.065 211.930 33.136 212.001Q33.208 212.073 33.218 212.183L33.218 213.252L34.281 213.252Q34.391 213.263 34.463 213.334Q34.534 213.406 34.534 213.519Q34.534 213.632 34.463 213.707Q34.391 213.782 34.281 213.792L33.218 213.792L33.218 214.855Q33.208 214.965 33.136 215.040Q33.065 215.115 32.952 215.115Q32.839 215.115 32.764 215.040Q32.689 214.965 32.678 214.855\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.907 -27.092)\">\u003Cpath d=\"M38.589 217.012L38.589 216.937Q38.626 216.745 38.807 216.725L39.176 216.725L39.176 213.136L38.807 213.136Q38.626 213.116 38.589 212.924L38.589 212.849Q38.630 212.664 38.807 212.644L39.522 212.644Q39.693 212.661 39.737 212.849L39.737 212.911Q39.922 212.764 40.152 212.687Q40.383 212.610 40.619 212.610Q40.916 212.610 41.176 212.736Q41.436 212.863 41.624 213.083Q41.812 213.304 41.912 213.577Q42.013 213.850 42.013 214.151Q42.013 214.558 41.815 214.917Q41.617 215.276 41.278 215.486Q40.940 215.696 40.530 215.696Q40.075 215.696 39.737 215.375L39.737 216.725L40.110 216.725Q40.291 216.745 40.325 216.937L40.325 217.012Q40.291 217.197 40.110 217.217L38.807 217.217Q38.630 217.197 38.589 217.012M40.492 215.207Q40.762 215.207 40.981 215.059Q41.200 214.910 41.326 214.664Q41.453 214.418 41.453 214.151Q41.453 213.898 41.343 213.654Q41.234 213.410 41.031 213.254Q40.827 213.099 40.564 213.099Q40.284 213.099 40.055 213.261Q39.826 213.423 39.737 213.686L39.737 214.432Q39.816 214.753 40.009 214.980Q40.202 215.207 40.492 215.207M44.098 215.696Q43.685 215.696 43.348 215.483Q43.011 215.269 42.817 214.910Q42.622 214.551 42.622 214.151Q42.622 213.850 42.731 213.568Q42.840 213.287 43.042 213.064Q43.244 212.842 43.512 212.716Q43.780 212.589 44.098 212.589Q44.416 212.589 44.690 212.717Q44.963 212.846 45.158 213.061Q45.353 213.276 45.464 213.557Q45.575 213.837 45.575 214.151Q45.575 214.551 45.378 214.912Q45.182 215.272 44.845 215.484Q44.508 215.696 44.098 215.696M44.098 215.207Q44.505 215.207 44.760 214.862Q45.014 214.517 45.014 214.093Q45.014 213.837 44.896 213.603Q44.778 213.369 44.568 213.223Q44.358 213.078 44.098 213.078Q43.832 213.078 43.623 213.223Q43.415 213.369 43.297 213.603Q43.179 213.837 43.179 214.093Q43.179 214.514 43.435 214.860Q43.692 215.207 44.098 215.207M46.470 215.488L46.470 214.688Q46.494 214.507 46.679 214.486L46.826 214.486Q46.969 214.507 47.021 214.647Q47.198 215.207 47.834 215.207Q48.015 215.207 48.215 215.177Q48.415 215.146 48.562 215.045Q48.709 214.944 48.709 214.766Q48.709 214.582 48.514 214.483Q48.319 214.384 48.080 214.346L47.468 214.247Q46.470 214.062 46.470 213.430Q46.470 213.177 46.597 213.011Q46.723 212.846 46.933 212.752Q47.144 212.658 47.368 212.623Q47.591 212.589 47.834 212.589Q48.053 212.589 48.222 212.615Q48.391 212.641 48.535 212.709Q48.603 212.606 48.716 212.589L48.784 212.589Q48.870 212.600 48.924 212.654Q48.979 212.709 48.989 212.791L48.989 213.410Q48.979 213.492 48.924 213.550Q48.870 213.608 48.784 213.618L48.637 213.618Q48.555 213.608 48.497 213.550Q48.439 213.492 48.429 213.410Q48.429 213.078 47.820 213.078Q47.516 213.078 47.238 213.150Q46.959 213.222 46.959 213.437Q46.959 213.669 47.547 213.765L48.162 213.871Q48.586 213.943 48.892 214.160Q49.198 214.377 49.198 214.766Q49.198 215.108 48.991 215.320Q48.784 215.532 48.478 215.614Q48.173 215.696 47.834 215.696Q47.328 215.696 46.980 215.474Q46.918 215.583 46.875 215.633Q46.833 215.683 46.740 215.696L46.679 215.696Q46.491 215.676 46.470 215.488M51.044 215.173Q51.044 214.978 51.189 214.833Q51.334 214.688 51.536 214.688Q51.666 214.688 51.777 214.756Q51.888 214.825 51.953 214.934Q52.018 215.043 52.018 215.173Q52.018 215.371 51.872 215.517Q51.727 215.662 51.536 215.662Q51.338 215.662 51.191 215.515Q51.044 215.368 51.044 215.173\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-40.907 -27.092)\">\u003Cpath d=\"M63.912 214.360L61.776 214.360Q61.823 214.602 61.996 214.797Q62.169 214.992 62.411 215.100Q62.654 215.207 62.903 215.207Q63.317 215.207 63.512 214.954Q63.519 214.944 63.568 214.852Q63.618 214.760 63.661 214.722Q63.703 214.684 63.785 214.674L63.912 214.674Q64.079 214.691 64.131 214.879L64.131 214.927Q64.072 215.190 63.871 215.363Q63.669 215.536 63.396 215.616Q63.122 215.696 62.856 215.696Q62.432 215.696 62.047 215.496Q61.663 215.296 61.429 214.946Q61.194 214.596 61.194 214.165L61.194 214.114Q61.194 213.704 61.410 213.351Q61.625 212.999 61.982 212.794Q62.339 212.589 62.750 212.589Q63.191 212.589 63.500 212.784Q63.809 212.979 63.970 213.319Q64.131 213.659 64.131 214.100L64.131 214.151Q64.079 214.339 63.912 214.360M61.782 213.878L63.556 213.878Q63.515 213.519 63.307 213.298Q63.098 213.078 62.750 213.078Q62.404 213.078 62.136 213.307Q61.868 213.536 61.782 213.878M64.616 215.454L64.616 215.375Q64.653 215.194 64.835 215.173L65.204 215.173L65.204 213.136L64.835 213.136Q64.653 213.116 64.616 212.924L64.616 212.849Q64.657 212.664 64.835 212.644L65.549 212.644Q65.720 212.664 65.764 212.849L65.764 212.924L65.757 212.945Q65.956 212.787 66.195 212.699Q66.434 212.610 66.691 212.610Q66.995 212.610 67.203 212.733Q67.412 212.856 67.513 213.081Q67.613 213.307 67.613 213.618L67.613 215.173L67.986 215.173Q68.167 215.194 68.201 215.375L68.201 215.454Q68.167 215.641 67.986 215.662L66.766 215.662Q66.595 215.641 66.550 215.454L66.550 215.375Q66.595 215.190 66.766 215.173L67.053 215.173L67.053 213.645Q67.053 213.375 66.974 213.237Q66.896 213.099 66.639 213.099Q66.403 213.099 66.204 213.213Q66.004 213.328 65.884 213.527Q65.764 213.727 65.764 213.960L65.764 215.173L66.137 215.173Q66.318 215.194 66.352 215.375L66.352 215.454Q66.318 215.641 66.137 215.662L64.835 215.662Q64.653 215.641 64.616 215.454M68.758 214.151Q68.758 213.731 68.972 213.369Q69.186 213.006 69.550 212.798Q69.914 212.589 70.334 212.589Q70.819 212.589 71.151 212.685Q71.483 212.781 71.483 213.136Q71.483 213.283 71.383 213.391Q71.284 213.498 71.134 213.498Q70.984 213.498 70.879 213.398Q70.775 213.297 70.775 213.150L70.775 213.099Q70.635 213.078 70.341 213.078Q70.054 213.078 69.820 213.227Q69.586 213.375 69.452 213.623Q69.319 213.871 69.319 214.151Q69.319 214.432 69.469 214.678Q69.620 214.924 69.869 215.066Q70.119 215.207 70.406 215.207Q70.679 215.207 70.790 215.117Q70.901 215.026 71.004 214.860Q71.107 214.695 71.209 214.681L71.356 214.681Q71.448 214.691 71.505 214.751Q71.561 214.811 71.561 214.900Q71.561 214.941 71.544 214.975Q71.448 215.231 71.271 215.389Q71.093 215.546 70.852 215.621Q70.611 215.696 70.334 215.696Q69.910 215.696 69.546 215.488Q69.182 215.279 68.970 214.927Q68.758 214.575 68.758 214.151M73.356 215.173Q73.356 214.978 73.501 214.833Q73.646 214.688 73.848 214.688Q73.978 214.688 74.089 214.756Q74.200 214.825 74.265 214.934Q74.330 215.043 74.330 215.173Q74.330 215.371 74.184 215.517Q74.039 215.662 73.848 215.662Q73.650 215.662 73.503 215.515Q73.356 215.368 73.356 215.173\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-48.778 153.066H36.58v-17.072h-85.358Z\"\u002F>\u003Cg transform=\"translate(-26.032 -68.993)\">\u003Cpath d=\"M-5.586 215.488L-5.586 214.688Q-5.562 214.507-5.378 214.486L-5.231 214.486Q-5.087 214.507-5.036 214.647Q-4.858 215.207-4.223 215.207Q-4.041 215.207-3.841 215.177Q-3.641 215.146-3.495 215.045Q-3.348 214.944-3.348 214.766Q-3.348 214.582-3.542 214.483Q-3.737 214.384-3.976 214.346L-4.588 214.247Q-5.586 214.062-5.586 213.430Q-5.586 213.177-5.460 213.011Q-5.333 212.846-5.123 212.752Q-4.913 212.658-4.689 212.623Q-4.465 212.589-4.223 212.589Q-4.004 212.589-3.835 212.615Q-3.665 212.641-3.522 212.709Q-3.453 212.606-3.341 212.589L-3.272 212.589Q-3.187 212.600-3.132 212.654Q-3.078 212.709-3.067 212.791L-3.067 213.410Q-3.078 213.492-3.132 213.550Q-3.187 213.608-3.272 213.618L-3.419 213.618Q-3.501 213.608-3.559 213.550Q-3.618 213.492-3.628 213.410Q-3.628 213.078-4.236 213.078Q-4.540 213.078-4.819 213.150Q-5.098 213.222-5.098 213.437Q-5.098 213.669-4.510 213.765L-3.894 213.871Q-3.471 213.943-3.165 214.160Q-2.859 214.377-2.859 214.766Q-2.859 215.108-3.066 215.320Q-3.272 215.532-3.578 215.614Q-3.884 215.696-4.223 215.696Q-4.728 215.696-5.077 215.474Q-5.139 215.583-5.181 215.633Q-5.224 215.683-5.316 215.696L-5.378 215.696Q-5.566 215.676-5.586 215.488M0.689 214.360L-1.447 214.360Q-1.399 214.602-1.227 214.797Q-1.054 214.992-0.811 215.100Q-0.569 215.207-0.319 215.207Q0.094 215.207 0.289 214.954Q0.296 214.944 0.346 214.852Q0.395 214.760 0.438 214.722Q0.481 214.684 0.563 214.674L0.689 214.674Q0.857 214.691 0.908 214.879L0.908 214.927Q0.850 215.190 0.648 215.363Q0.446 215.536 0.173 215.616Q-0.100 215.696-0.367 215.696Q-0.791 215.696-1.175 215.496Q-1.560 215.296-1.794 214.946Q-2.028 214.596-2.028 214.165L-2.028 214.114Q-2.028 213.704-1.813 213.351Q-1.598 212.999-1.240 212.794Q-0.883 212.589-0.473 212.589Q-0.032 212.589 0.277 212.784Q0.587 212.979 0.747 213.319Q0.908 213.659 0.908 214.100L0.908 214.151Q0.857 214.339 0.689 214.360M-1.440 213.878L0.334 213.878Q0.293 213.519 0.084 213.298Q-0.124 213.078-0.473 213.078Q-0.818 213.078-1.087 213.307Q-1.355 213.536-1.440 213.878M1.725 215.454L1.725 215.375Q1.769 215.194 1.940 215.173L2.907 215.173L2.907 211.875L1.940 211.875Q1.769 211.854 1.725 211.666L1.725 211.588Q1.769 211.407 1.940 211.386L3.249 211.386Q3.417 211.407 3.468 211.588L3.468 215.173L4.432 215.173Q4.606 215.194 4.651 215.375L4.651 215.454Q4.606 215.641 4.432 215.662L1.940 215.662Q1.769 215.641 1.725 215.454M5.327 215.454L5.327 215.375Q5.372 215.194 5.543 215.173L6.315 215.173L6.315 213.136L5.567 213.136Q5.392 213.116 5.348 212.924L5.348 212.849Q5.392 212.664 5.567 212.644L6.315 212.644L6.315 212.247Q6.315 211.841 6.671 211.595Q7.026 211.349 7.446 211.349Q7.720 211.349 7.933 211.454Q8.147 211.560 8.147 211.807Q8.147 211.950 8.051 212.053Q7.956 212.155 7.812 212.155Q7.682 212.155 7.576 212.063Q7.470 211.971 7.470 211.841L7.399 211.841Q7.265 211.841 7.146 211.894Q7.026 211.947 6.951 212.047Q6.876 212.148 6.876 212.275L6.876 212.644L7.778 212.644Q7.949 212.661 7.993 212.849L7.993 212.924Q7.949 213.116 7.778 213.136L6.876 213.136L6.876 215.173L7.645 215.173Q7.816 215.194 7.860 215.375L7.860 215.454Q7.816 215.641 7.645 215.662L5.543 215.662Q5.372 215.641 5.327 215.454M11.821 213.792L9.422 213.792Q9.313 213.782 9.237 213.707Q9.162 213.632 9.162 213.519Q9.162 213.406 9.237 213.334Q9.313 213.263 9.422 213.252L11.821 213.252Q11.931 213.263 12.003 213.334Q12.074 213.406 12.074 213.519Q12.074 213.632 12.003 213.707Q11.931 213.782 11.821 213.792M12.833 214.688Q12.833 214.298 13.195 214.073Q13.558 213.847 14.031 213.760Q14.505 213.673 14.949 213.666Q14.949 213.478 14.831 213.345Q14.713 213.211 14.532 213.145Q14.351 213.078 14.166 213.078Q13.865 213.078 13.725 213.099L13.725 213.150Q13.725 213.297 13.621 213.398Q13.517 213.498 13.373 213.498Q13.219 213.498 13.119 213.391Q13.018 213.283 13.018 213.136Q13.018 212.781 13.351 212.685Q13.684 212.589 14.173 212.589Q14.409 212.589 14.643 212.658Q14.877 212.726 15.074 212.858Q15.270 212.989 15.390 213.182Q15.509 213.375 15.509 213.618L15.509 215.122Q15.509 215.173 15.971 215.173Q16.142 215.190 16.186 215.375L16.186 215.454Q16.142 215.641 15.971 215.662L15.844 215.662Q15.544 215.662 15.344 215.621Q15.144 215.580 15.017 215.416Q14.614 215.696 13.995 215.696Q13.701 215.696 13.435 215.573Q13.168 215.450 13.001 215.221Q12.833 214.992 12.833 214.688M13.394 214.695Q13.394 214.934 13.606 215.071Q13.818 215.207 14.067 215.207Q14.258 215.207 14.462 215.156Q14.665 215.105 14.807 214.984Q14.949 214.862 14.949 214.667L14.949 214.151Q14.703 214.151 14.339 214.201Q13.975 214.250 13.684 214.372Q13.394 214.493 13.394 214.695M17.242 214.695L17.242 213.136L16.586 213.136Q16.412 213.116 16.367 212.924L16.367 212.849Q16.412 212.664 16.586 212.644L17.242 212.644L17.242 211.988Q17.287 211.807 17.461 211.783L17.588 211.783Q17.758 211.807 17.803 211.988L17.803 212.644L18.992 212.644Q19.160 212.661 19.211 212.849L19.211 212.924Q19.163 213.116 18.992 213.136L17.803 213.136L17.803 214.667Q17.803 215.207 18.305 215.207Q18.524 215.207 18.668 215.045Q18.811 214.883 18.811 214.667Q18.811 214.585 18.874 214.524Q18.938 214.462 19.026 214.452L19.153 214.452Q19.327 214.473 19.372 214.654L19.372 214.695Q19.372 214.978 19.211 215.209Q19.050 215.440 18.794 215.568Q18.538 215.696 18.257 215.696Q17.810 215.696 17.526 215.424Q17.242 215.153 17.242 214.695M20.958 214.695L20.958 213.136L20.301 213.136Q20.127 213.116 20.083 212.924L20.083 212.849Q20.127 212.664 20.301 212.644L20.958 212.644L20.958 211.988Q21.002 211.807 21.176 211.783L21.303 211.783Q21.474 211.807 21.518 211.988L21.518 212.644L22.708 212.644Q22.875 212.661 22.926 212.849L22.926 212.924Q22.879 213.116 22.708 213.136L21.518 213.136L21.518 214.667Q21.518 215.207 22.021 215.207Q22.239 215.207 22.383 215.045Q22.526 214.883 22.526 214.667Q22.526 214.585 22.590 214.524Q22.653 214.462 22.742 214.452L22.868 214.452Q23.043 214.473 23.087 214.654L23.087 214.695Q23.087 214.978 22.926 215.209Q22.766 215.440 22.509 215.568Q22.253 215.696 21.973 215.696Q21.525 215.696 21.241 215.424Q20.958 215.153 20.958 214.695M26.696 214.360L24.560 214.360Q24.608 214.602 24.781 214.797Q24.953 214.992 25.196 215.100Q25.439 215.207 25.688 215.207Q26.102 215.207 26.297 214.954Q26.303 214.944 26.353 214.852Q26.402 214.760 26.445 214.722Q26.488 214.684 26.570 214.674L26.696 214.674Q26.864 214.691 26.915 214.879L26.915 214.927Q26.857 215.190 26.655 215.363Q26.454 215.536 26.180 215.616Q25.907 215.696 25.640 215.696Q25.216 215.696 24.832 215.496Q24.447 215.296 24.213 214.946Q23.979 214.596 23.979 214.165L23.979 214.114Q23.979 213.704 24.194 213.351Q24.410 212.999 24.767 212.794Q25.124 212.589 25.534 212.589Q25.975 212.589 26.285 212.784Q26.594 212.979 26.755 213.319Q26.915 213.659 26.915 214.100L26.915 214.151Q26.864 214.339 26.696 214.360M24.567 213.878L26.341 213.878Q26.300 213.519 26.091 213.298Q25.883 213.078 25.534 213.078Q25.189 213.078 24.921 213.307Q24.652 213.536 24.567 213.878M27.401 215.454L27.401 215.375Q27.438 215.194 27.619 215.173L27.988 215.173L27.988 213.136L27.619 213.136Q27.438 213.116 27.401 212.924L27.401 212.849Q27.442 212.664 27.619 212.644L28.334 212.644Q28.505 212.664 28.549 212.849L28.549 212.924L28.542 212.945Q28.740 212.787 28.980 212.699Q29.219 212.610 29.475 212.610Q29.779 212.610 29.988 212.733Q30.196 212.856 30.297 213.081Q30.398 213.307 30.398 213.618L30.398 215.173L30.771 215.173Q30.952 215.194 30.986 215.375L30.986 215.454Q30.952 215.641 30.771 215.662L29.550 215.662Q29.380 215.641 29.335 215.454L29.335 215.375Q29.380 215.190 29.550 215.173L29.838 215.173L29.838 213.645Q29.838 213.375 29.759 213.237Q29.680 213.099 29.424 213.099Q29.188 213.099 28.988 213.213Q28.788 213.328 28.669 213.527Q28.549 213.727 28.549 213.960L28.549 215.173L28.922 215.173Q29.103 215.194 29.137 215.375L29.137 215.454Q29.103 215.641 28.922 215.662L27.619 215.662Q27.438 215.641 27.401 215.454M32.104 214.695L32.104 213.136L31.447 213.136Q31.273 213.116 31.229 212.924L31.229 212.849Q31.273 212.664 31.447 212.644L32.104 212.644L32.104 211.988Q32.148 211.807 32.322 211.783L32.449 211.783Q32.620 211.807 32.664 211.988L32.664 212.644L33.854 212.644Q34.021 212.661 34.072 212.849L34.072 212.924Q34.025 213.116 33.854 213.136L32.664 213.136L32.664 214.667Q32.664 215.207 33.167 215.207Q33.385 215.207 33.529 215.045Q33.672 214.883 33.672 214.667Q33.672 214.585 33.736 214.524Q33.799 214.462 33.888 214.452L34.014 214.452Q34.189 214.473 34.233 214.654L34.233 214.695Q34.233 214.978 34.072 215.209Q33.912 215.440 33.655 215.568Q33.399 215.696 33.119 215.696Q32.671 215.696 32.387 215.424Q32.104 215.153 32.104 214.695M35.310 215.454L35.310 215.375Q35.354 215.194 35.525 215.173L36.434 215.173L36.434 213.136L35.583 213.136Q35.409 213.116 35.364 212.924L35.364 212.849Q35.409 212.664 35.583 212.644L36.779 212.644Q36.950 212.661 36.995 212.849L36.995 215.173L37.795 215.173Q37.965 215.194 38.010 215.375L38.010 215.454Q37.965 215.641 37.795 215.662L35.525 215.662Q35.354 215.641 35.310 215.454M36.212 211.789L36.212 211.742Q36.212 211.591 36.332 211.485Q36.451 211.379 36.605 211.379Q36.755 211.379 36.875 211.485Q36.995 211.591 36.995 211.742L36.995 211.789Q36.995 211.943 36.875 212.049Q36.755 212.155 36.605 212.155Q36.451 212.155 36.332 212.049Q36.212 211.943 36.212 211.789M40.341 215.696Q39.927 215.696 39.591 215.483Q39.254 215.269 39.059 214.910Q38.864 214.551 38.864 214.151Q38.864 213.850 38.974 213.568Q39.083 213.287 39.285 213.064Q39.486 212.842 39.755 212.716Q40.023 212.589 40.341 212.589Q40.659 212.589 40.932 212.717Q41.206 212.846 41.401 213.061Q41.595 213.276 41.706 213.557Q41.818 213.837 41.818 214.151Q41.818 214.551 41.621 214.912Q41.424 215.272 41.088 215.484Q40.751 215.696 40.341 215.696M40.341 215.207Q40.748 215.207 41.002 214.862Q41.257 214.517 41.257 214.093Q41.257 213.837 41.139 213.603Q41.021 213.369 40.811 213.223Q40.601 213.078 40.341 213.078Q40.074 213.078 39.866 213.223Q39.657 213.369 39.539 213.603Q39.422 213.837 39.422 214.093Q39.422 214.514 39.678 214.860Q39.934 215.207 40.341 215.207M42.262 215.454L42.262 215.375Q42.299 215.194 42.481 215.173L42.850 215.173L42.850 213.136L42.481 213.136Q42.299 213.116 42.262 212.924L42.262 212.849Q42.303 212.664 42.481 212.644L43.195 212.644Q43.366 212.664 43.410 212.849L43.410 212.924L43.403 212.945Q43.602 212.787 43.841 212.699Q44.080 212.610 44.337 212.610Q44.641 212.610 44.849 212.733Q45.058 212.856 45.159 213.081Q45.259 213.307 45.259 213.618L45.259 215.173L45.632 215.173Q45.813 215.194 45.847 215.375L45.847 215.454Q45.813 215.641 45.632 215.662L44.412 215.662Q44.241 215.641 44.196 215.454L44.196 215.375Q44.241 215.190 44.412 215.173L44.699 215.173L44.699 213.645Q44.699 213.375 44.620 213.237Q44.542 213.099 44.285 213.099Q44.049 213.099 43.849 213.213Q43.650 213.328 43.530 213.527Q43.410 213.727 43.410 213.960L43.410 215.173L43.783 215.173Q43.964 215.194 43.998 215.375L43.998 215.454Q43.964 215.641 43.783 215.662L42.481 215.662Q42.299 215.641 42.262 215.454\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M-48.778 123.19H36.58v-14.226h-85.358Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(-18.594 -97.446)\">\u003Cpath d=\"M-5.744 214.688Q-5.744 214.298-5.381 214.073Q-5.019 213.847-4.546 213.760Q-4.072 213.673-3.628 213.666Q-3.628 213.478-3.746 213.345Q-3.864 213.211-4.045 213.145Q-4.226 213.078-4.411 213.078Q-4.711 213.078-4.851 213.099L-4.851 213.150Q-4.851 213.297-4.956 213.398Q-5.060 213.498-5.203 213.498Q-5.357 213.498-5.458 213.391Q-5.559 213.283-5.559 213.136Q-5.559 212.781-5.226 212.685Q-4.892 212.589-4.404 212.589Q-4.168 212.589-3.934 212.658Q-3.700 212.726-3.503 212.858Q-3.307 212.989-3.187 213.182Q-3.067 213.375-3.067 213.618L-3.067 215.122Q-3.067 215.173-2.606 215.173Q-2.435 215.190-2.391 215.375L-2.391 215.454Q-2.435 215.641-2.606 215.662L-2.732 215.662Q-3.033 215.662-3.233 215.621Q-3.433 215.580-3.559 215.416Q-3.963 215.696-4.581 215.696Q-4.875 215.696-5.142 215.573Q-5.409 215.450-5.576 215.221Q-5.744 214.992-5.744 214.688M-5.183 214.695Q-5.183 214.934-4.971 215.071Q-4.759 215.207-4.510 215.207Q-4.318 215.207-4.115 215.156Q-3.912 215.105-3.770 214.984Q-3.628 214.862-3.628 214.667L-3.628 214.151Q-3.874 214.151-4.238 214.201Q-4.602 214.250-4.892 214.372Q-5.183 214.493-5.183 214.695M-0.753 215.696Q-1.160 215.696-1.480 215.477Q-1.799 215.259-1.979 214.905Q-2.158 214.551-2.158 214.151Q-2.158 213.850-2.049 213.570Q-1.939 213.290-1.736 213.071Q-1.533 212.852-1.266 212.731Q-0.999 212.610-0.688 212.610Q-0.241 212.610 0.115 212.890L0.115 211.875L-0.254 211.875Q-0.439 211.854-0.473 211.666L-0.473 211.588Q-0.439 211.407-0.254 211.386L0.457 211.386Q0.631 211.407 0.675 211.588L0.675 215.173L1.048 215.173Q1.229 215.194 1.263 215.375L1.263 215.454Q1.229 215.641 1.048 215.662L0.334 215.662Q0.159 215.641 0.115 215.454L0.115 215.341Q-0.056 215.508-0.285 215.602Q-0.514 215.696-0.753 215.696M-0.719 215.207Q-0.405 215.207-0.184 214.972Q0.036 214.736 0.115 214.408L0.115 213.680Q0.064 213.516-0.047 213.384Q-0.159 213.252-0.314 213.175Q-0.470 213.099-0.641 213.099Q-0.911 213.099-1.129 213.247Q-1.348 213.396-1.474 213.645Q-1.601 213.895-1.601 214.158Q-1.601 214.551-1.351 214.879Q-1.102 215.207-0.719 215.207M2.962 215.696Q2.555 215.696 2.236 215.477Q1.916 215.259 1.737 214.905Q1.557 214.551 1.557 214.151Q1.557 213.850 1.667 213.570Q1.776 213.290 1.979 213.071Q2.183 212.852 2.449 212.731Q2.716 212.610 3.027 212.610Q3.475 212.610 3.830 212.890L3.830 211.875L3.461 211.875Q3.276 211.854 3.242 211.666L3.242 211.588Q3.276 211.407 3.461 211.386L4.172 211.386Q4.346 211.407 4.391 211.588L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L4.049 215.662Q3.875 215.641 3.830 215.454L3.830 215.341Q3.659 215.508 3.430 215.602Q3.201 215.696 2.962 215.696M2.996 215.207Q3.311 215.207 3.531 214.972Q3.752 214.736 3.830 214.408L3.830 213.680Q3.779 213.516 3.668 213.384Q3.557 213.252 3.401 213.175Q3.246 213.099 3.075 213.099Q2.805 213.099 2.586 213.247Q2.367 213.396 2.241 213.645Q2.114 213.895 2.114 214.158Q2.114 214.551 2.364 214.879Q2.613 215.207 2.996 215.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-18.594 -97.446)\">\u003Cpath d=\"M9.839 215.730Q9.579 215.730 9.383 215.580Q9.186 215.430 9.078 215.189Q8.971 214.948 8.971 214.702L8.971 214.654Q8.971 214.428 9.051 214.221Q9.131 214.015 9.272 213.878L9.672 213.478Q9.477 212.921 9.477 212.350L9.477 212.302Q9.477 212.070 9.571 211.839Q9.665 211.608 9.844 211.461Q10.024 211.314 10.266 211.314Q10.509 211.314 10.666 211.465Q10.823 211.615 10.892 211.844Q10.960 212.073 10.960 212.302L10.960 212.350Q10.960 212.586 10.849 212.810Q10.738 213.034 10.593 213.208Q10.447 213.382 10.218 213.611Q10.376 213.970 10.693 214.466Q10.881 214.114 11.155 213.379L11.254 213.122Q11.131 213.092 11.093 212.924L11.093 212.849Q11.138 212.664 11.309 212.644L12.030 212.644Q12.204 212.661 12.249 212.849L12.249 212.924Q12.204 213.116 12.030 213.136L11.743 213.136L11.575 213.577Q11.240 214.473 10.994 214.886Q11.145 215.050 11.271 215.146Q11.398 215.242 11.555 215.242Q11.661 215.242 11.709 215.122Q11.756 215.002 11.756 214.872Q11.811 214.667 11.989 214.667Q12.167 214.667 12.221 214.872L12.221 214.920Q12.221 215.238 12.038 215.484Q11.856 215.730 11.555 215.730Q11.138 215.730 10.721 215.276Q10.321 215.730 9.839 215.730M9.839 215.242Q10.147 215.242 10.420 214.900Q10.058 214.339 9.877 213.967Q9.777 214.059 9.716 214.129Q9.654 214.199 9.612 214.271Q9.569 214.343 9.550 214.440Q9.531 214.537 9.531 214.654Q9.531 214.845 9.605 215.043Q9.678 215.242 9.839 215.242M10.037 213.099Q10.235 212.883 10.367 212.695Q10.499 212.507 10.499 212.323Q10.499 212.159 10.446 211.983Q10.393 211.807 10.266 211.807Q10.106 211.807 10.022 211.979Q9.938 212.152 9.938 212.336Q9.938 212.719 10.037 213.099\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-18.594 -97.446)\">\u003Cpath d=\"M16.276 215.454L16.276 215.375Q16.313 215.194 16.494 215.173L16.863 215.173L16.863 213.136L16.494 213.136Q16.313 213.116 16.276 212.924L16.276 212.849Q16.317 212.664 16.494 212.644L17.209 212.644Q17.380 212.664 17.424 212.849L17.424 212.924L17.417 212.945Q17.615 212.787 17.855 212.699Q18.094 212.610 18.350 212.610Q18.654 212.610 18.863 212.733Q19.071 212.856 19.172 213.081Q19.273 213.307 19.273 213.618L19.273 215.173L19.646 215.173Q19.827 215.194 19.861 215.375L19.861 215.454Q19.827 215.641 19.646 215.662L18.425 215.662Q18.255 215.641 18.210 215.454L18.210 215.375Q18.255 215.190 18.425 215.173L18.713 215.173L18.713 213.645Q18.713 213.375 18.634 213.237Q18.555 213.099 18.299 213.099Q18.063 213.099 17.863 213.213Q17.663 213.328 17.544 213.527Q17.424 213.727 17.424 213.960L17.424 215.173L17.797 215.173Q17.978 215.194 18.012 215.375L18.012 215.454Q17.978 215.641 17.797 215.662L16.494 215.662Q16.313 215.641 16.276 215.454M21.785 215.696Q21.372 215.696 21.035 215.483Q20.698 215.269 20.504 214.910Q20.309 214.551 20.309 214.151Q20.309 213.850 20.418 213.568Q20.527 213.287 20.729 213.064Q20.931 212.842 21.199 212.716Q21.467 212.589 21.785 212.589Q22.103 212.589 22.377 212.717Q22.650 212.846 22.845 213.061Q23.040 213.276 23.151 213.557Q23.262 213.837 23.262 214.151Q23.262 214.551 23.065 214.912Q22.869 215.272 22.532 215.484Q22.195 215.696 21.785 215.696M21.785 215.207Q22.192 215.207 22.447 214.862Q22.701 214.517 22.701 214.093Q22.701 213.837 22.583 213.603Q22.465 213.369 22.255 213.223Q22.045 213.078 21.785 213.078Q21.519 213.078 21.310 213.223Q21.102 213.369 20.984 213.603Q20.866 213.837 20.866 214.093Q20.866 214.514 21.122 214.860Q21.379 215.207 21.785 215.207M23.839 215.454L23.839 215.375Q23.891 215.194 24.058 215.173L24.680 215.173L24.680 213.136L24.058 213.136Q23.887 213.116 23.839 212.924L23.839 212.849Q23.891 212.664 24.058 212.644L25.022 212.644Q25.196 212.661 25.241 212.849L25.241 213.136Q25.470 212.887 25.781 212.748Q26.092 212.610 26.430 212.610Q26.687 212.610 26.892 212.728Q27.097 212.846 27.097 213.078Q27.097 213.225 27.001 213.328Q26.905 213.430 26.758 213.430Q26.625 213.430 26.524 213.333Q26.423 213.235 26.423 213.099Q26.095 213.099 25.820 213.275Q25.545 213.451 25.393 213.743Q25.241 214.035 25.241 214.367L25.241 215.173L26.068 215.173Q26.249 215.194 26.283 215.375L26.283 215.454Q26.249 215.641 26.068 215.662L24.058 215.662Q23.891 215.641 23.839 215.454M27.312 215.454L27.312 215.375Q27.357 215.190 27.527 215.173L27.702 215.173L27.702 213.136L27.527 213.136Q27.346 213.116 27.312 212.924L27.312 212.849Q27.357 212.661 27.527 212.644L27.948 212.644Q28.115 212.664 28.167 212.849Q28.447 212.610 28.809 212.610Q28.977 212.610 29.124 212.705Q29.271 212.801 29.336 212.952Q29.489 212.784 29.684 212.697Q29.879 212.610 30.091 212.610Q30.457 212.610 30.592 212.909Q30.727 213.208 30.727 213.618L30.727 215.173L30.901 215.173Q31.086 215.194 31.120 215.375L31.120 215.454Q31.075 215.641 30.901 215.662L30.187 215.662Q30.016 215.641 29.971 215.454L29.971 215.375Q30.016 215.194 30.187 215.173L30.265 215.173L30.265 213.645Q30.265 213.099 30.047 213.099Q29.756 213.099 29.600 213.370Q29.445 213.642 29.445 213.960L29.445 215.173L29.623 215.173Q29.804 215.194 29.838 215.375L29.838 215.454Q29.794 215.641 29.623 215.662L28.908 215.662Q28.734 215.641 28.690 215.454L28.690 215.375Q28.734 215.194 28.908 215.173L28.984 215.173L28.984 213.645Q28.984 213.099 28.768 213.099Q28.478 213.099 28.322 213.372Q28.167 213.645 28.167 213.960L28.167 215.173L28.341 215.173Q28.522 215.194 28.556 215.375L28.556 215.454Q28.512 215.645 28.341 215.662L27.527 215.662Q27.346 215.641 27.312 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-48.778 93.315H36.58V76.243h-85.358Z\"\u002F>\u003Cg transform=\"translate(-22.313 -128.744)\">\u003Cpath d=\"M-5.819 215.454L-5.819 215.375Q-5.774 215.194-5.603 215.173L-4.831 215.173L-4.831 213.136L-5.579 213.136Q-5.754 213.116-5.798 212.924L-5.798 212.849Q-5.754 212.664-5.579 212.644L-4.831 212.644L-4.831 212.247Q-4.831 211.841-4.475 211.595Q-4.120 211.349-3.700 211.349Q-3.426 211.349-3.213 211.454Q-2.999 211.560-2.999 211.807Q-2.999 211.950-3.095 212.053Q-3.190 212.155-3.334 212.155Q-3.464 212.155-3.570 212.063Q-3.676 211.971-3.676 211.841L-3.747 211.841Q-3.881 211.841-4 211.894Q-4.120 211.947-4.195 212.047Q-4.270 212.148-4.270 212.275L-4.270 212.644L-3.368 212.644Q-3.197 212.661-3.153 212.849L-3.153 212.924Q-3.197 213.116-3.368 213.136L-4.270 213.136L-4.270 215.173L-3.501 215.173Q-3.330 215.194-3.286 215.375L-3.286 215.454Q-3.330 215.641-3.501 215.662L-5.603 215.662Q-5.774 215.641-5.819 215.454M0.689 214.360L-1.447 214.360Q-1.399 214.602-1.227 214.797Q-1.054 214.992-0.811 215.100Q-0.569 215.207-0.319 215.207Q0.094 215.207 0.289 214.954Q0.296 214.944 0.346 214.852Q0.395 214.760 0.438 214.722Q0.481 214.684 0.563 214.674L0.689 214.674Q0.857 214.691 0.908 214.879L0.908 214.927Q0.850 215.190 0.648 215.363Q0.446 215.536 0.173 215.616Q-0.100 215.696-0.367 215.696Q-0.791 215.696-1.175 215.496Q-1.560 215.296-1.794 214.946Q-2.028 214.596-2.028 214.165L-2.028 214.114Q-2.028 213.704-1.813 213.351Q-1.598 212.999-1.240 212.794Q-0.883 212.589-0.473 212.589Q-0.032 212.589 0.277 212.784Q0.587 212.979 0.747 213.319Q0.908 213.659 0.908 214.100L0.908 214.151Q0.857 214.339 0.689 214.360M-1.440 213.878L0.334 213.878Q0.293 213.519 0.084 213.298Q-0.124 213.078-0.473 213.078Q-0.818 213.078-1.087 213.307Q-1.355 213.536-1.440 213.878M4.404 214.360L2.268 214.360Q2.316 214.602 2.489 214.797Q2.661 214.992 2.904 215.100Q3.147 215.207 3.396 215.207Q3.810 215.207 4.005 214.954Q4.011 214.944 4.061 214.852Q4.110 214.760 4.153 214.722Q4.196 214.684 4.278 214.674L4.404 214.674Q4.572 214.691 4.623 214.879L4.623 214.927Q4.565 215.190 4.363 215.363Q4.162 215.536 3.888 215.616Q3.615 215.696 3.348 215.696Q2.924 215.696 2.540 215.496Q2.155 215.296 1.921 214.946Q1.687 214.596 1.687 214.165L1.687 214.114Q1.687 213.704 1.902 213.351Q2.118 212.999 2.475 212.794Q2.832 212.589 3.242 212.589Q3.683 212.589 3.993 212.784Q4.302 212.979 4.463 213.319Q4.623 213.659 4.623 214.100L4.623 214.151Q4.572 214.339 4.404 214.360M2.275 213.878L4.049 213.878Q4.008 213.519 3.799 213.298Q3.591 213.078 3.242 213.078Q2.897 213.078 2.629 213.307Q2.360 213.536 2.275 213.878M6.677 215.696Q6.271 215.696 5.951 215.477Q5.631 215.259 5.452 214.905Q5.273 214.551 5.273 214.151Q5.273 213.850 5.382 213.570Q5.491 213.290 5.695 213.071Q5.898 212.852 6.165 212.731Q6.431 212.610 6.742 212.610Q7.190 212.610 7.546 212.890L7.546 211.875L7.176 211.875Q6.992 211.854 6.958 211.666L6.958 211.588Q6.992 211.407 7.176 211.386L7.887 211.386Q8.062 211.407 8.106 211.588L8.106 215.173L8.479 215.173Q8.660 215.194 8.694 215.375L8.694 215.454Q8.660 215.641 8.479 215.662L7.764 215.662Q7.590 215.641 7.546 215.454L7.546 215.341Q7.375 215.508 7.146 215.602Q6.917 215.696 6.677 215.696M6.712 215.207Q7.026 215.207 7.246 214.972Q7.467 214.736 7.546 214.408L7.546 213.680Q7.494 213.516 7.383 213.384Q7.272 213.252 7.117 213.175Q6.961 213.099 6.790 213.099Q6.520 213.099 6.301 213.247Q6.083 213.396 5.956 213.645Q5.830 213.895 5.830 214.158Q5.830 214.551 6.079 214.879Q6.329 215.207 6.712 215.207M11.821 213.792L9.422 213.792Q9.313 213.782 9.237 213.707Q9.162 213.632 9.162 213.519Q9.162 213.406 9.237 213.334Q9.313 213.263 9.422 213.252L11.821 213.252Q11.931 213.263 12.003 213.334Q12.074 213.406 12.074 213.519Q12.074 213.632 12.003 213.707Q11.931 213.782 11.821 213.792M12.758 215.454L12.758 215.375Q12.802 215.194 12.973 215.173L13.746 215.173L13.746 213.136L12.997 213.136Q12.823 213.116 12.778 212.924L12.778 212.849Q12.823 212.664 12.997 212.644L13.746 212.644L13.746 212.247Q13.746 211.841 14.101 211.595Q14.457 211.349 14.877 211.349Q15.151 211.349 15.364 211.454Q15.578 211.560 15.578 211.807Q15.578 211.950 15.482 212.053Q15.386 212.155 15.243 212.155Q15.113 212.155 15.007 212.063Q14.901 211.971 14.901 211.841L14.829 211.841Q14.696 211.841 14.576 211.894Q14.457 211.947 14.381 212.047Q14.306 212.148 14.306 212.275L14.306 212.644L15.209 212.644Q15.380 212.661 15.424 212.849L15.424 212.924Q15.380 213.116 15.209 213.136L14.306 213.136L14.306 215.173L15.075 215.173Q15.246 215.194 15.291 215.375L15.291 215.454Q15.246 215.641 15.075 215.662L12.973 215.662Q12.802 215.641 12.758 215.454M18.049 215.696Q17.635 215.696 17.299 215.483Q16.962 215.269 16.767 214.910Q16.572 214.551 16.572 214.151Q16.572 213.850 16.682 213.568Q16.791 213.287 16.993 213.064Q17.194 212.842 17.463 212.716Q17.731 212.589 18.049 212.589Q18.367 212.589 18.640 212.717Q18.914 212.846 19.109 213.061Q19.303 213.276 19.414 213.557Q19.526 213.837 19.526 214.151Q19.526 214.551 19.329 214.912Q19.132 215.272 18.796 215.484Q18.459 215.696 18.049 215.696M18.049 215.207Q18.456 215.207 18.710 214.862Q18.965 214.517 18.965 214.093Q18.965 213.837 18.847 213.603Q18.729 213.369 18.519 213.223Q18.309 213.078 18.049 213.078Q17.782 213.078 17.574 213.223Q17.365 213.369 17.247 213.603Q17.130 213.837 17.130 214.093Q17.130 214.514 17.386 214.860Q17.642 215.207 18.049 215.207M20.103 215.454L20.103 215.375Q20.154 215.194 20.322 215.173L20.944 215.173L20.944 213.136L20.322 213.136Q20.151 213.116 20.103 212.924L20.103 212.849Q20.154 212.664 20.322 212.644L21.286 212.644Q21.460 212.661 21.505 212.849L21.505 213.136Q21.734 212.887 22.045 212.748Q22.356 212.610 22.694 212.610Q22.950 212.610 23.155 212.728Q23.360 212.846 23.360 213.078Q23.360 213.225 23.265 213.328Q23.169 213.430 23.022 213.430Q22.889 213.430 22.788 213.333Q22.687 213.235 22.687 213.099Q22.359 213.099 22.084 213.275Q21.809 213.451 21.657 213.743Q21.505 214.035 21.505 214.367L21.505 215.173L22.332 215.173Q22.513 215.194 22.547 215.375L22.547 215.454Q22.513 215.641 22.332 215.662L20.322 215.662Q20.154 215.641 20.103 215.454M24.505 215.467L24.099 213.136L23.959 213.136Q23.777 213.116 23.743 212.924L23.743 212.849Q23.777 212.664 23.959 212.644L24.981 212.644Q25.165 212.664 25.199 212.849L25.199 212.924Q25.165 213.116 24.981 213.136L24.567 213.136Q24.666 213.700 24.734 214.090Q24.803 214.479 24.847 214.758Q24.892 215.037 24.892 215.101Q24.899 214.951 25.148 214.079Q25.182 213.980 25.268 213.915Q25.353 213.850 25.459 213.850L25.527 213.850Q25.633 213.850 25.719 213.915Q25.804 213.980 25.835 214.079Q25.931 214.414 26.003 214.698Q26.074 214.982 26.074 215.101Q26.085 214.849 26.389 213.136L25.975 213.136Q25.794 213.116 25.760 212.924L25.760 212.849Q25.794 212.664 25.975 212.644L27.004 212.644Q27.172 212.664 27.223 212.849L27.223 212.924Q27.175 213.116 27.004 213.136L26.857 213.136L26.450 215.467Q26.430 215.570 26.353 215.633Q26.276 215.696 26.170 215.696L26.047 215.696Q25.941 215.696 25.857 215.633Q25.774 215.570 25.736 215.467Q25.695 215.310 25.632 215.086Q25.568 214.862 25.531 214.679Q25.493 214.496 25.493 214.408Q25.486 214.654 25.240 215.467Q25.216 215.563 25.131 215.630Q25.046 215.696 24.940 215.696L24.786 215.696Q24.680 215.696 24.603 215.633Q24.526 215.570 24.505 215.467M27.694 214.688Q27.694 214.298 28.057 214.073Q28.419 213.847 28.892 213.760Q29.366 213.673 29.810 213.666Q29.810 213.478 29.692 213.345Q29.574 213.211 29.393 213.145Q29.212 213.078 29.027 213.078Q28.727 213.078 28.587 213.099L28.587 213.150Q28.587 213.297 28.482 213.398Q28.378 213.498 28.234 213.498Q28.081 213.498 27.980 213.391Q27.879 213.283 27.879 213.136Q27.879 212.781 28.212 212.685Q28.546 212.589 29.034 212.589Q29.270 212.589 29.504 212.658Q29.738 212.726 29.935 212.858Q30.131 212.989 30.251 213.182Q30.371 213.375 30.371 213.618L30.371 215.122Q30.371 215.173 30.832 215.173Q31.003 215.190 31.047 215.375L31.047 215.454Q31.003 215.641 30.832 215.662L30.706 215.662Q30.405 215.662 30.205 215.621Q30.005 215.580 29.879 215.416Q29.475 215.696 28.857 215.696Q28.563 215.696 28.296 215.573Q28.029 215.450 27.862 215.221Q27.694 214.992 27.694 214.688M28.255 214.695Q28.255 214.934 28.467 215.071Q28.679 215.207 28.928 215.207Q29.120 215.207 29.323 215.156Q29.526 215.105 29.668 214.984Q29.810 214.862 29.810 214.667L29.810 214.151Q29.564 214.151 29.200 214.201Q28.836 214.250 28.546 214.372Q28.255 214.493 28.255 214.695M31.249 215.454L31.249 215.375Q31.300 215.194 31.468 215.173L32.090 215.173L32.090 213.136L31.468 213.136Q31.297 213.116 31.249 212.924L31.249 212.849Q31.300 212.664 31.468 212.644L32.432 212.644Q32.606 212.661 32.651 212.849L32.651 213.136Q32.880 212.887 33.191 212.748Q33.502 212.610 33.840 212.610Q34.096 212.610 34.301 212.728Q34.506 212.846 34.506 213.078Q34.506 213.225 34.411 213.328Q34.315 213.430 34.168 213.430Q34.035 213.430 33.934 213.333Q33.833 213.235 33.833 213.099Q33.505 213.099 33.230 213.275Q32.955 213.451 32.803 213.743Q32.651 214.035 32.651 214.367L32.651 215.173L33.478 215.173Q33.659 215.194 33.693 215.375L33.693 215.454Q33.659 215.641 33.478 215.662L31.468 215.662Q31.300 215.641 31.249 215.454M36.400 215.696Q35.993 215.696 35.674 215.477Q35.354 215.259 35.175 214.905Q34.995 214.551 34.995 214.151Q34.995 213.850 35.105 213.570Q35.214 213.290 35.417 213.071Q35.621 212.852 35.887 212.731Q36.154 212.610 36.465 212.610Q36.913 212.610 37.268 212.890L37.268 211.875L36.899 211.875Q36.714 211.854 36.680 211.666L36.680 211.588Q36.714 211.407 36.899 211.386L37.610 211.386Q37.784 211.407 37.829 211.588L37.829 215.173L38.201 215.173Q38.382 215.194 38.417 215.375L38.417 215.454Q38.382 215.641 38.201 215.662L37.487 215.662Q37.313 215.641 37.268 215.454L37.268 215.341Q37.097 215.508 36.868 215.602Q36.639 215.696 36.400 215.696M36.434 215.207Q36.749 215.207 36.969 214.972Q37.190 214.736 37.268 214.408L37.268 213.680Q37.217 213.516 37.106 213.384Q36.995 213.252 36.839 213.175Q36.684 213.099 36.513 213.099Q36.243 213.099 36.024 213.247Q35.805 213.396 35.679 213.645Q35.552 213.895 35.552 214.158Q35.552 214.551 35.802 214.879Q36.051 215.207 36.434 215.207\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M-48.778 63.44H36.58V49.212h-85.358Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(-18.594 -157.197)\">\u003Cpath d=\"M-5.744 214.688Q-5.744 214.298-5.381 214.073Q-5.019 213.847-4.546 213.760Q-4.072 213.673-3.628 213.666Q-3.628 213.478-3.746 213.345Q-3.864 213.211-4.045 213.145Q-4.226 213.078-4.411 213.078Q-4.711 213.078-4.851 213.099L-4.851 213.150Q-4.851 213.297-4.956 213.398Q-5.060 213.498-5.203 213.498Q-5.357 213.498-5.458 213.391Q-5.559 213.283-5.559 213.136Q-5.559 212.781-5.226 212.685Q-4.892 212.589-4.404 212.589Q-4.168 212.589-3.934 212.658Q-3.700 212.726-3.503 212.858Q-3.307 212.989-3.187 213.182Q-3.067 213.375-3.067 213.618L-3.067 215.122Q-3.067 215.173-2.606 215.173Q-2.435 215.190-2.391 215.375L-2.391 215.454Q-2.435 215.641-2.606 215.662L-2.732 215.662Q-3.033 215.662-3.233 215.621Q-3.433 215.580-3.559 215.416Q-3.963 215.696-4.581 215.696Q-4.875 215.696-5.142 215.573Q-5.409 215.450-5.576 215.221Q-5.744 214.992-5.744 214.688M-5.183 214.695Q-5.183 214.934-4.971 215.071Q-4.759 215.207-4.510 215.207Q-4.318 215.207-4.115 215.156Q-3.912 215.105-3.770 214.984Q-3.628 214.862-3.628 214.667L-3.628 214.151Q-3.874 214.151-4.238 214.201Q-4.602 214.250-4.892 214.372Q-5.183 214.493-5.183 214.695M-0.753 215.696Q-1.160 215.696-1.480 215.477Q-1.799 215.259-1.979 214.905Q-2.158 214.551-2.158 214.151Q-2.158 213.850-2.049 213.570Q-1.939 213.290-1.736 213.071Q-1.533 212.852-1.266 212.731Q-0.999 212.610-0.688 212.610Q-0.241 212.610 0.115 212.890L0.115 211.875L-0.254 211.875Q-0.439 211.854-0.473 211.666L-0.473 211.588Q-0.439 211.407-0.254 211.386L0.457 211.386Q0.631 211.407 0.675 211.588L0.675 215.173L1.048 215.173Q1.229 215.194 1.263 215.375L1.263 215.454Q1.229 215.641 1.048 215.662L0.334 215.662Q0.159 215.641 0.115 215.454L0.115 215.341Q-0.056 215.508-0.285 215.602Q-0.514 215.696-0.753 215.696M-0.719 215.207Q-0.405 215.207-0.184 214.972Q0.036 214.736 0.115 214.408L0.115 213.680Q0.064 213.516-0.047 213.384Q-0.159 213.252-0.314 213.175Q-0.470 213.099-0.641 213.099Q-0.911 213.099-1.129 213.247Q-1.348 213.396-1.474 213.645Q-1.601 213.895-1.601 214.158Q-1.601 214.551-1.351 214.879Q-1.102 215.207-0.719 215.207M2.962 215.696Q2.555 215.696 2.236 215.477Q1.916 215.259 1.737 214.905Q1.557 214.551 1.557 214.151Q1.557 213.850 1.667 213.570Q1.776 213.290 1.979 213.071Q2.183 212.852 2.449 212.731Q2.716 212.610 3.027 212.610Q3.475 212.610 3.830 212.890L3.830 211.875L3.461 211.875Q3.276 211.854 3.242 211.666L3.242 211.588Q3.276 211.407 3.461 211.386L4.172 211.386Q4.346 211.407 4.391 211.588L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L4.049 215.662Q3.875 215.641 3.830 215.454L3.830 215.341Q3.659 215.508 3.430 215.602Q3.201 215.696 2.962 215.696M2.996 215.207Q3.311 215.207 3.531 214.972Q3.752 214.736 3.830 214.408L3.830 213.680Q3.779 213.516 3.668 213.384Q3.557 213.252 3.401 213.175Q3.246 213.099 3.075 213.099Q2.805 213.099 2.586 213.247Q2.367 213.396 2.241 213.645Q2.114 213.895 2.114 214.158Q2.114 214.551 2.364 214.879Q2.613 215.207 2.996 215.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-18.594 -157.197)\">\u003Cpath d=\"M9.839 215.730Q9.579 215.730 9.383 215.580Q9.186 215.430 9.078 215.189Q8.971 214.948 8.971 214.702L8.971 214.654Q8.971 214.428 9.051 214.221Q9.131 214.015 9.272 213.878L9.672 213.478Q9.477 212.921 9.477 212.350L9.477 212.302Q9.477 212.070 9.571 211.839Q9.665 211.608 9.844 211.461Q10.024 211.314 10.266 211.314Q10.509 211.314 10.666 211.465Q10.823 211.615 10.892 211.844Q10.960 212.073 10.960 212.302L10.960 212.350Q10.960 212.586 10.849 212.810Q10.738 213.034 10.593 213.208Q10.447 213.382 10.218 213.611Q10.376 213.970 10.693 214.466Q10.881 214.114 11.155 213.379L11.254 213.122Q11.131 213.092 11.093 212.924L11.093 212.849Q11.138 212.664 11.309 212.644L12.030 212.644Q12.204 212.661 12.249 212.849L12.249 212.924Q12.204 213.116 12.030 213.136L11.743 213.136L11.575 213.577Q11.240 214.473 10.994 214.886Q11.145 215.050 11.271 215.146Q11.398 215.242 11.555 215.242Q11.661 215.242 11.709 215.122Q11.756 215.002 11.756 214.872Q11.811 214.667 11.989 214.667Q12.167 214.667 12.221 214.872L12.221 214.920Q12.221 215.238 12.038 215.484Q11.856 215.730 11.555 215.730Q11.138 215.730 10.721 215.276Q10.321 215.730 9.839 215.730M9.839 215.242Q10.147 215.242 10.420 214.900Q10.058 214.339 9.877 213.967Q9.777 214.059 9.716 214.129Q9.654 214.199 9.612 214.271Q9.569 214.343 9.550 214.440Q9.531 214.537 9.531 214.654Q9.531 214.845 9.605 215.043Q9.678 215.242 9.839 215.242M10.037 213.099Q10.235 212.883 10.367 212.695Q10.499 212.507 10.499 212.323Q10.499 212.159 10.446 211.983Q10.393 211.807 10.266 211.807Q10.106 211.807 10.022 211.979Q9.938 212.152 9.938 212.336Q9.938 212.719 10.037 213.099\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-18.594 -157.197)\">\u003Cpath d=\"M16.276 215.454L16.276 215.375Q16.313 215.194 16.494 215.173L16.863 215.173L16.863 213.136L16.494 213.136Q16.313 213.116 16.276 212.924L16.276 212.849Q16.317 212.664 16.494 212.644L17.209 212.644Q17.380 212.664 17.424 212.849L17.424 212.924L17.417 212.945Q17.615 212.787 17.855 212.699Q18.094 212.610 18.350 212.610Q18.654 212.610 18.863 212.733Q19.071 212.856 19.172 213.081Q19.273 213.307 19.273 213.618L19.273 215.173L19.646 215.173Q19.827 215.194 19.861 215.375L19.861 215.454Q19.827 215.641 19.646 215.662L18.425 215.662Q18.255 215.641 18.210 215.454L18.210 215.375Q18.255 215.190 18.425 215.173L18.713 215.173L18.713 213.645Q18.713 213.375 18.634 213.237Q18.555 213.099 18.299 213.099Q18.063 213.099 17.863 213.213Q17.663 213.328 17.544 213.527Q17.424 213.727 17.424 213.960L17.424 215.173L17.797 215.173Q17.978 215.194 18.012 215.375L18.012 215.454Q17.978 215.641 17.797 215.662L16.494 215.662Q16.313 215.641 16.276 215.454M21.785 215.696Q21.372 215.696 21.035 215.483Q20.698 215.269 20.504 214.910Q20.309 214.551 20.309 214.151Q20.309 213.850 20.418 213.568Q20.527 213.287 20.729 213.064Q20.931 212.842 21.199 212.716Q21.467 212.589 21.785 212.589Q22.103 212.589 22.377 212.717Q22.650 212.846 22.845 213.061Q23.040 213.276 23.151 213.557Q23.262 213.837 23.262 214.151Q23.262 214.551 23.065 214.912Q22.869 215.272 22.532 215.484Q22.195 215.696 21.785 215.696M21.785 215.207Q22.192 215.207 22.447 214.862Q22.701 214.517 22.701 214.093Q22.701 213.837 22.583 213.603Q22.465 213.369 22.255 213.223Q22.045 213.078 21.785 213.078Q21.519 213.078 21.310 213.223Q21.102 213.369 20.984 213.603Q20.866 213.837 20.866 214.093Q20.866 214.514 21.122 214.860Q21.379 215.207 21.785 215.207M23.839 215.454L23.839 215.375Q23.891 215.194 24.058 215.173L24.680 215.173L24.680 213.136L24.058 213.136Q23.887 213.116 23.839 212.924L23.839 212.849Q23.891 212.664 24.058 212.644L25.022 212.644Q25.196 212.661 25.241 212.849L25.241 213.136Q25.470 212.887 25.781 212.748Q26.092 212.610 26.430 212.610Q26.687 212.610 26.892 212.728Q27.097 212.846 27.097 213.078Q27.097 213.225 27.001 213.328Q26.905 213.430 26.758 213.430Q26.625 213.430 26.524 213.333Q26.423 213.235 26.423 213.099Q26.095 213.099 25.820 213.275Q25.545 213.451 25.393 213.743Q25.241 214.035 25.241 214.367L25.241 215.173L26.068 215.173Q26.249 215.194 26.283 215.375L26.283 215.454Q26.249 215.641 26.068 215.662L24.058 215.662Q23.891 215.641 23.839 215.454M27.312 215.454L27.312 215.375Q27.357 215.190 27.527 215.173L27.702 215.173L27.702 213.136L27.527 213.136Q27.346 213.116 27.312 212.924L27.312 212.849Q27.357 212.661 27.527 212.644L27.948 212.644Q28.115 212.664 28.167 212.849Q28.447 212.610 28.809 212.610Q28.977 212.610 29.124 212.705Q29.271 212.801 29.336 212.952Q29.489 212.784 29.684 212.697Q29.879 212.610 30.091 212.610Q30.457 212.610 30.592 212.909Q30.727 213.208 30.727 213.618L30.727 215.173L30.901 215.173Q31.086 215.194 31.120 215.375L31.120 215.454Q31.075 215.641 30.901 215.662L30.187 215.662Q30.016 215.641 29.971 215.454L29.971 215.375Q30.016 215.194 30.187 215.173L30.265 215.173L30.265 213.645Q30.265 213.099 30.047 213.099Q29.756 213.099 29.600 213.370Q29.445 213.642 29.445 213.960L29.445 215.173L29.623 215.173Q29.804 215.194 29.838 215.375L29.838 215.454Q29.794 215.641 29.623 215.662L28.908 215.662Q28.734 215.641 28.690 215.454L28.690 215.375Q28.734 215.194 28.908 215.173L28.984 215.173L28.984 213.645Q28.984 213.099 28.768 213.099Q28.478 213.099 28.322 213.372Q28.167 213.645 28.167 213.960L28.167 215.173L28.341 215.173Q28.522 215.194 28.556 215.375L28.556 215.454Q28.512 215.645 28.341 215.662L27.527 215.662Q27.346 215.641 27.312 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(-33.47 -186.136)\">\u003Cpath d=\"M-5.925 215.454L-5.925 215.375Q-5.880 215.194-5.706 215.173L-5.470 215.173L-5.470 211.875L-5.706 211.875Q-5.880 211.854-5.925 211.666L-5.925 211.588Q-5.880 211.407-5.706 211.386L-5.022 211.386Q-4.910 211.386-4.817 211.451Q-4.725 211.516-4.691 211.615Q-4.448 212.306-4.308 212.699Q-4.168 213.092-3.946 213.721Q-3.724 214.350-3.602 214.708Q-3.481 215.067-3.481 215.101L-3.481 211.875L-3.720 211.875Q-3.891 211.854-3.935 211.666L-3.935 211.588Q-3.891 211.407-3.720 211.386L-2.780 211.386Q-2.609 211.407-2.565 211.588L-2.565 211.666Q-2.609 211.854-2.780 211.875L-3.019 211.875L-3.019 215.454Q-3.064 215.641-3.235 215.662L-3.467 215.662Q-3.577 215.662-3.667 215.597Q-3.758 215.532-3.795 215.430Q-4.055 214.688-4.381 213.770Q-4.708 212.852-4.857 212.425Q-5.005 211.998-5.009 211.947L-5.009 215.173L-4.769 215.173Q-4.602 215.194-4.551 215.375L-4.551 215.454Q-4.602 215.641-4.769 215.662L-5.706 215.662Q-5.880 215.641-5.925 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-33.47 -186.136)\">\u003Cpath d=\"M1.732 215.454L1.732 215.375Q1.777 215.194 1.947 215.173L2.915 215.173L2.915 211.875L1.947 211.875Q1.777 211.854 1.732 211.666L1.732 211.588Q1.777 211.407 1.947 211.386L3.256 211.386Q3.424 211.407 3.475 211.588L3.475 215.173L4.439 215.173Q4.613 215.194 4.658 215.375L4.658 215.454Q4.613 215.641 4.439 215.662L1.947 215.662Q1.777 215.641 1.732 215.454M5.410 214.688Q5.410 214.298 5.772 214.073Q6.134 213.847 6.608 213.760Q7.081 213.673 7.526 213.666Q7.526 213.478 7.408 213.345Q7.290 213.211 7.109 213.145Q6.927 213.078 6.743 213.078Q6.442 213.078 6.302 213.099L6.302 213.150Q6.302 213.297 6.198 213.398Q6.093 213.498 5.950 213.498Q5.796 213.498 5.695 213.391Q5.594 213.283 5.594 213.136Q5.594 212.781 5.928 212.685Q6.261 212.589 6.750 212.589Q6.985 212.589 7.220 212.658Q7.454 212.726 7.650 212.858Q7.847 212.989 7.966 213.182Q8.086 213.375 8.086 213.618L8.086 215.122Q8.086 215.173 8.547 215.173Q8.718 215.190 8.763 215.375L8.763 215.454Q8.718 215.641 8.547 215.662L8.421 215.662Q8.120 215.662 7.920 215.621Q7.720 215.580 7.594 215.416Q7.191 215.696 6.572 215.696Q6.278 215.696 6.011 215.573Q5.745 215.450 5.577 215.221Q5.410 214.992 5.410 214.688M5.970 214.695Q5.970 214.934 6.182 215.071Q6.394 215.207 6.644 215.207Q6.835 215.207 7.038 215.156Q7.242 215.105 7.384 214.984Q7.526 214.862 7.526 214.667L7.526 214.151Q7.279 214.151 6.915 214.201Q6.551 214.250 6.261 214.372Q5.970 214.493 5.970 214.695M9.070 216.643Q9.070 216.547 9.115 216.467Q9.159 216.387 9.240 216.342Q9.320 216.298 9.412 216.298Q9.508 216.298 9.588 216.342Q9.669 216.387 9.713 216.467Q9.757 216.547 9.757 216.643L9.631 216.643Q9.631 216.763 9.652 216.763Q9.877 216.763 10.041 216.595Q10.205 216.428 10.280 216.195L10.465 215.662L9.470 213.136L9.183 213.136Q9.012 213.116 8.964 212.924L8.964 212.849Q9.016 212.664 9.183 212.644L10.198 212.644Q10.369 212.664 10.414 212.849L10.414 212.924Q10.369 213.116 10.198 213.136L9.966 213.136Q10.260 213.878 10.474 214.450Q10.687 215.023 10.687 215.101L10.694 215.101Q10.694 215.050 10.774 214.794Q10.855 214.537 11.024 214.027Q11.193 213.516 11.316 213.136L11.073 213.136Q10.889 213.116 10.855 212.924L10.855 212.849Q10.899 212.661 11.073 212.644L12.082 212.644Q12.263 212.664 12.297 212.849L12.297 212.924Q12.263 213.116 12.082 213.136L11.801 213.136L10.773 216.195Q10.626 216.633 10.340 216.942Q10.055 217.251 9.652 217.251Q9.412 217.251 9.241 217.067Q9.070 216.882 9.070 216.643M15.558 214.360L13.422 214.360Q13.469 214.602 13.642 214.797Q13.815 214.992 14.057 215.100Q14.300 215.207 14.549 215.207Q14.963 215.207 15.158 214.954Q15.165 214.944 15.214 214.852Q15.264 214.760 15.307 214.722Q15.349 214.684 15.431 214.674L15.558 214.674Q15.725 214.691 15.777 214.879L15.777 214.927Q15.718 215.190 15.517 215.363Q15.315 215.536 15.042 215.616Q14.768 215.696 14.502 215.696Q14.078 215.696 13.693 215.496Q13.309 215.296 13.075 214.946Q12.840 214.596 12.840 214.165L12.840 214.114Q12.840 213.704 13.056 213.351Q13.271 212.999 13.628 212.794Q13.985 212.589 14.396 212.589Q14.837 212.589 15.146 212.784Q15.455 212.979 15.616 213.319Q15.777 213.659 15.777 214.100L15.777 214.151Q15.725 214.339 15.558 214.360M13.428 213.878L15.202 213.878Q15.161 213.519 14.953 213.298Q14.744 213.078 14.396 213.078Q14.050 213.078 13.782 213.307Q13.514 213.536 13.428 213.878M16.395 215.454L16.395 215.375Q16.446 215.194 16.614 215.173L17.236 215.173L17.236 213.136L16.614 213.136Q16.443 213.116 16.395 212.924L16.395 212.849Q16.446 212.664 16.614 212.644L17.578 212.644Q17.752 212.661 17.797 212.849L17.797 213.136Q18.026 212.887 18.337 212.748Q18.648 212.610 18.986 212.610Q19.242 212.610 19.447 212.728Q19.652 212.846 19.652 213.078Q19.652 213.225 19.557 213.328Q19.461 213.430 19.314 213.430Q19.181 213.430 19.080 213.333Q18.979 213.235 18.979 213.099Q18.651 213.099 18.376 213.275Q18.101 213.451 17.949 213.743Q17.797 214.035 17.797 214.367L17.797 215.173L18.624 215.173Q18.805 215.194 18.839 215.375L18.839 215.454Q18.805 215.641 18.624 215.662L16.614 215.662Q16.446 215.641 16.395 215.454M20.428 215.488L20.428 214.688Q20.452 214.507 20.637 214.486L20.784 214.486Q20.927 214.507 20.979 214.647Q21.156 215.207 21.792 215.207Q21.973 215.207 22.173 215.177Q22.373 215.146 22.520 215.045Q22.667 214.944 22.667 214.766Q22.667 214.582 22.472 214.483Q22.277 214.384 22.038 214.346L21.426 214.247Q20.428 214.062 20.428 213.430Q20.428 213.177 20.555 213.011Q20.681 212.846 20.891 212.752Q21.102 212.658 21.326 212.623Q21.549 212.589 21.792 212.589Q22.011 212.589 22.180 212.615Q22.349 212.641 22.493 212.709Q22.561 212.606 22.674 212.589L22.742 212.589Q22.828 212.600 22.882 212.654Q22.937 212.709 22.947 212.791L22.947 213.410Q22.937 213.492 22.882 213.550Q22.828 213.608 22.742 213.618L22.595 213.618Q22.513 213.608 22.455 213.550Q22.397 213.492 22.387 213.410Q22.387 213.078 21.778 213.078Q21.474 213.078 21.196 213.150Q20.917 213.222 20.917 213.437Q20.917 213.669 21.505 213.765L22.120 213.871Q22.544 213.943 22.850 214.160Q23.156 214.377 23.156 214.766Q23.156 215.108 22.949 215.320Q22.742 215.532 22.436 215.614Q22.131 215.696 21.792 215.696Q21.286 215.696 20.938 215.474Q20.876 215.583 20.833 215.633Q20.791 215.683 20.698 215.696L20.637 215.696Q20.449 215.676 20.428 215.488\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-33.47 -186.136)\">\u003Cpath d=\"M30.094 216.223Q29.629 215.953 29.279 215.525Q28.929 215.098 28.744 214.579Q28.559 214.059 28.559 213.519Q28.559 212.979 28.742 212.464Q28.925 211.950 29.272 211.530Q29.619 211.109 30.087 210.826Q30.149 210.805 30.176 210.805L30.255 210.805Q30.340 210.815 30.398 210.873Q30.456 210.932 30.456 211.020Q30.456 211.147 30.368 211.202Q29.974 211.454 29.689 211.818Q29.404 212.183 29.262 212.613Q29.120 213.044 29.120 213.519Q29.120 213.874 29.204 214.213Q29.287 214.551 29.443 214.845Q29.599 215.139 29.826 215.387Q30.053 215.635 30.357 215.836Q30.456 215.905 30.456 216.024Q30.456 216.110 30.398 216.171Q30.340 216.233 30.255 216.243L30.176 216.243Q30.125 216.243 30.094 216.223M34.158 214.360L32.022 214.360Q32.070 214.602 32.242 214.797Q32.415 214.992 32.658 215.100Q32.900 215.207 33.150 215.207Q33.563 215.207 33.758 214.954Q33.765 214.944 33.815 214.852Q33.864 214.760 33.907 214.722Q33.950 214.684 34.032 214.674L34.158 214.674Q34.326 214.691 34.377 214.879L34.377 214.927Q34.319 215.190 34.117 215.363Q33.915 215.536 33.642 215.616Q33.369 215.696 33.102 215.696Q32.678 215.696 32.294 215.496Q31.909 215.296 31.675 214.946Q31.441 214.596 31.441 214.165L31.441 214.114Q31.441 213.704 31.656 213.351Q31.871 212.999 32.229 212.794Q32.586 212.589 32.996 212.589Q33.437 212.589 33.746 212.784Q34.056 212.979 34.216 213.319Q34.377 213.659 34.377 214.100L34.377 214.151Q34.326 214.339 34.158 214.360M32.029 213.878L33.803 213.878Q33.762 213.519 33.553 213.298Q33.345 213.078 32.996 213.078Q32.651 213.078 32.382 213.307Q32.114 213.536 32.029 213.878M34.862 215.454L34.862 215.375Q34.900 215.194 35.081 215.173L35.450 215.173L35.450 213.136L35.081 213.136Q34.900 213.116 34.862 212.924L34.862 212.849Q34.903 212.664 35.081 212.644L35.795 212.644Q35.966 212.664 36.011 212.849L36.011 212.924L36.004 212.945Q36.202 212.787 36.441 212.699Q36.681 212.610 36.937 212.610Q37.241 212.610 37.450 212.733Q37.658 212.856 37.759 213.081Q37.860 213.307 37.860 213.618L37.860 215.173L38.232 215.173Q38.413 215.194 38.448 215.375L38.448 215.454Q38.413 215.641 38.232 215.662L37.012 215.662Q36.841 215.641 36.797 215.454L36.797 215.375Q36.841 215.190 37.012 215.173L37.299 215.173L37.299 213.645Q37.299 213.375 37.221 213.237Q37.142 213.099 36.886 213.099Q36.650 213.099 36.450 213.213Q36.250 213.328 36.130 213.527Q36.011 213.727 36.011 213.960L36.011 215.173L36.383 215.173Q36.564 215.194 36.599 215.375L36.599 215.454Q36.564 215.641 36.383 215.662L35.081 215.662Q34.900 215.641 34.862 215.454M39.005 214.151Q39.005 213.731 39.218 213.369Q39.432 213.006 39.796 212.798Q40.160 212.589 40.580 212.589Q41.066 212.589 41.397 212.685Q41.729 212.781 41.729 213.136Q41.729 213.283 41.630 213.391Q41.531 213.498 41.380 213.498Q41.230 213.498 41.126 213.398Q41.021 213.297 41.021 213.150L41.021 213.099Q40.881 213.078 40.587 213.078Q40.300 213.078 40.066 213.227Q39.832 213.375 39.699 213.623Q39.565 213.871 39.565 214.151Q39.565 214.432 39.716 214.678Q39.866 214.924 40.116 215.066Q40.365 215.207 40.652 215.207Q40.926 215.207 41.037 215.117Q41.148 215.026 41.250 214.860Q41.353 214.695 41.455 214.681L41.602 214.681Q41.695 214.691 41.751 214.751Q41.808 214.811 41.808 214.900Q41.808 214.941 41.790 214.975Q41.695 215.231 41.517 215.389Q41.339 215.546 41.098 215.621Q40.857 215.696 40.580 215.696Q40.157 215.696 39.793 215.488Q39.429 215.279 39.217 214.927Q39.005 214.575 39.005 214.151M44.087 215.696Q43.674 215.696 43.337 215.483Q43 215.269 42.806 214.910Q42.611 214.551 42.611 214.151Q42.611 213.850 42.720 213.568Q42.829 213.287 43.031 213.064Q43.233 212.842 43.501 212.716Q43.769 212.589 44.087 212.589Q44.405 212.589 44.679 212.717Q44.952 212.846 45.147 213.061Q45.342 213.276 45.453 213.557Q45.564 213.837 45.564 214.151Q45.564 214.551 45.367 214.912Q45.171 215.272 44.834 215.484Q44.497 215.696 44.087 215.696M44.087 215.207Q44.494 215.207 44.749 214.862Q45.003 214.517 45.003 214.093Q45.003 213.837 44.885 213.603Q44.767 213.369 44.557 213.223Q44.347 213.078 44.087 213.078Q43.821 213.078 43.612 213.223Q43.404 213.369 43.286 213.603Q43.168 213.837 43.168 214.093Q43.168 214.514 43.424 214.860Q43.681 215.207 44.087 215.207M47.577 215.696Q47.170 215.696 46.851 215.477Q46.531 215.259 46.352 214.905Q46.172 214.551 46.172 214.151Q46.172 213.850 46.282 213.570Q46.391 213.290 46.594 213.071Q46.798 212.852 47.064 212.731Q47.331 212.610 47.642 212.610Q48.090 212.610 48.445 212.890L48.445 211.875L48.076 211.875Q47.891 211.854 47.857 211.666L47.857 211.588Q47.891 211.407 48.076 211.386L48.787 211.386Q48.961 211.407 49.006 211.588L49.006 215.173L49.378 215.173Q49.559 215.194 49.594 215.375L49.594 215.454Q49.559 215.641 49.378 215.662L48.664 215.662Q48.490 215.641 48.445 215.454L48.445 215.341Q48.274 215.508 48.045 215.602Q47.816 215.696 47.577 215.696M47.611 215.207Q47.926 215.207 48.146 214.972Q48.367 214.736 48.445 214.408L48.445 213.680Q48.394 213.516 48.283 213.384Q48.172 213.252 48.016 213.175Q47.861 213.099 47.690 213.099Q47.420 213.099 47.201 213.247Q46.982 213.396 46.856 213.645Q46.729 213.895 46.729 214.158Q46.729 214.551 46.979 214.879Q47.228 215.207 47.611 215.207M52.735 214.360L50.599 214.360Q50.646 214.602 50.819 214.797Q50.992 214.992 51.234 215.100Q51.477 215.207 51.726 215.207Q52.140 215.207 52.335 214.954Q52.342 214.944 52.391 214.852Q52.441 214.760 52.484 214.722Q52.526 214.684 52.608 214.674L52.735 214.674Q52.902 214.691 52.953 214.879L52.953 214.927Q52.895 215.190 52.694 215.363Q52.492 215.536 52.219 215.616Q51.945 215.696 51.679 215.696Q51.255 215.696 50.870 215.496Q50.486 215.296 50.252 214.946Q50.017 214.596 50.017 214.165L50.017 214.114Q50.017 213.704 50.233 213.351Q50.448 212.999 50.805 212.794Q51.162 212.589 51.573 212.589Q52.014 212.589 52.323 212.784Q52.632 212.979 52.793 213.319Q52.953 213.659 52.953 214.100L52.953 214.151Q52.902 214.339 52.735 214.360M50.605 213.878L52.379 213.878Q52.338 213.519 52.130 213.298Q51.921 213.078 51.573 213.078Q51.227 213.078 50.959 213.307Q50.691 213.536 50.605 213.878M53.572 215.454L53.572 215.375Q53.623 215.194 53.791 215.173L54.413 215.173L54.413 213.136L53.791 213.136Q53.620 213.116 53.572 212.924L53.572 212.849Q53.623 212.664 53.791 212.644L54.755 212.644Q54.929 212.661 54.974 212.849L54.974 213.136Q55.203 212.887 55.514 212.748Q55.825 212.610 56.163 212.610Q56.419 212.610 56.624 212.728Q56.829 212.846 56.829 213.078Q56.829 213.225 56.734 213.328Q56.638 213.430 56.491 213.430Q56.358 213.430 56.257 213.333Q56.156 213.235 56.156 213.099Q55.828 213.099 55.553 213.275Q55.278 213.451 55.126 213.743Q54.974 214.035 54.974 214.367L54.974 215.173L55.801 215.173Q55.982 215.194 56.016 215.375L56.016 215.454Q55.982 215.641 55.801 215.662L53.791 215.662Q53.623 215.641 53.572 215.454M58.002 216.243L57.927 216.243Q57.834 216.233 57.775 216.170Q57.715 216.106 57.715 216.024Q57.715 215.901 57.807 215.843Q58.101 215.655 58.337 215.402Q58.573 215.149 58.733 214.845Q58.894 214.541 58.973 214.209Q59.051 213.878 59.051 213.519Q59.051 213.047 58.908 212.617Q58.764 212.186 58.485 211.824Q58.207 211.461 57.821 211.208Q57.715 211.137 57.715 211.020Q57.715 210.935 57.775 210.875Q57.834 210.815 57.927 210.805L58.002 210.805Q58.050 210.805 58.080 210.826Q58.419 211.020 58.716 211.325Q59.014 211.629 59.207 211.974Q59.400 212.319 59.506 212.709Q59.612 213.099 59.612 213.519Q59.612 213.943 59.506 214.338Q59.400 214.732 59.203 215.079Q59.007 215.426 58.723 215.718Q58.439 216.011 58.087 216.223Q58.026 216.243 58.002 216.243\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-6.099 206.926v-8.381\"\u002F>\u003Cpath stroke=\"none\" d=\"m-6.099 195.945-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-6.099 178.473v-22.407\"\u002F>\u003Cpath stroke=\"none\" d=\"m-6.099 153.466-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-6.099 135.594v-9.604\"\u002F>\u003Cpath stroke=\"none\" d=\"m-6.099 123.39-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-6.099 108.764v-12.45\"\u002F>\u003Cpath stroke=\"none\" d=\"m-6.099 93.715-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-6.099 75.843v-9.604\"\u002F>\u003Cpath stroke=\"none\" d=\"m-6.099 63.64-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-6.099 49.013V37.215\"\u002F>\u003Cpath stroke=\"none\" d=\"m-6.099 34.615-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M129.052 158.756V-17.65h105.275v176.407ZM234.327-17.65\" style=\"stroke-dasharray:3.0,3.0\"\u002F>\u003Cpath fill=\"none\" d=\"M139.01 224.197h85.359v-17.071H139.01Z\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(158.038 1.653)\">\u003Cpath d=\"M-5.050 214.695L-5.050 213.136L-5.706 213.136Q-5.880 213.116-5.925 212.924L-5.925 212.849Q-5.880 212.664-5.706 212.644L-5.050 212.644L-5.050 211.988Q-5.005 211.807-4.831 211.783L-4.704 211.783Q-4.534 211.807-4.489 211.988L-4.489 212.644L-3.300 212.644Q-3.132 212.661-3.081 212.849L-3.081 212.924Q-3.129 213.116-3.300 213.136L-4.489 213.136L-4.489 214.667Q-4.489 215.207-3.987 215.207Q-3.768 215.207-3.624 215.045Q-3.481 214.883-3.481 214.667Q-3.481 214.585-3.418 214.524Q-3.354 214.462-3.266 214.452L-3.139 214.452Q-2.965 214.473-2.920 214.654L-2.920 214.695Q-2.920 214.978-3.081 215.209Q-3.242 215.440-3.498 215.568Q-3.754 215.696-4.035 215.696Q-4.482 215.696-4.766 215.424Q-5.050 215.153-5.050 214.695M-2.028 214.688Q-2.028 214.298-1.666 214.073Q-1.304 213.847-0.830 213.760Q-0.357 213.673 0.088 213.666Q0.088 213.478-0.030 213.345Q-0.148 213.211-0.329 213.145Q-0.511 213.078-0.695 213.078Q-0.996 213.078-1.136 213.099L-1.136 213.150Q-1.136 213.297-1.240 213.398Q-1.345 213.498-1.488 213.498Q-1.642 213.498-1.743 213.391Q-1.844 213.283-1.844 213.136Q-1.844 212.781-1.510 212.685Q-1.177 212.589-0.688 212.589Q-0.453 212.589-0.218 212.658Q0.016 212.726 0.212 212.858Q0.409 212.989 0.528 213.182Q0.648 213.375 0.648 213.618L0.648 215.122Q0.648 215.173 1.109 215.173Q1.280 215.190 1.325 215.375L1.325 215.454Q1.280 215.641 1.109 215.662L0.983 215.662Q0.682 215.662 0.482 215.621Q0.282 215.580 0.156 215.416Q-0.247 215.696-0.866 215.696Q-1.160 215.696-1.427 215.573Q-1.693 215.450-1.861 215.221Q-2.028 214.992-2.028 214.688M-1.468 214.695Q-1.468 214.934-1.256 215.071Q-1.044 215.207-0.794 215.207Q-0.603 215.207-0.400 215.156Q-0.196 215.105-0.054 214.984Q0.088 214.862 0.088 214.667L0.088 214.151Q-0.159 214.151-0.523 214.201Q-0.887 214.250-1.177 214.372Q-1.468 214.493-1.468 214.695M1.526 215.454L1.526 215.375Q1.578 215.194 1.745 215.173L2.367 215.173L2.367 213.136L1.745 213.136Q1.574 213.116 1.526 212.924L1.526 212.849Q1.578 212.664 1.745 212.644L2.709 212.644Q2.883 212.661 2.928 212.849L2.928 213.136Q3.157 212.887 3.468 212.748Q3.779 212.610 4.117 212.610Q4.374 212.610 4.579 212.728Q4.784 212.846 4.784 213.078Q4.784 213.225 4.688 213.328Q4.592 213.430 4.445 213.430Q4.312 213.430 4.211 213.333Q4.110 213.235 4.110 213.099Q3.782 213.099 3.507 213.275Q3.232 213.451 3.080 213.743Q2.928 214.035 2.928 214.367L2.928 215.173L3.755 215.173Q3.936 215.194 3.970 215.375L3.970 215.454Q3.936 215.641 3.755 215.662L1.745 215.662Q1.578 215.641 1.526 215.454M5.255 216.229Q5.255 215.966 5.385 215.737Q5.515 215.508 5.734 215.368Q5.573 215.146 5.573 214.866Q5.573 214.616 5.707 214.387Q5.488 214.103 5.488 213.738Q5.488 213.423 5.655 213.163Q5.823 212.904 6.101 212.757Q6.380 212.610 6.698 212.610Q6.879 212.610 7.057 212.663Q7.234 212.716 7.378 212.805Q7.713 212.576 8.127 212.576Q8.335 212.576 8.494 212.690Q8.653 212.805 8.653 213.003Q8.653 213.133 8.564 213.225Q8.475 213.317 8.338 213.317Q8.222 213.317 8.139 213.249Q8.055 213.181 8.027 213.071Q7.901 213.078 7.727 213.157Q7.904 213.430 7.904 213.738Q7.904 213.984 7.807 214.187Q7.710 214.391 7.539 214.546Q7.368 214.702 7.147 214.787Q6.927 214.872 6.698 214.872Q6.359 214.872 6.069 214.708Q6.059 214.708 6.050 214.772Q6.042 214.835 6.042 214.866Q6.042 214.972 6.100 215.066Q6.158 215.160 6.264 215.194Q6.277 215.190 6.289 215.189Q6.301 215.187 6.322 215.187Q6.336 215.187 6.363 215.194Q6.390 215.201 6.397 215.201L6.917 215.201Q7.600 215.201 8.074 215.412Q8.547 215.624 8.547 216.229Q8.547 216.493 8.390 216.691Q8.233 216.889 7.973 217.016Q7.713 217.142 7.433 217.200Q7.152 217.258 6.903 217.258Q6.561 217.258 6.175 217.151Q5.789 217.043 5.522 216.809Q5.255 216.575 5.255 216.229M5.727 216.223Q5.727 216.414 5.937 216.537Q6.148 216.660 6.431 216.718Q6.715 216.776 6.903 216.776Q7.091 216.776 7.375 216.718Q7.658 216.660 7.869 216.537Q8.079 216.414 8.079 216.223Q8.079 215.970 7.882 215.848Q7.686 215.727 7.440 215.698Q7.193 215.669 6.889 215.669L6.349 215.669Q6.189 215.669 6.047 215.739Q5.905 215.809 5.816 215.937Q5.727 216.065 5.727 216.223M6.698 214.387Q6.961 214.387 7.152 214.196Q7.344 214.004 7.344 213.738Q7.344 213.601 7.296 213.486Q7.248 213.372 7.156 213.280Q7.064 213.187 6.949 213.140Q6.835 213.092 6.698 213.092Q6.431 213.092 6.240 213.283Q6.048 213.475 6.048 213.738Q6.048 213.997 6.243 214.192Q6.438 214.387 6.698 214.387M11.835 214.360L9.699 214.360Q9.747 214.602 9.919 214.797Q10.092 214.992 10.335 215.100Q10.577 215.207 10.827 215.207Q11.240 215.207 11.435 214.954Q11.442 214.944 11.492 214.852Q11.541 214.760 11.584 214.722Q11.627 214.684 11.709 214.674L11.835 214.674Q12.003 214.691 12.054 214.879L12.054 214.927Q11.996 215.190 11.794 215.363Q11.592 215.536 11.319 215.616Q11.046 215.696 10.779 215.696Q10.355 215.696 9.971 215.496Q9.586 215.296 9.352 214.946Q9.118 214.596 9.118 214.165L9.118 214.114Q9.118 213.704 9.333 213.351Q9.548 212.999 9.906 212.794Q10.263 212.589 10.673 212.589Q11.114 212.589 11.423 212.784Q11.733 212.979 11.893 213.319Q12.054 213.659 12.054 214.100L12.054 214.151Q12.003 214.339 11.835 214.360M9.706 213.878L11.480 213.878Q11.439 213.519 11.230 213.298Q11.022 213.078 10.673 213.078Q10.328 213.078 10.059 213.307Q9.791 213.536 9.706 213.878M13.527 214.695L13.527 213.136L12.871 213.136Q12.696 213.116 12.652 212.924L12.652 212.849Q12.696 212.664 12.871 212.644L13.527 212.644L13.527 211.988Q13.571 211.807 13.746 211.783L13.872 211.783Q14.043 211.807 14.088 211.988L14.088 212.644L15.277 212.644Q15.444 212.661 15.496 212.849L15.496 212.924Q15.448 213.116 15.277 213.136L14.088 213.136L14.088 214.667Q14.088 215.207 14.590 215.207Q14.809 215.207 14.952 215.045Q15.096 214.883 15.096 214.667Q15.096 214.585 15.159 214.524Q15.222 214.462 15.311 214.452L15.438 214.452Q15.612 214.473 15.656 214.654L15.656 214.695Q15.656 214.978 15.496 215.209Q15.335 215.440 15.079 215.568Q14.822 215.696 14.542 215.696Q14.094 215.696 13.811 215.424Q13.527 215.153 13.527 214.695\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(158.038 1.653)\">\u003Cpath d=\"M22.657 216.223Q22.192 215.953 21.842 215.525Q21.492 215.098 21.307 214.579Q21.122 214.059 21.122 213.519Q21.122 212.979 21.305 212.464Q21.488 211.950 21.835 211.530Q22.182 211.109 22.650 210.826Q22.712 210.805 22.739 210.805L22.818 210.805Q22.903 210.815 22.961 210.873Q23.019 210.932 23.019 211.020Q23.019 211.147 22.931 211.202Q22.537 211.454 22.252 211.818Q21.967 212.183 21.825 212.613Q21.683 213.044 21.683 213.519Q21.683 213.874 21.767 214.213Q21.850 214.551 22.006 214.845Q22.162 215.139 22.389 215.387Q22.616 215.635 22.920 215.836Q23.019 215.905 23.019 216.024Q23.019 216.110 22.961 216.171Q22.903 216.233 22.818 216.243L22.739 216.243Q22.688 216.243 22.657 216.223M24.161 215.488L24.161 214.688Q24.185 214.507 24.370 214.486L24.516 214.486Q24.660 214.507 24.711 214.647Q24.889 215.207 25.525 215.207Q25.706 215.207 25.906 215.177Q26.106 215.146 26.253 215.045Q26.400 214.944 26.400 214.766Q26.400 214.582 26.205 214.483Q26.010 214.384 25.771 214.346L25.159 214.247Q24.161 214.062 24.161 213.430Q24.161 213.177 24.287 213.011Q24.414 212.846 24.624 212.752Q24.834 212.658 25.058 212.623Q25.282 212.589 25.525 212.589Q25.744 212.589 25.913 212.615Q26.082 212.641 26.225 212.709Q26.294 212.606 26.407 212.589L26.475 212.589Q26.560 212.600 26.615 212.654Q26.670 212.709 26.680 212.791L26.680 213.410Q26.670 213.492 26.615 213.550Q26.560 213.608 26.475 213.618L26.328 213.618Q26.246 213.608 26.188 213.550Q26.130 213.492 26.120 213.410Q26.120 213.078 25.511 213.078Q25.207 213.078 24.928 213.150Q24.650 213.222 24.650 213.437Q24.650 213.669 25.238 213.765L25.853 213.871Q26.277 213.943 26.583 214.160Q26.889 214.377 26.889 214.766Q26.889 215.108 26.682 215.320Q26.475 215.532 26.169 215.614Q25.863 215.696 25.525 215.696Q25.019 215.696 24.670 215.474Q24.609 215.583 24.566 215.633Q24.523 215.683 24.431 215.696L24.370 215.696Q24.182 215.676 24.161 215.488M27.425 215.454L27.425 215.375Q27.463 215.194 27.644 215.173L28.013 215.173L28.013 211.875L27.644 211.875Q27.463 211.854 27.425 211.666L27.425 211.588Q27.463 211.407 27.644 211.386L28.358 211.386Q28.529 211.407 28.574 211.588L28.574 212.945Q28.977 212.610 29.500 212.610Q29.804 212.610 30.013 212.733Q30.221 212.856 30.322 213.081Q30.423 213.307 30.423 213.618L30.423 215.173L30.795 215.173Q30.976 215.194 31.011 215.375L31.011 215.454Q30.976 215.641 30.795 215.662L29.575 215.662Q29.404 215.641 29.360 215.454L29.360 215.375Q29.404 215.190 29.575 215.173L29.862 215.173L29.862 213.645Q29.862 213.375 29.784 213.237Q29.705 213.099 29.449 213.099Q29.213 213.099 29.013 213.213Q28.813 213.328 28.693 213.527Q28.574 213.727 28.574 213.960L28.574 215.173L28.946 215.173Q29.127 215.194 29.162 215.375L29.162 215.454Q29.127 215.641 28.946 215.662L27.644 215.662Q27.463 215.641 27.425 215.454M31.619 215.454L31.619 215.375Q31.663 215.194 31.834 215.173L32.744 215.173L32.744 213.136L31.892 213.136Q31.718 213.116 31.674 212.924L31.674 212.849Q31.718 212.664 31.892 212.644L33.089 212.644Q33.260 212.661 33.304 212.849L33.304 215.173L34.104 215.173Q34.275 215.194 34.319 215.375L34.319 215.454Q34.275 215.641 34.104 215.662L31.834 215.662Q31.663 215.641 31.619 215.454M32.521 211.789L32.521 211.742Q32.521 211.591 32.641 211.485Q32.761 211.379 32.914 211.379Q33.065 211.379 33.184 211.485Q33.304 211.591 33.304 211.742L33.304 211.789Q33.304 211.943 33.184 212.049Q33.065 212.155 32.914 212.155Q32.761 212.155 32.641 212.049Q32.521 211.943 32.521 211.789M35.075 215.454L35.075 215.375Q35.119 215.194 35.290 215.173L36.062 215.173L36.062 213.136L35.314 213.136Q35.140 213.116 35.095 212.924L35.095 212.849Q35.140 212.664 35.314 212.644L36.062 212.644L36.062 212.247Q36.062 211.841 36.418 211.595Q36.773 211.349 37.194 211.349Q37.467 211.349 37.681 211.454Q37.894 211.560 37.894 211.807Q37.894 211.950 37.799 212.053Q37.703 212.155 37.559 212.155Q37.430 212.155 37.324 212.063Q37.218 211.971 37.218 211.841L37.146 211.841Q37.013 211.841 36.893 211.894Q36.773 211.947 36.698 212.047Q36.623 212.148 36.623 212.275L36.623 212.644L37.525 212.644Q37.696 212.661 37.741 212.849L37.741 212.924Q37.696 213.116 37.525 213.136L36.623 213.136L36.623 215.173L37.392 215.173Q37.563 215.194 37.607 215.375L37.607 215.454Q37.563 215.641 37.392 215.662L35.290 215.662Q35.119 215.641 35.075 215.454M39.559 214.695L39.559 213.136L38.903 213.136Q38.728 213.116 38.684 212.924L38.684 212.849Q38.728 212.664 38.903 212.644L39.559 212.644L39.559 211.988Q39.603 211.807 39.778 211.783L39.904 211.783Q40.075 211.807 40.120 211.988L40.120 212.644L41.309 212.644Q41.476 212.661 41.528 212.849L41.528 212.924Q41.480 213.116 41.309 213.136L40.120 213.136L40.120 214.667Q40.120 215.207 40.622 215.207Q40.841 215.207 40.984 215.045Q41.128 214.883 41.128 214.667Q41.128 214.585 41.191 214.524Q41.254 214.462 41.343 214.452L41.470 214.452Q41.644 214.473 41.688 214.654L41.688 214.695Q41.688 214.978 41.528 215.209Q41.367 215.440 41.111 215.568Q40.854 215.696 40.574 215.696Q40.126 215.696 39.843 215.424Q39.559 215.153 39.559 214.695M45.298 214.360L43.162 214.360Q43.209 214.602 43.382 214.797Q43.555 214.992 43.797 215.100Q44.040 215.207 44.289 215.207Q44.703 215.207 44.898 214.954Q44.905 214.944 44.954 214.852Q45.004 214.760 45.047 214.722Q45.089 214.684 45.171 214.674L45.298 214.674Q45.465 214.691 45.516 214.879L45.516 214.927Q45.458 215.190 45.257 215.363Q45.055 215.536 44.782 215.616Q44.508 215.696 44.242 215.696Q43.818 215.696 43.433 215.496Q43.049 215.296 42.815 214.946Q42.580 214.596 42.580 214.165L42.580 214.114Q42.580 213.704 42.796 213.351Q43.011 212.999 43.368 212.794Q43.725 212.589 44.136 212.589Q44.577 212.589 44.886 212.784Q45.195 212.979 45.356 213.319Q45.516 213.659 45.516 214.100L45.516 214.151Q45.465 214.339 45.298 214.360M43.168 213.878L44.942 213.878Q44.901 213.519 44.693 213.298Q44.484 213.078 44.136 213.078Q43.790 213.078 43.522 213.307Q43.254 213.536 43.168 213.878M47.571 215.696Q47.164 215.696 46.844 215.477Q46.525 215.259 46.345 214.905Q46.166 214.551 46.166 214.151Q46.166 213.850 46.275 213.570Q46.385 213.290 46.588 213.071Q46.791 212.852 47.058 212.731Q47.325 212.610 47.636 212.610Q48.083 212.610 48.439 212.890L48.439 211.875L48.070 211.875Q47.885 211.854 47.851 211.666L47.851 211.588Q47.885 211.407 48.070 211.386L48.781 211.386Q48.955 211.407 48.999 211.588L48.999 215.173L49.372 215.173Q49.553 215.194 49.587 215.375L49.587 215.454Q49.553 215.641 49.372 215.662L48.658 215.662Q48.483 215.641 48.439 215.454L48.439 215.341Q48.268 215.508 48.039 215.602Q47.810 215.696 47.571 215.696M47.605 215.207Q47.919 215.207 48.140 214.972Q48.360 214.736 48.439 214.408L48.439 213.680Q48.388 213.516 48.277 213.384Q48.165 213.252 48.010 213.175Q47.854 213.099 47.683 213.099Q47.413 213.099 47.195 213.247Q46.976 213.396 46.850 213.645Q46.723 213.895 46.723 214.158Q46.723 214.551 46.973 214.879Q47.222 215.207 47.605 215.207M50.565 216.243L50.490 216.243Q50.397 216.233 50.338 216.170Q50.278 216.106 50.278 216.024Q50.278 215.901 50.370 215.843Q50.664 215.655 50.900 215.402Q51.136 215.149 51.296 214.845Q51.457 214.541 51.536 214.209Q51.614 213.878 51.614 213.519Q51.614 213.047 51.471 212.617Q51.327 212.186 51.048 211.824Q50.770 211.461 50.384 211.208Q50.278 211.137 50.278 211.020Q50.278 210.935 50.338 210.875Q50.397 210.815 50.490 210.805L50.565 210.805Q50.613 210.805 50.643 210.826Q50.982 211.020 51.279 211.325Q51.577 211.629 51.770 211.974Q51.963 212.319 52.069 212.709Q52.175 213.099 52.175 213.519Q52.175 213.943 52.069 214.338Q51.963 214.732 51.766 215.079Q51.570 215.426 51.286 215.718Q51.002 216.011 50.650 216.223Q50.589 216.243 50.565 216.243\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M137.45 195.745h88.48v-17.072h-88.48Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(146.882 -27.092)\">\u003Cpath d=\"M-3.026 214.360L-5.162 214.360Q-5.115 214.602-4.942 214.797Q-4.769 214.992-4.527 215.100Q-4.284 215.207-4.035 215.207Q-3.621 215.207-3.426 214.954Q-3.419 214.944-3.370 214.852Q-3.320 214.760-3.277 214.722Q-3.235 214.684-3.153 214.674L-3.026 214.674Q-2.859 214.691-2.807 214.879L-2.807 214.927Q-2.866 215.190-3.067 215.363Q-3.269 215.536-3.542 215.616Q-3.816 215.696-4.082 215.696Q-4.506 215.696-4.891 215.496Q-5.275 215.296-5.509 214.946Q-5.744 214.596-5.744 214.165L-5.744 214.114Q-5.744 213.704-5.528 213.351Q-5.313 212.999-4.956 212.794Q-4.599 212.589-4.188 212.589Q-3.747 212.589-3.438 212.784Q-3.129 212.979-2.968 213.319Q-2.807 213.659-2.807 214.100L-2.807 214.151Q-2.859 214.339-3.026 214.360M-5.156 213.878L-3.382 213.878Q-3.423 213.519-3.631 213.298Q-3.840 213.078-4.188 213.078Q-4.534 213.078-4.802 213.307Q-5.070 213.536-5.156 213.878M-2.432 215.454L-2.432 215.375Q-2.387 215.190-2.216 215.173L-2.042 215.173L-2.042 213.136L-2.216 213.136Q-2.397 213.116-2.432 212.924L-2.432 212.849Q-2.387 212.661-2.216 212.644L-1.796 212.644Q-1.628 212.664-1.577 212.849Q-1.297 212.610-0.934 212.610Q-0.767 212.610-0.620 212.705Q-0.473 212.801-0.408 212.952Q-0.254 212.784-0.059 212.697Q0.135 212.610 0.347 212.610Q0.713 212.610 0.848 212.909Q0.983 213.208 0.983 213.618L0.983 215.173L1.157 215.173Q1.342 215.194 1.376 215.375L1.376 215.454Q1.332 215.641 1.157 215.662L0.443 215.662Q0.272 215.641 0.228 215.454L0.228 215.375Q0.272 215.194 0.443 215.173L0.522 215.173L0.522 213.645Q0.522 213.099 0.303 213.099Q0.012 213.099-0.143 213.370Q-0.299 213.642-0.299 213.960L-0.299 215.173L-0.121 215.173Q0.060 215.194 0.094 215.375L0.094 215.454Q0.050 215.641-0.121 215.662L-0.835 215.662Q-1.010 215.641-1.054 215.454L-1.054 215.375Q-1.010 215.194-0.835 215.173L-0.760 215.173L-0.760 213.645Q-0.760 213.099-0.975 213.099Q-1.266 213.099-1.422 213.372Q-1.577 213.645-1.577 213.960L-1.577 215.173L-1.403 215.173Q-1.222 215.194-1.187 215.375L-1.187 215.454Q-1.232 215.645-1.403 215.662L-2.216 215.662Q-2.397 215.641-2.432 215.454M1.981 215.454L1.981 211.875L1.612 211.875Q1.431 211.854 1.393 211.666L1.393 211.588Q1.431 211.407 1.612 211.386L2.326 211.386Q2.497 211.407 2.542 211.588L2.542 212.911Q2.726 212.764 2.957 212.687Q3.188 212.610 3.423 212.610Q3.721 212.610 3.981 212.736Q4.240 212.863 4.428 213.083Q4.616 213.304 4.717 213.577Q4.818 213.850 4.818 214.151Q4.818 214.558 4.620 214.917Q4.422 215.276 4.083 215.486Q3.745 215.696 3.335 215.696Q2.880 215.696 2.542 215.375L2.542 215.454Q2.497 215.645 2.326 215.662L2.200 215.662Q2.032 215.641 1.981 215.454M3.297 215.207Q3.567 215.207 3.786 215.059Q4.005 214.910 4.131 214.664Q4.257 214.418 4.257 214.151Q4.257 213.898 4.148 213.654Q4.039 213.410 3.835 213.254Q3.632 213.099 3.369 213.099Q3.088 213.099 2.859 213.261Q2.630 213.423 2.542 213.686L2.542 214.432Q2.620 214.753 2.813 214.980Q3.006 215.207 3.297 215.207M8.120 214.360L5.984 214.360Q6.031 214.602 6.204 214.797Q6.377 214.992 6.619 215.100Q6.862 215.207 7.111 215.207Q7.525 215.207 7.720 214.954Q7.727 214.944 7.776 214.852Q7.826 214.760 7.869 214.722Q7.911 214.684 7.993 214.674L8.120 214.674Q8.287 214.691 8.338 214.879L8.338 214.927Q8.280 215.190 8.079 215.363Q7.877 215.536 7.604 215.616Q7.330 215.696 7.064 215.696Q6.640 215.696 6.255 215.496Q5.871 215.296 5.637 214.946Q5.402 214.596 5.402 214.165L5.402 214.114Q5.402 213.704 5.618 213.351Q5.833 212.999 6.190 212.794Q6.547 212.589 6.958 212.589Q7.399 212.589 7.708 212.784Q8.017 212.979 8.178 213.319Q8.338 213.659 8.338 214.100L8.338 214.151Q8.287 214.339 8.120 214.360M5.990 213.878L7.764 213.878Q7.723 213.519 7.515 213.298Q7.306 213.078 6.958 213.078Q6.612 213.078 6.344 213.307Q6.076 213.536 5.990 213.878M10.393 215.696Q9.986 215.696 9.666 215.477Q9.347 215.259 9.167 214.905Q8.988 214.551 8.988 214.151Q8.988 213.850 9.097 213.570Q9.207 213.290 9.410 213.071Q9.613 212.852 9.880 212.731Q10.147 212.610 10.458 212.610Q10.905 212.610 11.261 212.890L11.261 211.875L10.892 211.875Q10.707 211.854 10.673 211.666L10.673 211.588Q10.707 211.407 10.892 211.386L11.603 211.386Q11.777 211.407 11.821 211.588L11.821 215.173L12.194 215.173Q12.375 215.194 12.409 215.375L12.409 215.454Q12.375 215.641 12.194 215.662L11.480 215.662Q11.305 215.641 11.261 215.454L11.261 215.341Q11.090 215.508 10.861 215.602Q10.632 215.696 10.393 215.696M10.427 215.207Q10.741 215.207 10.962 214.972Q11.182 214.736 11.261 214.408L11.261 213.680Q11.210 213.516 11.099 213.384Q10.987 213.252 10.832 213.175Q10.676 213.099 10.505 213.099Q10.235 213.099 10.017 213.247Q9.798 213.396 9.672 213.645Q9.545 213.895 9.545 214.158Q9.545 214.551 9.795 214.879Q10.044 215.207 10.427 215.207M14.108 215.696Q13.701 215.696 13.382 215.477Q13.062 215.259 12.883 214.905Q12.703 214.551 12.703 214.151Q12.703 213.850 12.813 213.570Q12.922 213.290 13.125 213.071Q13.329 212.852 13.595 212.731Q13.862 212.610 14.173 212.610Q14.621 212.610 14.976 212.890L14.976 211.875L14.607 211.875Q14.422 211.854 14.388 211.666L14.388 211.588Q14.422 211.407 14.607 211.386L15.318 211.386Q15.492 211.407 15.537 211.588L15.537 215.173L15.909 215.173Q16.090 215.194 16.125 215.375L16.125 215.454Q16.090 215.641 15.909 215.662L15.195 215.662Q15.021 215.641 14.976 215.454L14.976 215.341Q14.805 215.508 14.576 215.602Q14.347 215.696 14.108 215.696M14.142 215.207Q14.457 215.207 14.677 214.972Q14.898 214.736 14.976 214.408L14.976 213.680Q14.925 213.516 14.814 213.384Q14.703 213.252 14.547 213.175Q14.392 213.099 14.221 213.099Q13.951 213.099 13.732 213.247Q13.513 213.396 13.387 213.645Q13.260 213.895 13.260 214.158Q13.260 214.551 13.510 214.879Q13.759 215.207 14.142 215.207M16.733 215.454L16.733 215.375Q16.777 215.194 16.948 215.173L17.858 215.173L17.858 213.136L17.006 213.136Q16.832 213.116 16.788 212.924L16.788 212.849Q16.832 212.664 17.006 212.644L18.203 212.644Q18.374 212.661 18.418 212.849L18.418 215.173L19.218 215.173Q19.389 215.194 19.433 215.375L19.433 215.454Q19.389 215.641 19.218 215.662L16.948 215.662Q16.777 215.641 16.733 215.454M17.635 211.789L17.635 211.742Q17.635 211.591 17.755 211.485Q17.875 211.379 18.028 211.379Q18.179 211.379 18.298 211.485Q18.418 211.591 18.418 211.742L18.418 211.789Q18.418 211.943 18.298 212.049Q18.179 212.155 18.028 212.155Q17.875 212.155 17.755 212.049Q17.635 211.943 17.635 211.789M19.970 215.454L19.970 215.375Q20.007 215.194 20.189 215.173L20.558 215.173L20.558 213.136L20.189 213.136Q20.007 213.116 19.970 212.924L19.970 212.849Q20.011 212.664 20.189 212.644L20.903 212.644Q21.074 212.664 21.118 212.849L21.118 212.924L21.111 212.945Q21.310 212.787 21.549 212.699Q21.788 212.610 22.045 212.610Q22.349 212.610 22.557 212.733Q22.766 212.856 22.867 213.081Q22.967 213.307 22.967 213.618L22.967 215.173L23.340 215.173Q23.521 215.194 23.555 215.375L23.555 215.454Q23.521 215.641 23.340 215.662L22.120 215.662Q21.949 215.641 21.904 215.454L21.904 215.375Q21.949 215.190 22.120 215.173L22.407 215.173L22.407 213.645Q22.407 213.375 22.328 213.237Q22.250 213.099 21.993 213.099Q21.757 213.099 21.557 213.213Q21.358 213.328 21.238 213.527Q21.118 213.727 21.118 213.960L21.118 215.173L21.491 215.173Q21.672 215.194 21.706 215.375L21.706 215.454Q21.672 215.641 21.491 215.662L20.189 215.662Q20.007 215.641 19.970 215.454M23.832 216.229Q23.832 215.966 23.962 215.737Q24.092 215.508 24.311 215.368Q24.150 215.146 24.150 214.866Q24.150 214.616 24.283 214.387Q24.065 214.103 24.065 213.738Q24.065 213.423 24.232 213.163Q24.400 212.904 24.678 212.757Q24.957 212.610 25.275 212.610Q25.456 212.610 25.633 212.663Q25.811 212.716 25.955 212.805Q26.290 212.576 26.703 212.576Q26.912 212.576 27.071 212.690Q27.230 212.805 27.230 213.003Q27.230 213.133 27.141 213.225Q27.052 213.317 26.915 213.317Q26.799 213.317 26.715 213.249Q26.631 213.181 26.604 213.071Q26.478 213.078 26.303 213.157Q26.481 213.430 26.481 213.738Q26.481 213.984 26.384 214.187Q26.286 214.391 26.115 214.546Q25.944 214.702 25.724 214.787Q25.504 214.872 25.275 214.872Q24.936 214.872 24.646 214.708Q24.635 214.708 24.627 214.772Q24.618 214.835 24.618 214.866Q24.618 214.972 24.676 215.066Q24.734 215.160 24.840 215.194Q24.854 215.190 24.866 215.189Q24.878 215.187 24.899 215.187Q24.912 215.187 24.940 215.194Q24.967 215.201 24.974 215.201L25.493 215.201Q26.177 215.201 26.650 215.412Q27.124 215.624 27.124 216.229Q27.124 216.493 26.966 216.691Q26.809 216.889 26.549 217.016Q26.290 217.142 26.009 217.200Q25.729 217.258 25.480 217.258Q25.138 217.258 24.752 217.151Q24.365 217.043 24.099 216.809Q23.832 216.575 23.832 216.229M24.304 216.223Q24.304 216.414 24.514 216.537Q24.724 216.660 25.008 216.718Q25.292 216.776 25.480 216.776Q25.668 216.776 25.951 216.718Q26.235 216.660 26.445 216.537Q26.655 216.414 26.655 216.223Q26.655 215.970 26.459 215.848Q26.262 215.727 26.016 215.698Q25.770 215.669 25.466 215.669L24.926 215.669Q24.765 215.669 24.623 215.739Q24.482 215.809 24.393 215.937Q24.304 216.065 24.304 216.223M25.275 214.387Q25.538 214.387 25.729 214.196Q25.921 214.004 25.921 213.738Q25.921 213.601 25.873 213.486Q25.825 213.372 25.733 213.280Q25.640 213.187 25.526 213.140Q25.411 213.092 25.275 213.092Q25.008 213.092 24.817 213.283Q24.625 213.475 24.625 213.738Q24.625 213.997 24.820 214.192Q25.015 214.387 25.275 214.387\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(146.882 -27.092)\">\u003Cpath d=\"M32.678 214.855L32.678 213.792L31.615 213.792Q31.506 213.782 31.431 213.707Q31.356 213.632 31.356 213.519Q31.356 213.406 31.431 213.334Q31.506 213.263 31.615 213.252L32.678 213.252L32.678 212.183Q32.689 212.073 32.764 212.001Q32.839 211.930 32.952 211.930Q33.065 211.930 33.136 212.001Q33.208 212.073 33.218 212.183L33.218 213.252L34.281 213.252Q34.391 213.263 34.463 213.334Q34.534 213.406 34.534 213.519Q34.534 213.632 34.463 213.707Q34.391 213.782 34.281 213.792L33.218 213.792L33.218 214.855Q33.208 214.965 33.136 215.040Q33.065 215.115 32.952 215.115Q32.839 215.115 32.764 215.040Q32.689 214.965 32.678 214.855\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(146.882 -27.092)\">\u003Cpath d=\"M38.589 217.012L38.589 216.937Q38.626 216.745 38.807 216.725L39.176 216.725L39.176 213.136L38.807 213.136Q38.626 213.116 38.589 212.924L38.589 212.849Q38.630 212.664 38.807 212.644L39.522 212.644Q39.693 212.661 39.737 212.849L39.737 212.911Q39.922 212.764 40.152 212.687Q40.383 212.610 40.619 212.610Q40.916 212.610 41.176 212.736Q41.436 212.863 41.624 213.083Q41.812 213.304 41.912 213.577Q42.013 213.850 42.013 214.151Q42.013 214.558 41.815 214.917Q41.617 215.276 41.278 215.486Q40.940 215.696 40.530 215.696Q40.075 215.696 39.737 215.375L39.737 216.725L40.110 216.725Q40.291 216.745 40.325 216.937L40.325 217.012Q40.291 217.197 40.110 217.217L38.807 217.217Q38.630 217.197 38.589 217.012M40.492 215.207Q40.762 215.207 40.981 215.059Q41.200 214.910 41.326 214.664Q41.453 214.418 41.453 214.151Q41.453 213.898 41.343 213.654Q41.234 213.410 41.031 213.254Q40.827 213.099 40.564 213.099Q40.284 213.099 40.055 213.261Q39.826 213.423 39.737 213.686L39.737 214.432Q39.816 214.753 40.009 214.980Q40.202 215.207 40.492 215.207M44.098 215.696Q43.685 215.696 43.348 215.483Q43.011 215.269 42.817 214.910Q42.622 214.551 42.622 214.151Q42.622 213.850 42.731 213.568Q42.840 213.287 43.042 213.064Q43.244 212.842 43.512 212.716Q43.780 212.589 44.098 212.589Q44.416 212.589 44.690 212.717Q44.963 212.846 45.158 213.061Q45.353 213.276 45.464 213.557Q45.575 213.837 45.575 214.151Q45.575 214.551 45.378 214.912Q45.182 215.272 44.845 215.484Q44.508 215.696 44.098 215.696M44.098 215.207Q44.505 215.207 44.760 214.862Q45.014 214.517 45.014 214.093Q45.014 213.837 44.896 213.603Q44.778 213.369 44.568 213.223Q44.358 213.078 44.098 213.078Q43.832 213.078 43.623 213.223Q43.415 213.369 43.297 213.603Q43.179 213.837 43.179 214.093Q43.179 214.514 43.435 214.860Q43.692 215.207 44.098 215.207M46.470 215.488L46.470 214.688Q46.494 214.507 46.679 214.486L46.826 214.486Q46.969 214.507 47.021 214.647Q47.198 215.207 47.834 215.207Q48.015 215.207 48.215 215.177Q48.415 215.146 48.562 215.045Q48.709 214.944 48.709 214.766Q48.709 214.582 48.514 214.483Q48.319 214.384 48.080 214.346L47.468 214.247Q46.470 214.062 46.470 213.430Q46.470 213.177 46.597 213.011Q46.723 212.846 46.933 212.752Q47.144 212.658 47.368 212.623Q47.591 212.589 47.834 212.589Q48.053 212.589 48.222 212.615Q48.391 212.641 48.535 212.709Q48.603 212.606 48.716 212.589L48.784 212.589Q48.870 212.600 48.924 212.654Q48.979 212.709 48.989 212.791L48.989 213.410Q48.979 213.492 48.924 213.550Q48.870 213.608 48.784 213.618L48.637 213.618Q48.555 213.608 48.497 213.550Q48.439 213.492 48.429 213.410Q48.429 213.078 47.820 213.078Q47.516 213.078 47.238 213.150Q46.959 213.222 46.959 213.437Q46.959 213.669 47.547 213.765L48.162 213.871Q48.586 213.943 48.892 214.160Q49.198 214.377 49.198 214.766Q49.198 215.108 48.991 215.320Q48.784 215.532 48.478 215.614Q48.173 215.696 47.834 215.696Q47.328 215.696 46.980 215.474Q46.918 215.583 46.875 215.633Q46.833 215.683 46.740 215.696L46.679 215.696Q46.491 215.676 46.470 215.488M51.044 215.173Q51.044 214.978 51.189 214.833Q51.334 214.688 51.536 214.688Q51.666 214.688 51.777 214.756Q51.888 214.825 51.953 214.934Q52.018 215.043 52.018 215.173Q52.018 215.371 51.872 215.517Q51.727 215.662 51.536 215.662Q51.338 215.662 51.191 215.515Q51.044 215.368 51.044 215.173\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(146.882 -27.092)\">\u003Cpath d=\"M63.912 214.360L61.776 214.360Q61.823 214.602 61.996 214.797Q62.169 214.992 62.411 215.100Q62.654 215.207 62.903 215.207Q63.317 215.207 63.512 214.954Q63.519 214.944 63.568 214.852Q63.618 214.760 63.661 214.722Q63.703 214.684 63.785 214.674L63.912 214.674Q64.079 214.691 64.131 214.879L64.131 214.927Q64.072 215.190 63.871 215.363Q63.669 215.536 63.396 215.616Q63.122 215.696 62.856 215.696Q62.432 215.696 62.047 215.496Q61.663 215.296 61.429 214.946Q61.194 214.596 61.194 214.165L61.194 214.114Q61.194 213.704 61.410 213.351Q61.625 212.999 61.982 212.794Q62.339 212.589 62.750 212.589Q63.191 212.589 63.500 212.784Q63.809 212.979 63.970 213.319Q64.131 213.659 64.131 214.100L64.131 214.151Q64.079 214.339 63.912 214.360M61.782 213.878L63.556 213.878Q63.515 213.519 63.307 213.298Q63.098 213.078 62.750 213.078Q62.404 213.078 62.136 213.307Q61.868 213.536 61.782 213.878M64.616 215.454L64.616 215.375Q64.653 215.194 64.835 215.173L65.204 215.173L65.204 213.136L64.835 213.136Q64.653 213.116 64.616 212.924L64.616 212.849Q64.657 212.664 64.835 212.644L65.549 212.644Q65.720 212.664 65.764 212.849L65.764 212.924L65.757 212.945Q65.956 212.787 66.195 212.699Q66.434 212.610 66.691 212.610Q66.995 212.610 67.203 212.733Q67.412 212.856 67.513 213.081Q67.613 213.307 67.613 213.618L67.613 215.173L67.986 215.173Q68.167 215.194 68.201 215.375L68.201 215.454Q68.167 215.641 67.986 215.662L66.766 215.662Q66.595 215.641 66.550 215.454L66.550 215.375Q66.595 215.190 66.766 215.173L67.053 215.173L67.053 213.645Q67.053 213.375 66.974 213.237Q66.896 213.099 66.639 213.099Q66.403 213.099 66.204 213.213Q66.004 213.328 65.884 213.527Q65.764 213.727 65.764 213.960L65.764 215.173L66.137 215.173Q66.318 215.194 66.352 215.375L66.352 215.454Q66.318 215.641 66.137 215.662L64.835 215.662Q64.653 215.641 64.616 215.454M68.758 214.151Q68.758 213.731 68.972 213.369Q69.186 213.006 69.550 212.798Q69.914 212.589 70.334 212.589Q70.819 212.589 71.151 212.685Q71.483 212.781 71.483 213.136Q71.483 213.283 71.383 213.391Q71.284 213.498 71.134 213.498Q70.984 213.498 70.879 213.398Q70.775 213.297 70.775 213.150L70.775 213.099Q70.635 213.078 70.341 213.078Q70.054 213.078 69.820 213.227Q69.586 213.375 69.452 213.623Q69.319 213.871 69.319 214.151Q69.319 214.432 69.469 214.678Q69.620 214.924 69.869 215.066Q70.119 215.207 70.406 215.207Q70.679 215.207 70.790 215.117Q70.901 215.026 71.004 214.860Q71.107 214.695 71.209 214.681L71.356 214.681Q71.448 214.691 71.505 214.751Q71.561 214.811 71.561 214.900Q71.561 214.941 71.544 214.975Q71.448 215.231 71.271 215.389Q71.093 215.546 70.852 215.621Q70.611 215.696 70.334 215.696Q69.910 215.696 69.546 215.488Q69.182 215.279 68.970 214.927Q68.758 214.575 68.758 214.151M73.356 215.173Q73.356 214.978 73.501 214.833Q73.646 214.688 73.848 214.688Q73.978 214.688 74.089 214.756Q74.200 214.825 74.265 214.934Q74.330 215.043 74.330 215.173Q74.330 215.371 74.184 215.517Q74.039 215.662 73.848 215.662Q73.650 215.662 73.503 215.515Q73.356 215.368 73.356 215.173\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-warn)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M139.01 153.066h85.359v-17.072H139.01Z\"\u002F>\u003Cg fill=\"var(--tk-warn)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(148.741 -68.993)\">\u003Cpath d=\"M-6.147 215.454L-6.147 215.375Q-6.102 215.190-5.932 215.173L-5.757 215.173L-5.757 213.136L-5.932 213.136Q-6.113 213.116-6.147 212.924L-6.147 212.849Q-6.102 212.661-5.932 212.644L-5.511 212.644Q-5.344 212.664-5.292 212.849Q-5.012 212.610-4.650 212.610Q-4.482 212.610-4.335 212.705Q-4.188 212.801-4.123 212.952Q-3.970 212.784-3.775 212.697Q-3.580 212.610-3.368 212.610Q-3.002 212.610-2.867 212.909Q-2.732 213.208-2.732 213.618L-2.732 215.173L-2.558 215.173Q-2.373 215.194-2.339 215.375L-2.339 215.454Q-2.384 215.641-2.558 215.662L-3.272 215.662Q-3.443 215.641-3.488 215.454L-3.488 215.375Q-3.443 215.194-3.272 215.173L-3.194 215.173L-3.194 213.645Q-3.194 213.099-3.412 213.099Q-3.703 213.099-3.859 213.370Q-4.014 213.642-4.014 213.960L-4.014 215.173L-3.836 215.173Q-3.655 215.194-3.621 215.375L-3.621 215.454Q-3.665 215.641-3.836 215.662L-4.551 215.662Q-4.725 215.641-4.769 215.454L-4.769 215.375Q-4.725 215.194-4.551 215.173L-4.475 215.173L-4.475 213.645Q-4.475 213.099-4.691 213.099Q-4.981 213.099-5.137 213.372Q-5.292 213.645-5.292 213.960L-5.292 215.173L-5.118 215.173Q-4.937 215.194-4.903 215.375L-4.903 215.454Q-4.947 215.645-5.118 215.662L-5.932 215.662Q-6.113 215.641-6.147 215.454M-2.028 214.688Q-2.028 214.298-1.666 214.073Q-1.304 213.847-0.830 213.760Q-0.357 213.673 0.088 213.666Q0.088 213.478-0.030 213.345Q-0.148 213.211-0.329 213.145Q-0.511 213.078-0.695 213.078Q-0.996 213.078-1.136 213.099L-1.136 213.150Q-1.136 213.297-1.240 213.398Q-1.345 213.498-1.488 213.498Q-1.642 213.498-1.743 213.391Q-1.844 213.283-1.844 213.136Q-1.844 212.781-1.510 212.685Q-1.177 212.589-0.688 212.589Q-0.453 212.589-0.218 212.658Q0.016 212.726 0.212 212.858Q0.409 212.989 0.528 213.182Q0.648 213.375 0.648 213.618L0.648 215.122Q0.648 215.173 1.109 215.173Q1.280 215.190 1.325 215.375L1.325 215.454Q1.280 215.641 1.109 215.662L0.983 215.662Q0.682 215.662 0.482 215.621Q0.282 215.580 0.156 215.416Q-0.247 215.696-0.866 215.696Q-1.160 215.696-1.427 215.573Q-1.693 215.450-1.861 215.221Q-2.028 214.992-2.028 214.688M-1.468 214.695Q-1.468 214.934-1.256 215.071Q-1.044 215.207-0.794 215.207Q-0.603 215.207-0.400 215.156Q-0.196 215.105-0.054 214.984Q0.088 214.862 0.088 214.667L0.088 214.151Q-0.159 214.151-0.523 214.201Q-0.887 214.250-1.177 214.372Q-1.468 214.493-1.468 214.695M1.844 215.488L1.844 214.688Q1.868 214.507 2.053 214.486L2.200 214.486Q2.343 214.507 2.395 214.647Q2.572 215.207 3.208 215.207Q3.389 215.207 3.589 215.177Q3.789 215.146 3.936 215.045Q4.083 214.944 4.083 214.766Q4.083 214.582 3.888 214.483Q3.693 214.384 3.454 214.346L2.842 214.247Q1.844 214.062 1.844 213.430Q1.844 213.177 1.971 213.011Q2.097 212.846 2.307 212.752Q2.518 212.658 2.742 212.623Q2.965 212.589 3.208 212.589Q3.427 212.589 3.596 212.615Q3.765 212.641 3.909 212.709Q3.977 212.606 4.090 212.589L4.158 212.589Q4.244 212.600 4.298 212.654Q4.353 212.709 4.363 212.791L4.363 213.410Q4.353 213.492 4.298 213.550Q4.244 213.608 4.158 213.618L4.011 213.618Q3.929 213.608 3.871 213.550Q3.813 213.492 3.803 213.410Q3.803 213.078 3.194 213.078Q2.890 213.078 2.612 213.150Q2.333 213.222 2.333 213.437Q2.333 213.669 2.921 213.765L3.536 213.871Q3.960 213.943 4.266 214.160Q4.572 214.377 4.572 214.766Q4.572 215.108 4.365 215.320Q4.158 215.532 3.852 215.614Q3.547 215.696 3.208 215.696Q2.702 215.696 2.354 215.474Q2.292 215.583 2.249 215.633Q2.207 215.683 2.114 215.696L2.053 215.696Q1.865 215.676 1.844 215.488M5.173 215.454L5.173 215.375Q5.218 215.194 5.389 215.173L5.796 215.173L5.796 211.875L5.389 211.875Q5.218 211.854 5.173 211.666L5.173 211.588Q5.218 211.407 5.389 211.386L6.042 211.386Q6.213 211.403 6.257 211.588L6.257 214.059L7.258 213.136L6.999 213.136Q6.818 213.116 6.783 212.924L6.783 212.849Q6.818 212.664 6.999 212.644L8.267 212.644Q8.444 212.664 8.485 212.849L8.485 212.924Q8.448 213.116 8.267 213.136L7.945 213.136L7.118 213.891L8.127 215.173L8.421 215.173Q8.602 215.194 8.639 215.375L8.639 215.454Q8.602 215.641 8.421 215.662L7.399 215.662Q7.228 215.641 7.183 215.454L7.183 215.375Q7.228 215.194 7.399 215.173L7.539 215.173L6.783 214.206L6.257 214.688L6.257 215.173L6.664 215.173Q6.831 215.194 6.882 215.375L6.882 215.454Q6.831 215.641 6.664 215.662L5.389 215.662Q5.218 215.641 5.173 215.454M11.835 214.360L9.699 214.360Q9.747 214.602 9.919 214.797Q10.092 214.992 10.335 215.100Q10.577 215.207 10.827 215.207Q11.240 215.207 11.435 214.954Q11.442 214.944 11.492 214.852Q11.541 214.760 11.584 214.722Q11.627 214.684 11.709 214.674L11.835 214.674Q12.003 214.691 12.054 214.879L12.054 214.927Q11.996 215.190 11.794 215.363Q11.592 215.536 11.319 215.616Q11.046 215.696 10.779 215.696Q10.355 215.696 9.971 215.496Q9.586 215.296 9.352 214.946Q9.118 214.596 9.118 214.165L9.118 214.114Q9.118 213.704 9.333 213.351Q9.548 212.999 9.906 212.794Q10.263 212.589 10.673 212.589Q11.114 212.589 11.423 212.784Q11.733 212.979 11.893 213.319Q12.054 213.659 12.054 214.100L12.054 214.151Q12.003 214.339 11.835 214.360M9.706 213.878L11.480 213.878Q11.439 213.519 11.230 213.298Q11.022 213.078 10.673 213.078Q10.328 213.078 10.059 213.307Q9.791 213.536 9.706 213.878M14.108 215.696Q13.701 215.696 13.382 215.477Q13.062 215.259 12.883 214.905Q12.703 214.551 12.703 214.151Q12.703 213.850 12.813 213.570Q12.922 213.290 13.125 213.071Q13.329 212.852 13.595 212.731Q13.862 212.610 14.173 212.610Q14.621 212.610 14.976 212.890L14.976 211.875L14.607 211.875Q14.422 211.854 14.388 211.666L14.388 211.588Q14.422 211.407 14.607 211.386L15.318 211.386Q15.492 211.407 15.537 211.588L15.537 215.173L15.909 215.173Q16.090 215.194 16.125 215.375L16.125 215.454Q16.090 215.641 15.909 215.662L15.195 215.662Q15.021 215.641 14.976 215.454L14.976 215.341Q14.805 215.508 14.576 215.602Q14.347 215.696 14.108 215.696M14.142 215.207Q14.457 215.207 14.677 214.972Q14.898 214.736 14.976 214.408L14.976 213.680Q14.925 213.516 14.814 213.384Q14.703 213.252 14.547 213.175Q14.392 213.099 14.221 213.099Q13.951 213.099 13.732 213.247Q13.513 213.396 13.387 213.645Q13.260 213.895 13.260 214.158Q13.260 214.551 13.510 214.879Q13.759 215.207 14.142 215.207\" fill=\"var(--tk-warn)\" stroke=\"var(--tk-warn)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(148.741 -68.993)\">\u003Cpath d=\"M20.446 215.488L20.446 214.688Q20.470 214.507 20.654 214.486L20.801 214.486Q20.945 214.507 20.996 214.647Q21.174 215.207 21.809 215.207Q21.991 215.207 22.191 215.177Q22.391 215.146 22.537 215.045Q22.684 214.944 22.684 214.766Q22.684 214.582 22.490 214.483Q22.295 214.384 22.056 214.346L21.444 214.247Q20.446 214.062 20.446 213.430Q20.446 213.177 20.572 213.011Q20.699 212.846 20.909 212.752Q21.119 212.658 21.343 212.623Q21.567 212.589 21.809 212.589Q22.028 212.589 22.197 212.615Q22.367 212.641 22.510 212.709Q22.579 212.606 22.691 212.589L22.760 212.589Q22.845 212.600 22.900 212.654Q22.954 212.709 22.965 212.791L22.965 213.410Q22.954 213.492 22.900 213.550Q22.845 213.608 22.760 213.618L22.613 213.618Q22.531 213.608 22.473 213.550Q22.414 213.492 22.404 213.410Q22.404 213.078 21.796 213.078Q21.492 213.078 21.213 213.150Q20.934 213.222 20.934 213.437Q20.934 213.669 21.522 213.765L22.138 213.871Q22.561 213.943 22.867 214.160Q23.173 214.377 23.173 214.766Q23.173 215.108 22.966 215.320Q22.760 215.532 22.454 215.614Q22.148 215.696 21.809 215.696Q21.304 215.696 20.955 215.474Q20.893 215.583 20.851 215.633Q20.808 215.683 20.716 215.696L20.654 215.696Q20.466 215.676 20.446 215.488M26.721 214.360L24.585 214.360Q24.633 214.602 24.805 214.797Q24.978 214.992 25.221 215.100Q25.463 215.207 25.713 215.207Q26.126 215.207 26.321 214.954Q26.328 214.944 26.378 214.852Q26.427 214.760 26.470 214.722Q26.513 214.684 26.595 214.674L26.721 214.674Q26.889 214.691 26.940 214.879L26.940 214.927Q26.882 215.190 26.680 215.363Q26.478 215.536 26.205 215.616Q25.932 215.696 25.665 215.696Q25.241 215.696 24.857 215.496Q24.472 215.296 24.238 214.946Q24.004 214.596 24.004 214.165L24.004 214.114Q24.004 213.704 24.219 213.351Q24.434 212.999 24.792 212.794Q25.149 212.589 25.559 212.589Q26 212.589 26.309 212.784Q26.619 212.979 26.779 213.319Q26.940 213.659 26.940 214.100L26.940 214.151Q26.889 214.339 26.721 214.360M24.592 213.878L26.366 213.878Q26.325 213.519 26.116 213.298Q25.908 213.078 25.559 213.078Q25.214 213.078 24.945 213.307Q24.677 213.536 24.592 213.878M27.757 215.454L27.757 215.375Q27.801 215.194 27.972 215.173L28.939 215.173L28.939 211.875L27.972 211.875Q27.801 211.854 27.757 211.666L27.757 211.588Q27.801 211.407 27.972 211.386L29.281 211.386Q29.449 211.407 29.500 211.588L29.500 215.173L30.464 215.173Q30.638 215.194 30.683 215.375L30.683 215.454Q30.638 215.641 30.464 215.662L27.972 215.662Q27.801 215.641 27.757 215.454M31.359 215.454L31.359 215.375Q31.404 215.194 31.575 215.173L32.347 215.173L32.347 213.136L31.599 213.136Q31.424 213.116 31.380 212.924L31.380 212.849Q31.424 212.664 31.599 212.644L32.347 212.644L32.347 212.247Q32.347 211.841 32.703 211.595Q33.058 211.349 33.478 211.349Q33.752 211.349 33.965 211.454Q34.179 211.560 34.179 211.807Q34.179 211.950 34.083 212.053Q33.988 212.155 33.844 212.155Q33.714 212.155 33.608 212.063Q33.502 211.971 33.502 211.841L33.431 211.841Q33.297 211.841 33.178 211.894Q33.058 211.947 32.983 212.047Q32.908 212.148 32.908 212.275L32.908 212.644L33.810 212.644Q33.981 212.661 34.025 212.849L34.025 212.924Q33.981 213.116 33.810 213.136L32.908 213.136L32.908 215.173L33.677 215.173Q33.848 215.194 33.892 215.375L33.892 215.454Q33.848 215.641 33.677 215.662L31.575 215.662Q31.404 215.641 31.359 215.454M37.853 213.792L35.454 213.792Q35.345 213.782 35.269 213.707Q35.194 213.632 35.194 213.519Q35.194 213.406 35.269 213.334Q35.345 213.263 35.454 213.252L37.853 213.252Q37.963 213.263 38.035 213.334Q38.106 213.406 38.106 213.519Q38.106 213.632 38.035 213.707Q37.963 213.782 37.853 213.792M38.865 214.688Q38.865 214.298 39.227 214.073Q39.590 213.847 40.063 213.760Q40.537 213.673 40.981 213.666Q40.981 213.478 40.863 213.345Q40.745 213.211 40.564 213.145Q40.383 213.078 40.198 213.078Q39.897 213.078 39.757 213.099L39.757 213.150Q39.757 213.297 39.653 213.398Q39.549 213.498 39.405 213.498Q39.251 213.498 39.151 213.391Q39.050 213.283 39.050 213.136Q39.050 212.781 39.383 212.685Q39.716 212.589 40.205 212.589Q40.441 212.589 40.675 212.658Q40.909 212.726 41.106 212.858Q41.302 212.989 41.422 213.182Q41.541 213.375 41.541 213.618L41.541 215.122Q41.541 215.173 42.003 215.173Q42.174 215.190 42.218 215.375L42.218 215.454Q42.174 215.641 42.003 215.662L41.876 215.662Q41.576 215.662 41.376 215.621Q41.176 215.580 41.049 215.416Q40.646 215.696 40.027 215.696Q39.733 215.696 39.467 215.573Q39.200 215.450 39.033 215.221Q38.865 214.992 38.865 214.688M39.426 214.695Q39.426 214.934 39.638 215.071Q39.850 215.207 40.099 215.207Q40.290 215.207 40.494 215.156Q40.697 215.105 40.839 214.984Q40.981 214.862 40.981 214.667L40.981 214.151Q40.735 214.151 40.371 214.201Q40.007 214.250 39.716 214.372Q39.426 214.493 39.426 214.695M43.274 214.695L43.274 213.136L42.618 213.136Q42.444 213.116 42.399 212.924L42.399 212.849Q42.444 212.664 42.618 212.644L43.274 212.644L43.274 211.988Q43.319 211.807 43.493 211.783L43.620 211.783Q43.790 211.807 43.835 211.988L43.835 212.644L45.024 212.644Q45.192 212.661 45.243 212.849L45.243 212.924Q45.195 213.116 45.024 213.136L43.835 213.136L43.835 214.667Q43.835 215.207 44.337 215.207Q44.556 215.207 44.700 215.045Q44.843 214.883 44.843 214.667Q44.843 214.585 44.906 214.524Q44.970 214.462 45.058 214.452L45.185 214.452Q45.359 214.473 45.404 214.654L45.404 214.695Q45.404 214.978 45.243 215.209Q45.082 215.440 44.826 215.568Q44.570 215.696 44.289 215.696Q43.842 215.696 43.558 215.424Q43.274 215.153 43.274 214.695M46.990 214.695L46.990 213.136L46.333 213.136Q46.159 213.116 46.115 212.924L46.115 212.849Q46.159 212.664 46.333 212.644L46.990 212.644L46.990 211.988Q47.034 211.807 47.208 211.783L47.335 211.783Q47.506 211.807 47.550 211.988L47.550 212.644L48.740 212.644Q48.907 212.661 48.958 212.849L48.958 212.924Q48.911 213.116 48.740 213.136L47.550 213.136L47.550 214.667Q47.550 215.207 48.053 215.207Q48.271 215.207 48.415 215.045Q48.558 214.883 48.558 214.667Q48.558 214.585 48.622 214.524Q48.685 214.462 48.774 214.452L48.900 214.452Q49.075 214.473 49.119 214.654L49.119 214.695Q49.119 214.978 48.958 215.209Q48.798 215.440 48.541 215.568Q48.285 215.696 48.005 215.696Q47.557 215.696 47.273 215.424Q46.990 215.153 46.990 214.695M52.728 214.360L50.592 214.360Q50.640 214.602 50.813 214.797Q50.985 214.992 51.228 215.100Q51.471 215.207 51.720 215.207Q52.134 215.207 52.329 214.954Q52.335 214.944 52.385 214.852Q52.434 214.760 52.477 214.722Q52.520 214.684 52.602 214.674L52.728 214.674Q52.896 214.691 52.947 214.879L52.947 214.927Q52.889 215.190 52.687 215.363Q52.486 215.536 52.212 215.616Q51.939 215.696 51.672 215.696Q51.248 215.696 50.864 215.496Q50.479 215.296 50.245 214.946Q50.011 214.596 50.011 214.165L50.011 214.114Q50.011 213.704 50.226 213.351Q50.442 212.999 50.799 212.794Q51.156 212.589 51.566 212.589Q52.007 212.589 52.317 212.784Q52.626 212.979 52.787 213.319Q52.947 213.659 52.947 214.100L52.947 214.151Q52.896 214.339 52.728 214.360M50.599 213.878L52.373 213.878Q52.332 213.519 52.123 213.298Q51.915 213.078 51.566 213.078Q51.221 213.078 50.953 213.307Q50.684 213.536 50.599 213.878M53.433 215.454L53.433 215.375Q53.470 215.194 53.651 215.173L54.020 215.173L54.020 213.136L53.651 213.136Q53.470 213.116 53.433 212.924L53.433 212.849Q53.474 212.664 53.651 212.644L54.366 212.644Q54.537 212.664 54.581 212.849L54.581 212.924L54.574 212.945Q54.772 212.787 55.012 212.699Q55.251 212.610 55.507 212.610Q55.811 212.610 56.020 212.733Q56.228 212.856 56.329 213.081Q56.430 213.307 56.430 213.618L56.430 215.173L56.803 215.173Q56.984 215.194 57.018 215.375L57.018 215.454Q56.984 215.641 56.803 215.662L55.582 215.662Q55.412 215.641 55.367 215.454L55.367 215.375Q55.412 215.190 55.582 215.173L55.870 215.173L55.870 213.645Q55.870 213.375 55.791 213.237Q55.712 213.099 55.456 213.099Q55.220 213.099 55.020 213.213Q54.820 213.328 54.701 213.527Q54.581 213.727 54.581 213.960L54.581 215.173L54.954 215.173Q55.135 215.194 55.169 215.375L55.169 215.454Q55.135 215.641 54.954 215.662L53.651 215.662Q53.470 215.641 53.433 215.454M58.136 214.695L58.136 213.136L57.479 213.136Q57.305 213.116 57.261 212.924L57.261 212.849Q57.305 212.664 57.479 212.644L58.136 212.644L58.136 211.988Q58.180 211.807 58.354 211.783L58.481 211.783Q58.652 211.807 58.696 211.988L58.696 212.644L59.886 212.644Q60.053 212.661 60.104 212.849L60.104 212.924Q60.057 213.116 59.886 213.136L58.696 213.136L58.696 214.667Q58.696 215.207 59.199 215.207Q59.417 215.207 59.561 215.045Q59.704 214.883 59.704 214.667Q59.704 214.585 59.768 214.524Q59.831 214.462 59.920 214.452L60.046 214.452Q60.221 214.473 60.265 214.654L60.265 214.695Q60.265 214.978 60.104 215.209Q59.944 215.440 59.687 215.568Q59.431 215.696 59.151 215.696Q58.703 215.696 58.419 215.424Q58.136 215.153 58.136 214.695M61.342 215.454L61.342 215.375Q61.386 215.194 61.557 215.173L62.466 215.173L62.466 213.136L61.615 213.136Q61.441 213.116 61.396 212.924L61.396 212.849Q61.441 212.664 61.615 212.644L62.811 212.644Q62.982 212.661 63.027 212.849L63.027 215.173L63.827 215.173Q63.997 215.194 64.042 215.375L64.042 215.454Q63.997 215.641 63.827 215.662L61.557 215.662Q61.386 215.641 61.342 215.454M62.244 211.789L62.244 211.742Q62.244 211.591 62.364 211.485Q62.483 211.379 62.637 211.379Q62.787 211.379 62.907 211.485Q63.027 211.591 63.027 211.742L63.027 211.789Q63.027 211.943 62.907 212.049Q62.787 212.155 62.637 212.155Q62.483 212.155 62.364 212.049Q62.244 211.943 62.244 211.789M66.373 215.696Q65.959 215.696 65.623 215.483Q65.286 215.269 65.091 214.910Q64.896 214.551 64.896 214.151Q64.896 213.850 65.006 213.568Q65.115 213.287 65.317 213.064Q65.518 212.842 65.787 212.716Q66.055 212.589 66.373 212.589Q66.691 212.589 66.964 212.717Q67.238 212.846 67.433 213.061Q67.627 213.276 67.738 213.557Q67.850 213.837 67.850 214.151Q67.850 214.551 67.653 214.912Q67.456 215.272 67.120 215.484Q66.783 215.696 66.373 215.696M66.373 215.207Q66.780 215.207 67.034 214.862Q67.289 214.517 67.289 214.093Q67.289 213.837 67.171 213.603Q67.053 213.369 66.843 213.223Q66.633 213.078 66.373 213.078Q66.106 213.078 65.898 213.223Q65.689 213.369 65.571 213.603Q65.454 213.837 65.454 214.093Q65.454 214.514 65.710 214.860Q65.966 215.207 66.373 215.207M68.294 215.454L68.294 215.375Q68.331 215.194 68.513 215.173L68.882 215.173L68.882 213.136L68.513 213.136Q68.331 213.116 68.294 212.924L68.294 212.849Q68.335 212.664 68.513 212.644L69.227 212.644Q69.398 212.664 69.442 212.849L69.442 212.924L69.435 212.945Q69.634 212.787 69.873 212.699Q70.112 212.610 70.369 212.610Q70.673 212.610 70.881 212.733Q71.090 212.856 71.191 213.081Q71.291 213.307 71.291 213.618L71.291 215.173L71.664 215.173Q71.845 215.194 71.879 215.375L71.879 215.454Q71.845 215.641 71.664 215.662L70.444 215.662Q70.273 215.641 70.228 215.454L70.228 215.375Q70.273 215.190 70.444 215.173L70.731 215.173L70.731 213.645Q70.731 213.375 70.652 213.237Q70.574 213.099 70.317 213.099Q70.081 213.099 69.881 213.213Q69.682 213.328 69.562 213.527Q69.442 213.727 69.442 213.960L69.442 215.173L69.815 215.173Q69.996 215.194 70.030 215.375L70.030 215.454Q69.996 215.641 69.815 215.662L68.513 215.662Q68.331 215.641 68.294 215.454\" fill=\"var(--tk-warn)\" stroke=\"var(--tk-warn)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M139.01 123.19h85.359v-14.226H139.01Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(169.194 -97.446)\">\u003Cpath d=\"M-5.744 214.688Q-5.744 214.298-5.381 214.073Q-5.019 213.847-4.546 213.760Q-4.072 213.673-3.628 213.666Q-3.628 213.478-3.746 213.345Q-3.864 213.211-4.045 213.145Q-4.226 213.078-4.411 213.078Q-4.711 213.078-4.851 213.099L-4.851 213.150Q-4.851 213.297-4.956 213.398Q-5.060 213.498-5.203 213.498Q-5.357 213.498-5.458 213.391Q-5.559 213.283-5.559 213.136Q-5.559 212.781-5.226 212.685Q-4.892 212.589-4.404 212.589Q-4.168 212.589-3.934 212.658Q-3.700 212.726-3.503 212.858Q-3.307 212.989-3.187 213.182Q-3.067 213.375-3.067 213.618L-3.067 215.122Q-3.067 215.173-2.606 215.173Q-2.435 215.190-2.391 215.375L-2.391 215.454Q-2.435 215.641-2.606 215.662L-2.732 215.662Q-3.033 215.662-3.233 215.621Q-3.433 215.580-3.559 215.416Q-3.963 215.696-4.581 215.696Q-4.875 215.696-5.142 215.573Q-5.409 215.450-5.576 215.221Q-5.744 214.992-5.744 214.688M-5.183 214.695Q-5.183 214.934-4.971 215.071Q-4.759 215.207-4.510 215.207Q-4.318 215.207-4.115 215.156Q-3.912 215.105-3.770 214.984Q-3.628 214.862-3.628 214.667L-3.628 214.151Q-3.874 214.151-4.238 214.201Q-4.602 214.250-4.892 214.372Q-5.183 214.493-5.183 214.695M-0.753 215.696Q-1.160 215.696-1.480 215.477Q-1.799 215.259-1.979 214.905Q-2.158 214.551-2.158 214.151Q-2.158 213.850-2.049 213.570Q-1.939 213.290-1.736 213.071Q-1.533 212.852-1.266 212.731Q-0.999 212.610-0.688 212.610Q-0.241 212.610 0.115 212.890L0.115 211.875L-0.254 211.875Q-0.439 211.854-0.473 211.666L-0.473 211.588Q-0.439 211.407-0.254 211.386L0.457 211.386Q0.631 211.407 0.675 211.588L0.675 215.173L1.048 215.173Q1.229 215.194 1.263 215.375L1.263 215.454Q1.229 215.641 1.048 215.662L0.334 215.662Q0.159 215.641 0.115 215.454L0.115 215.341Q-0.056 215.508-0.285 215.602Q-0.514 215.696-0.753 215.696M-0.719 215.207Q-0.405 215.207-0.184 214.972Q0.036 214.736 0.115 214.408L0.115 213.680Q0.064 213.516-0.047 213.384Q-0.159 213.252-0.314 213.175Q-0.470 213.099-0.641 213.099Q-0.911 213.099-1.129 213.247Q-1.348 213.396-1.474 213.645Q-1.601 213.895-1.601 214.158Q-1.601 214.551-1.351 214.879Q-1.102 215.207-0.719 215.207M2.962 215.696Q2.555 215.696 2.236 215.477Q1.916 215.259 1.737 214.905Q1.557 214.551 1.557 214.151Q1.557 213.850 1.667 213.570Q1.776 213.290 1.979 213.071Q2.183 212.852 2.449 212.731Q2.716 212.610 3.027 212.610Q3.475 212.610 3.830 212.890L3.830 211.875L3.461 211.875Q3.276 211.854 3.242 211.666L3.242 211.588Q3.276 211.407 3.461 211.386L4.172 211.386Q4.346 211.407 4.391 211.588L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L4.049 215.662Q3.875 215.641 3.830 215.454L3.830 215.341Q3.659 215.508 3.430 215.602Q3.201 215.696 2.962 215.696M2.996 215.207Q3.311 215.207 3.531 214.972Q3.752 214.736 3.830 214.408L3.830 213.680Q3.779 213.516 3.668 213.384Q3.557 213.252 3.401 213.175Q3.246 213.099 3.075 213.099Q2.805 213.099 2.586 213.247Q2.367 213.396 2.241 213.645Q2.114 213.895 2.114 214.158Q2.114 214.551 2.364 214.879Q2.613 215.207 2.996 215.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(169.194 -97.446)\">\u003Cpath d=\"M9.839 215.730Q9.579 215.730 9.383 215.580Q9.186 215.430 9.078 215.189Q8.971 214.948 8.971 214.702L8.971 214.654Q8.971 214.428 9.051 214.221Q9.131 214.015 9.272 213.878L9.672 213.478Q9.477 212.921 9.477 212.350L9.477 212.302Q9.477 212.070 9.571 211.839Q9.665 211.608 9.844 211.461Q10.024 211.314 10.266 211.314Q10.509 211.314 10.666 211.465Q10.823 211.615 10.892 211.844Q10.960 212.073 10.960 212.302L10.960 212.350Q10.960 212.586 10.849 212.810Q10.738 213.034 10.593 213.208Q10.447 213.382 10.218 213.611Q10.376 213.970 10.693 214.466Q10.881 214.114 11.155 213.379L11.254 213.122Q11.131 213.092 11.093 212.924L11.093 212.849Q11.138 212.664 11.309 212.644L12.030 212.644Q12.204 212.661 12.249 212.849L12.249 212.924Q12.204 213.116 12.030 213.136L11.743 213.136L11.575 213.577Q11.240 214.473 10.994 214.886Q11.145 215.050 11.271 215.146Q11.398 215.242 11.555 215.242Q11.661 215.242 11.709 215.122Q11.756 215.002 11.756 214.872Q11.811 214.667 11.989 214.667Q12.167 214.667 12.221 214.872L12.221 214.920Q12.221 215.238 12.038 215.484Q11.856 215.730 11.555 215.730Q11.138 215.730 10.721 215.276Q10.321 215.730 9.839 215.730M9.839 215.242Q10.147 215.242 10.420 214.900Q10.058 214.339 9.877 213.967Q9.777 214.059 9.716 214.129Q9.654 214.199 9.612 214.271Q9.569 214.343 9.550 214.440Q9.531 214.537 9.531 214.654Q9.531 214.845 9.605 215.043Q9.678 215.242 9.839 215.242M10.037 213.099Q10.235 212.883 10.367 212.695Q10.499 212.507 10.499 212.323Q10.499 212.159 10.446 211.983Q10.393 211.807 10.266 211.807Q10.106 211.807 10.022 211.979Q9.938 212.152 9.938 212.336Q9.938 212.719 10.037 213.099\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(169.194 -97.446)\">\u003Cpath d=\"M16.276 215.454L16.276 215.375Q16.313 215.194 16.494 215.173L16.863 215.173L16.863 213.136L16.494 213.136Q16.313 213.116 16.276 212.924L16.276 212.849Q16.317 212.664 16.494 212.644L17.209 212.644Q17.380 212.664 17.424 212.849L17.424 212.924L17.417 212.945Q17.615 212.787 17.855 212.699Q18.094 212.610 18.350 212.610Q18.654 212.610 18.863 212.733Q19.071 212.856 19.172 213.081Q19.273 213.307 19.273 213.618L19.273 215.173L19.646 215.173Q19.827 215.194 19.861 215.375L19.861 215.454Q19.827 215.641 19.646 215.662L18.425 215.662Q18.255 215.641 18.210 215.454L18.210 215.375Q18.255 215.190 18.425 215.173L18.713 215.173L18.713 213.645Q18.713 213.375 18.634 213.237Q18.555 213.099 18.299 213.099Q18.063 213.099 17.863 213.213Q17.663 213.328 17.544 213.527Q17.424 213.727 17.424 213.960L17.424 215.173L17.797 215.173Q17.978 215.194 18.012 215.375L18.012 215.454Q17.978 215.641 17.797 215.662L16.494 215.662Q16.313 215.641 16.276 215.454M21.785 215.696Q21.372 215.696 21.035 215.483Q20.698 215.269 20.504 214.910Q20.309 214.551 20.309 214.151Q20.309 213.850 20.418 213.568Q20.527 213.287 20.729 213.064Q20.931 212.842 21.199 212.716Q21.467 212.589 21.785 212.589Q22.103 212.589 22.377 212.717Q22.650 212.846 22.845 213.061Q23.040 213.276 23.151 213.557Q23.262 213.837 23.262 214.151Q23.262 214.551 23.065 214.912Q22.869 215.272 22.532 215.484Q22.195 215.696 21.785 215.696M21.785 215.207Q22.192 215.207 22.447 214.862Q22.701 214.517 22.701 214.093Q22.701 213.837 22.583 213.603Q22.465 213.369 22.255 213.223Q22.045 213.078 21.785 213.078Q21.519 213.078 21.310 213.223Q21.102 213.369 20.984 213.603Q20.866 213.837 20.866 214.093Q20.866 214.514 21.122 214.860Q21.379 215.207 21.785 215.207M23.839 215.454L23.839 215.375Q23.891 215.194 24.058 215.173L24.680 215.173L24.680 213.136L24.058 213.136Q23.887 213.116 23.839 212.924L23.839 212.849Q23.891 212.664 24.058 212.644L25.022 212.644Q25.196 212.661 25.241 212.849L25.241 213.136Q25.470 212.887 25.781 212.748Q26.092 212.610 26.430 212.610Q26.687 212.610 26.892 212.728Q27.097 212.846 27.097 213.078Q27.097 213.225 27.001 213.328Q26.905 213.430 26.758 213.430Q26.625 213.430 26.524 213.333Q26.423 213.235 26.423 213.099Q26.095 213.099 25.820 213.275Q25.545 213.451 25.393 213.743Q25.241 214.035 25.241 214.367L25.241 215.173L26.068 215.173Q26.249 215.194 26.283 215.375L26.283 215.454Q26.249 215.641 26.068 215.662L24.058 215.662Q23.891 215.641 23.839 215.454M27.312 215.454L27.312 215.375Q27.357 215.190 27.527 215.173L27.702 215.173L27.702 213.136L27.527 213.136Q27.346 213.116 27.312 212.924L27.312 212.849Q27.357 212.661 27.527 212.644L27.948 212.644Q28.115 212.664 28.167 212.849Q28.447 212.610 28.809 212.610Q28.977 212.610 29.124 212.705Q29.271 212.801 29.336 212.952Q29.489 212.784 29.684 212.697Q29.879 212.610 30.091 212.610Q30.457 212.610 30.592 212.909Q30.727 213.208 30.727 213.618L30.727 215.173L30.901 215.173Q31.086 215.194 31.120 215.375L31.120 215.454Q31.075 215.641 30.901 215.662L30.187 215.662Q30.016 215.641 29.971 215.454L29.971 215.375Q30.016 215.194 30.187 215.173L30.265 215.173L30.265 213.645Q30.265 213.099 30.047 213.099Q29.756 213.099 29.600 213.370Q29.445 213.642 29.445 213.960L29.445 215.173L29.623 215.173Q29.804 215.194 29.838 215.375L29.838 215.454Q29.794 215.641 29.623 215.662L28.908 215.662Q28.734 215.641 28.690 215.454L28.690 215.375Q28.734 215.194 28.908 215.173L28.984 215.173L28.984 213.645Q28.984 213.099 28.768 213.099Q28.478 213.099 28.322 213.372Q28.167 213.645 28.167 213.960L28.167 215.173L28.341 215.173Q28.522 215.194 28.556 215.375L28.556 215.454Q28.512 215.645 28.341 215.662L27.527 215.662Q27.346 215.641 27.312 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M139.01 93.315h85.359V76.243H139.01Z\"\u002F>\u003Cg transform=\"translate(159.897 -128.744)\">\u003Cpath d=\"M-5.610 214.151Q-5.610 213.731-5.397 213.369Q-5.183 213.006-4.819 212.798Q-4.455 212.589-4.035 212.589Q-3.549 212.589-3.218 212.685Q-2.886 212.781-2.886 213.136Q-2.886 213.283-2.985 213.391Q-3.084 213.498-3.235 213.498Q-3.385 213.498-3.489 213.398Q-3.594 213.297-3.594 213.150L-3.594 213.099Q-3.734 213.078-4.028 213.078Q-4.315 213.078-4.549 213.227Q-4.783 213.375-4.916 213.623Q-5.050 213.871-5.050 214.151Q-5.050 214.432-4.899 214.678Q-4.749 214.924-4.499 215.066Q-4.250 215.207-3.963 215.207Q-3.689 215.207-3.578 215.117Q-3.467 215.026-3.365 214.860Q-3.262 214.695-3.160 214.681L-3.013 214.681Q-2.920 214.691-2.864 214.751Q-2.807 214.811-2.807 214.900Q-2.807 214.941-2.825 214.975Q-2.920 215.231-3.098 215.389Q-3.276 215.546-3.517 215.621Q-3.758 215.696-4.035 215.696Q-4.458 215.696-4.822 215.488Q-5.186 215.279-5.398 214.927Q-5.610 214.575-5.610 214.151M-2.189 215.454L-2.189 215.375Q-2.138 215.194-1.970 215.173L-1.348 215.173L-1.348 213.136L-1.970 213.136Q-2.141 213.116-2.189 212.924L-2.189 212.849Q-2.138 212.664-1.970 212.644L-1.006 212.644Q-0.832 212.661-0.787 212.849L-0.787 213.136Q-0.558 212.887-0.247 212.748Q0.064 212.610 0.402 212.610Q0.658 212.610 0.863 212.728Q1.068 212.846 1.068 213.078Q1.068 213.225 0.973 213.328Q0.877 213.430 0.730 213.430Q0.597 213.430 0.496 213.333Q0.395 213.235 0.395 213.099Q0.067 213.099-0.208 213.275Q-0.483 213.451-0.635 213.743Q-0.787 214.035-0.787 214.367L-0.787 215.173L0.040 215.173Q0.221 215.194 0.255 215.375L0.255 215.454Q0.221 215.641 0.040 215.662L-1.970 215.662Q-2.138 215.641-2.189 215.454M3.188 215.696Q2.774 215.696 2.437 215.483Q2.101 215.269 1.906 214.910Q1.711 214.551 1.711 214.151Q1.711 213.850 1.820 213.568Q1.930 213.287 2.131 213.064Q2.333 212.842 2.601 212.716Q2.870 212.589 3.188 212.589Q3.505 212.589 3.779 212.717Q4.052 212.846 4.247 213.061Q4.442 213.276 4.553 213.557Q4.664 213.837 4.664 214.151Q4.664 214.551 4.468 214.912Q4.271 215.272 3.934 215.484Q3.598 215.696 3.188 215.696M3.188 215.207Q3.594 215.207 3.849 214.862Q4.104 214.517 4.104 214.093Q4.104 213.837 3.986 213.603Q3.868 213.369 3.658 213.223Q3.447 213.078 3.188 213.078Q2.921 213.078 2.713 213.223Q2.504 213.369 2.386 213.603Q2.268 213.837 2.268 214.093Q2.268 214.514 2.525 214.860Q2.781 215.207 3.188 215.207M5.560 215.488L5.560 214.688Q5.584 214.507 5.768 214.486L5.915 214.486Q6.059 214.507 6.110 214.647Q6.288 215.207 6.923 215.207Q7.105 215.207 7.305 215.177Q7.505 215.146 7.651 215.045Q7.798 214.944 7.798 214.766Q7.798 214.582 7.604 214.483Q7.409 214.384 7.170 214.346L6.558 214.247Q5.560 214.062 5.560 213.430Q5.560 213.177 5.686 213.011Q5.813 212.846 6.023 212.752Q6.233 212.658 6.457 212.623Q6.681 212.589 6.923 212.589Q7.142 212.589 7.311 212.615Q7.481 212.641 7.624 212.709Q7.693 212.606 7.805 212.589L7.874 212.589Q7.959 212.600 8.014 212.654Q8.068 212.709 8.079 212.791L8.079 213.410Q8.068 213.492 8.014 213.550Q7.959 213.608 7.874 213.618L7.727 213.618Q7.645 213.608 7.587 213.550Q7.528 213.492 7.518 213.410Q7.518 213.078 6.910 213.078Q6.606 213.078 6.327 213.150Q6.048 213.222 6.048 213.437Q6.048 213.669 6.636 213.765L7.252 213.871Q7.675 213.943 7.981 214.160Q8.287 214.377 8.287 214.766Q8.287 215.108 8.080 215.320Q7.874 215.532 7.568 215.614Q7.262 215.696 6.923 215.696Q6.418 215.696 6.069 215.474Q6.007 215.583 5.965 215.633Q5.922 215.683 5.830 215.696L5.768 215.696Q5.580 215.676 5.560 215.488M9.275 215.488L9.275 214.688Q9.299 214.507 9.484 214.486L9.630 214.486Q9.774 214.507 9.825 214.647Q10.003 215.207 10.639 215.207Q10.820 215.207 11.020 215.177Q11.220 215.146 11.367 215.045Q11.514 214.944 11.514 214.766Q11.514 214.582 11.319 214.483Q11.124 214.384 10.885 214.346L10.273 214.247Q9.275 214.062 9.275 213.430Q9.275 213.177 9.401 213.011Q9.528 212.846 9.738 212.752Q9.948 212.658 10.172 212.623Q10.396 212.589 10.639 212.589Q10.858 212.589 11.027 212.615Q11.196 212.641 11.339 212.709Q11.408 212.606 11.521 212.589L11.589 212.589Q11.674 212.600 11.729 212.654Q11.784 212.709 11.794 212.791L11.794 213.410Q11.784 213.492 11.729 213.550Q11.674 213.608 11.589 213.618L11.442 213.618Q11.360 213.608 11.302 213.550Q11.244 213.492 11.234 213.410Q11.234 213.078 10.625 213.078Q10.321 213.078 10.042 213.150Q9.764 213.222 9.764 213.437Q9.764 213.669 10.352 213.765L10.967 213.871Q11.391 213.943 11.697 214.160Q12.003 214.377 12.003 214.766Q12.003 215.108 11.796 215.320Q11.589 215.532 11.283 215.614Q10.977 215.696 10.639 215.696Q10.133 215.696 9.784 215.474Q9.723 215.583 9.680 215.633Q9.637 215.683 9.545 215.696L9.484 215.696Q9.296 215.676 9.275 215.488M15.537 213.792L13.137 213.792Q13.028 213.782 12.953 213.707Q12.878 213.632 12.878 213.519Q12.878 213.406 12.953 213.334Q13.028 213.263 13.137 213.252L15.537 213.252Q15.646 213.263 15.718 213.334Q15.790 213.406 15.790 213.519Q15.790 213.632 15.718 213.707Q15.646 213.782 15.537 213.792M16.548 214.688Q16.548 214.298 16.911 214.073Q17.273 213.847 17.746 213.760Q18.220 213.673 18.664 213.666Q18.664 213.478 18.546 213.345Q18.428 213.211 18.247 213.145Q18.066 213.078 17.881 213.078Q17.581 213.078 17.441 213.099L17.441 213.150Q17.441 213.297 17.336 213.398Q17.232 213.498 17.088 213.498Q16.935 213.498 16.834 213.391Q16.733 213.283 16.733 213.136Q16.733 212.781 17.066 212.685Q17.400 212.589 17.888 212.589Q18.124 212.589 18.358 212.658Q18.592 212.726 18.789 212.858Q18.985 212.989 19.105 213.182Q19.225 213.375 19.225 213.618L19.225 215.122Q19.225 215.173 19.686 215.173Q19.857 215.190 19.901 215.375L19.901 215.454Q19.857 215.641 19.686 215.662L19.560 215.662Q19.259 215.662 19.059 215.621Q18.859 215.580 18.733 215.416Q18.329 215.696 17.711 215.696Q17.417 215.696 17.150 215.573Q16.883 215.450 16.716 215.221Q16.548 214.992 16.548 214.688M17.109 214.695Q17.109 214.934 17.321 215.071Q17.533 215.207 17.782 215.207Q17.974 215.207 18.177 215.156Q18.380 215.105 18.522 214.984Q18.664 214.862 18.664 214.667L18.664 214.151Q18.418 214.151 18.054 214.201Q17.690 214.250 17.400 214.372Q17.109 214.493 17.109 214.695M20.958 214.695L20.958 213.136L20.301 213.136Q20.127 213.116 20.083 212.924L20.083 212.849Q20.127 212.664 20.301 212.644L20.958 212.644L20.958 211.988Q21.002 211.807 21.176 211.783L21.303 211.783Q21.474 211.807 21.518 211.988L21.518 212.644L22.708 212.644Q22.875 212.661 22.926 212.849L22.926 212.924Q22.879 213.116 22.708 213.136L21.518 213.136L21.518 214.667Q21.518 215.207 22.021 215.207Q22.239 215.207 22.383 215.045Q22.526 214.883 22.526 214.667Q22.526 214.585 22.590 214.524Q22.653 214.462 22.742 214.452L22.868 214.452Q23.043 214.473 23.087 214.654L23.087 214.695Q23.087 214.978 22.926 215.209Q22.766 215.440 22.509 215.568Q22.253 215.696 21.973 215.696Q21.525 215.696 21.241 215.424Q20.958 215.153 20.958 214.695M24.673 214.695L24.673 213.136L24.017 213.136Q23.842 213.116 23.798 212.924L23.798 212.849Q23.842 212.664 24.017 212.644L24.673 212.644L24.673 211.988Q24.717 211.807 24.892 211.783L25.018 211.783Q25.189 211.807 25.234 211.988L25.234 212.644L26.423 212.644Q26.590 212.661 26.642 212.849L26.642 212.924Q26.594 213.116 26.423 213.136L25.234 213.136L25.234 214.667Q25.234 215.207 25.736 215.207Q25.955 215.207 26.098 215.045Q26.242 214.883 26.242 214.667Q26.242 214.585 26.305 214.524Q26.368 214.462 26.457 214.452L26.584 214.452Q26.758 214.473 26.802 214.654L26.802 214.695Q26.802 214.978 26.642 215.209Q26.481 215.440 26.225 215.568Q25.968 215.696 25.688 215.696Q25.240 215.696 24.957 215.424Q24.673 215.153 24.673 214.695M30.412 214.360L28.276 214.360Q28.323 214.602 28.496 214.797Q28.669 214.992 28.911 215.100Q29.154 215.207 29.403 215.207Q29.817 215.207 30.012 214.954Q30.019 214.944 30.068 214.852Q30.118 214.760 30.161 214.722Q30.203 214.684 30.285 214.674L30.412 214.674Q30.579 214.691 30.630 214.879L30.630 214.927Q30.572 215.190 30.371 215.363Q30.169 215.536 29.896 215.616Q29.622 215.696 29.356 215.696Q28.932 215.696 28.547 215.496Q28.163 215.296 27.929 214.946Q27.694 214.596 27.694 214.165L27.694 214.114Q27.694 213.704 27.910 213.351Q28.125 212.999 28.482 212.794Q28.839 212.589 29.250 212.589Q29.691 212.589 30 212.784Q30.309 212.979 30.470 213.319Q30.630 213.659 30.630 214.100L30.630 214.151Q30.579 214.339 30.412 214.360M28.282 213.878L30.056 213.878Q30.015 213.519 29.807 213.298Q29.598 213.078 29.250 213.078Q28.904 213.078 28.636 213.307Q28.368 213.536 28.282 213.878M31.116 215.454L31.116 215.375Q31.153 215.194 31.335 215.173L31.704 215.173L31.704 213.136L31.335 213.136Q31.153 213.116 31.116 212.924L31.116 212.849Q31.157 212.664 31.335 212.644L32.049 212.644Q32.220 212.664 32.264 212.849L32.264 212.924L32.257 212.945Q32.456 212.787 32.695 212.699Q32.934 212.610 33.191 212.610Q33.495 212.610 33.703 212.733Q33.912 212.856 34.013 213.081Q34.113 213.307 34.113 213.618L34.113 215.173L34.486 215.173Q34.667 215.194 34.701 215.375L34.701 215.454Q34.667 215.641 34.486 215.662L33.266 215.662Q33.095 215.641 33.050 215.454L33.050 215.375Q33.095 215.190 33.266 215.173L33.553 215.173L33.553 213.645Q33.553 213.375 33.474 213.237Q33.396 213.099 33.139 213.099Q32.903 213.099 32.703 213.213Q32.504 213.328 32.384 213.527Q32.264 213.727 32.264 213.960L32.264 215.173L32.637 215.173Q32.818 215.194 32.852 215.375L32.852 215.454Q32.818 215.641 32.637 215.662L31.335 215.662Q31.153 215.641 31.116 215.454M35.819 214.695L35.819 213.136L35.163 213.136Q34.988 213.116 34.944 212.924L34.944 212.849Q34.988 212.664 35.163 212.644L35.819 212.644L35.819 211.988Q35.863 211.807 36.038 211.783L36.164 211.783Q36.335 211.807 36.380 211.988L36.380 212.644L37.569 212.644Q37.736 212.661 37.788 212.849L37.788 212.924Q37.740 213.116 37.569 213.136L36.380 213.136L36.380 214.667Q36.380 215.207 36.882 215.207Q37.101 215.207 37.244 215.045Q37.388 214.883 37.388 214.667Q37.388 214.585 37.451 214.524Q37.514 214.462 37.603 214.452L37.730 214.452Q37.904 214.473 37.948 214.654L37.948 214.695Q37.948 214.978 37.788 215.209Q37.627 215.440 37.371 215.568Q37.114 215.696 36.834 215.696Q36.386 215.696 36.103 215.424Q35.819 215.153 35.819 214.695M39.025 215.454L39.025 215.375Q39.069 215.194 39.240 215.173L40.150 215.173L40.150 213.136L39.298 213.136Q39.124 213.116 39.080 212.924L39.080 212.849Q39.124 212.664 39.298 212.644L40.495 212.644Q40.666 212.661 40.710 212.849L40.710 215.173L41.510 215.173Q41.681 215.194 41.725 215.375L41.725 215.454Q41.681 215.641 41.510 215.662L39.240 215.662Q39.069 215.641 39.025 215.454M39.927 211.789L39.927 211.742Q39.927 211.591 40.047 211.485Q40.167 211.379 40.320 211.379Q40.471 211.379 40.590 211.485Q40.710 211.591 40.710 211.742L40.710 211.789Q40.710 211.943 40.590 212.049Q40.471 212.155 40.320 212.155Q40.167 212.155 40.047 212.049Q39.927 211.943 39.927 211.789M44.056 215.696Q43.643 215.696 43.306 215.483Q42.969 215.269 42.775 214.910Q42.580 214.551 42.580 214.151Q42.580 213.850 42.689 213.568Q42.798 213.287 43 213.064Q43.202 212.842 43.470 212.716Q43.738 212.589 44.056 212.589Q44.374 212.589 44.648 212.717Q44.921 212.846 45.116 213.061Q45.311 213.276 45.422 213.557Q45.533 213.837 45.533 214.151Q45.533 214.551 45.336 214.912Q45.140 215.272 44.803 215.484Q44.466 215.696 44.056 215.696M44.056 215.207Q44.463 215.207 44.718 214.862Q44.972 214.517 44.972 214.093Q44.972 213.837 44.854 213.603Q44.736 213.369 44.526 213.223Q44.316 213.078 44.056 213.078Q43.790 213.078 43.581 213.223Q43.373 213.369 43.255 213.603Q43.137 213.837 43.137 214.093Q43.137 214.514 43.393 214.860Q43.650 215.207 44.056 215.207M45.977 215.454L45.977 215.375Q46.015 215.194 46.196 215.173L46.565 215.173L46.565 213.136L46.196 213.136Q46.015 213.116 45.977 212.924L45.977 212.849Q46.018 212.664 46.196 212.644L46.910 212.644Q47.081 212.664 47.126 212.849L47.126 212.924L47.119 212.945Q47.317 212.787 47.556 212.699Q47.796 212.610 48.052 212.610Q48.356 212.610 48.565 212.733Q48.773 212.856 48.874 213.081Q48.975 213.307 48.975 213.618L48.975 215.173L49.347 215.173Q49.528 215.194 49.563 215.375L49.563 215.454Q49.528 215.641 49.347 215.662L48.127 215.662Q47.956 215.641 47.912 215.454L47.912 215.375Q47.956 215.190 48.127 215.173L48.414 215.173L48.414 213.645Q48.414 213.375 48.336 213.237Q48.257 213.099 48.001 213.099Q47.765 213.099 47.565 213.213Q47.365 213.328 47.245 213.527Q47.126 213.727 47.126 213.960L47.126 215.173L47.498 215.173Q47.679 215.194 47.713 215.375L47.713 215.454Q47.679 215.641 47.498 215.662L46.196 215.662Q46.015 215.641 45.977 215.454\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M139.01 63.44h85.359V49.212H139.01Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(169.194 -157.197)\">\u003Cpath d=\"M-5.744 214.688Q-5.744 214.298-5.381 214.073Q-5.019 213.847-4.546 213.760Q-4.072 213.673-3.628 213.666Q-3.628 213.478-3.746 213.345Q-3.864 213.211-4.045 213.145Q-4.226 213.078-4.411 213.078Q-4.711 213.078-4.851 213.099L-4.851 213.150Q-4.851 213.297-4.956 213.398Q-5.060 213.498-5.203 213.498Q-5.357 213.498-5.458 213.391Q-5.559 213.283-5.559 213.136Q-5.559 212.781-5.226 212.685Q-4.892 212.589-4.404 212.589Q-4.168 212.589-3.934 212.658Q-3.700 212.726-3.503 212.858Q-3.307 212.989-3.187 213.182Q-3.067 213.375-3.067 213.618L-3.067 215.122Q-3.067 215.173-2.606 215.173Q-2.435 215.190-2.391 215.375L-2.391 215.454Q-2.435 215.641-2.606 215.662L-2.732 215.662Q-3.033 215.662-3.233 215.621Q-3.433 215.580-3.559 215.416Q-3.963 215.696-4.581 215.696Q-4.875 215.696-5.142 215.573Q-5.409 215.450-5.576 215.221Q-5.744 214.992-5.744 214.688M-5.183 214.695Q-5.183 214.934-4.971 215.071Q-4.759 215.207-4.510 215.207Q-4.318 215.207-4.115 215.156Q-3.912 215.105-3.770 214.984Q-3.628 214.862-3.628 214.667L-3.628 214.151Q-3.874 214.151-4.238 214.201Q-4.602 214.250-4.892 214.372Q-5.183 214.493-5.183 214.695M-0.753 215.696Q-1.160 215.696-1.480 215.477Q-1.799 215.259-1.979 214.905Q-2.158 214.551-2.158 214.151Q-2.158 213.850-2.049 213.570Q-1.939 213.290-1.736 213.071Q-1.533 212.852-1.266 212.731Q-0.999 212.610-0.688 212.610Q-0.241 212.610 0.115 212.890L0.115 211.875L-0.254 211.875Q-0.439 211.854-0.473 211.666L-0.473 211.588Q-0.439 211.407-0.254 211.386L0.457 211.386Q0.631 211.407 0.675 211.588L0.675 215.173L1.048 215.173Q1.229 215.194 1.263 215.375L1.263 215.454Q1.229 215.641 1.048 215.662L0.334 215.662Q0.159 215.641 0.115 215.454L0.115 215.341Q-0.056 215.508-0.285 215.602Q-0.514 215.696-0.753 215.696M-0.719 215.207Q-0.405 215.207-0.184 214.972Q0.036 214.736 0.115 214.408L0.115 213.680Q0.064 213.516-0.047 213.384Q-0.159 213.252-0.314 213.175Q-0.470 213.099-0.641 213.099Q-0.911 213.099-1.129 213.247Q-1.348 213.396-1.474 213.645Q-1.601 213.895-1.601 214.158Q-1.601 214.551-1.351 214.879Q-1.102 215.207-0.719 215.207M2.962 215.696Q2.555 215.696 2.236 215.477Q1.916 215.259 1.737 214.905Q1.557 214.551 1.557 214.151Q1.557 213.850 1.667 213.570Q1.776 213.290 1.979 213.071Q2.183 212.852 2.449 212.731Q2.716 212.610 3.027 212.610Q3.475 212.610 3.830 212.890L3.830 211.875L3.461 211.875Q3.276 211.854 3.242 211.666L3.242 211.588Q3.276 211.407 3.461 211.386L4.172 211.386Q4.346 211.407 4.391 211.588L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L4.049 215.662Q3.875 215.641 3.830 215.454L3.830 215.341Q3.659 215.508 3.430 215.602Q3.201 215.696 2.962 215.696M2.996 215.207Q3.311 215.207 3.531 214.972Q3.752 214.736 3.830 214.408L3.830 213.680Q3.779 213.516 3.668 213.384Q3.557 213.252 3.401 213.175Q3.246 213.099 3.075 213.099Q2.805 213.099 2.586 213.247Q2.367 213.396 2.241 213.645Q2.114 213.895 2.114 214.158Q2.114 214.551 2.364 214.879Q2.613 215.207 2.996 215.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(169.194 -157.197)\">\u003Cpath d=\"M9.839 215.730Q9.579 215.730 9.383 215.580Q9.186 215.430 9.078 215.189Q8.971 214.948 8.971 214.702L8.971 214.654Q8.971 214.428 9.051 214.221Q9.131 214.015 9.272 213.878L9.672 213.478Q9.477 212.921 9.477 212.350L9.477 212.302Q9.477 212.070 9.571 211.839Q9.665 211.608 9.844 211.461Q10.024 211.314 10.266 211.314Q10.509 211.314 10.666 211.465Q10.823 211.615 10.892 211.844Q10.960 212.073 10.960 212.302L10.960 212.350Q10.960 212.586 10.849 212.810Q10.738 213.034 10.593 213.208Q10.447 213.382 10.218 213.611Q10.376 213.970 10.693 214.466Q10.881 214.114 11.155 213.379L11.254 213.122Q11.131 213.092 11.093 212.924L11.093 212.849Q11.138 212.664 11.309 212.644L12.030 212.644Q12.204 212.661 12.249 212.849L12.249 212.924Q12.204 213.116 12.030 213.136L11.743 213.136L11.575 213.577Q11.240 214.473 10.994 214.886Q11.145 215.050 11.271 215.146Q11.398 215.242 11.555 215.242Q11.661 215.242 11.709 215.122Q11.756 215.002 11.756 214.872Q11.811 214.667 11.989 214.667Q12.167 214.667 12.221 214.872L12.221 214.920Q12.221 215.238 12.038 215.484Q11.856 215.730 11.555 215.730Q11.138 215.730 10.721 215.276Q10.321 215.730 9.839 215.730M9.839 215.242Q10.147 215.242 10.420 214.900Q10.058 214.339 9.877 213.967Q9.777 214.059 9.716 214.129Q9.654 214.199 9.612 214.271Q9.569 214.343 9.550 214.440Q9.531 214.537 9.531 214.654Q9.531 214.845 9.605 215.043Q9.678 215.242 9.839 215.242M10.037 213.099Q10.235 212.883 10.367 212.695Q10.499 212.507 10.499 212.323Q10.499 212.159 10.446 211.983Q10.393 211.807 10.266 211.807Q10.106 211.807 10.022 211.979Q9.938 212.152 9.938 212.336Q9.938 212.719 10.037 213.099\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(169.194 -157.197)\">\u003Cpath d=\"M16.276 215.454L16.276 215.375Q16.313 215.194 16.494 215.173L16.863 215.173L16.863 213.136L16.494 213.136Q16.313 213.116 16.276 212.924L16.276 212.849Q16.317 212.664 16.494 212.644L17.209 212.644Q17.380 212.664 17.424 212.849L17.424 212.924L17.417 212.945Q17.615 212.787 17.855 212.699Q18.094 212.610 18.350 212.610Q18.654 212.610 18.863 212.733Q19.071 212.856 19.172 213.081Q19.273 213.307 19.273 213.618L19.273 215.173L19.646 215.173Q19.827 215.194 19.861 215.375L19.861 215.454Q19.827 215.641 19.646 215.662L18.425 215.662Q18.255 215.641 18.210 215.454L18.210 215.375Q18.255 215.190 18.425 215.173L18.713 215.173L18.713 213.645Q18.713 213.375 18.634 213.237Q18.555 213.099 18.299 213.099Q18.063 213.099 17.863 213.213Q17.663 213.328 17.544 213.527Q17.424 213.727 17.424 213.960L17.424 215.173L17.797 215.173Q17.978 215.194 18.012 215.375L18.012 215.454Q17.978 215.641 17.797 215.662L16.494 215.662Q16.313 215.641 16.276 215.454M21.785 215.696Q21.372 215.696 21.035 215.483Q20.698 215.269 20.504 214.910Q20.309 214.551 20.309 214.151Q20.309 213.850 20.418 213.568Q20.527 213.287 20.729 213.064Q20.931 212.842 21.199 212.716Q21.467 212.589 21.785 212.589Q22.103 212.589 22.377 212.717Q22.650 212.846 22.845 213.061Q23.040 213.276 23.151 213.557Q23.262 213.837 23.262 214.151Q23.262 214.551 23.065 214.912Q22.869 215.272 22.532 215.484Q22.195 215.696 21.785 215.696M21.785 215.207Q22.192 215.207 22.447 214.862Q22.701 214.517 22.701 214.093Q22.701 213.837 22.583 213.603Q22.465 213.369 22.255 213.223Q22.045 213.078 21.785 213.078Q21.519 213.078 21.310 213.223Q21.102 213.369 20.984 213.603Q20.866 213.837 20.866 214.093Q20.866 214.514 21.122 214.860Q21.379 215.207 21.785 215.207M23.839 215.454L23.839 215.375Q23.891 215.194 24.058 215.173L24.680 215.173L24.680 213.136L24.058 213.136Q23.887 213.116 23.839 212.924L23.839 212.849Q23.891 212.664 24.058 212.644L25.022 212.644Q25.196 212.661 25.241 212.849L25.241 213.136Q25.470 212.887 25.781 212.748Q26.092 212.610 26.430 212.610Q26.687 212.610 26.892 212.728Q27.097 212.846 27.097 213.078Q27.097 213.225 27.001 213.328Q26.905 213.430 26.758 213.430Q26.625 213.430 26.524 213.333Q26.423 213.235 26.423 213.099Q26.095 213.099 25.820 213.275Q25.545 213.451 25.393 213.743Q25.241 214.035 25.241 214.367L25.241 215.173L26.068 215.173Q26.249 215.194 26.283 215.375L26.283 215.454Q26.249 215.641 26.068 215.662L24.058 215.662Q23.891 215.641 23.839 215.454M27.312 215.454L27.312 215.375Q27.357 215.190 27.527 215.173L27.702 215.173L27.702 213.136L27.527 213.136Q27.346 213.116 27.312 212.924L27.312 212.849Q27.357 212.661 27.527 212.644L27.948 212.644Q28.115 212.664 28.167 212.849Q28.447 212.610 28.809 212.610Q28.977 212.610 29.124 212.705Q29.271 212.801 29.336 212.952Q29.489 212.784 29.684 212.697Q29.879 212.610 30.091 212.610Q30.457 212.610 30.592 212.909Q30.727 213.208 30.727 213.618L30.727 215.173L30.901 215.173Q31.086 215.194 31.120 215.375L31.120 215.454Q31.075 215.641 30.901 215.662L30.187 215.662Q30.016 215.641 29.971 215.454L29.971 215.375Q30.016 215.194 30.187 215.173L30.265 215.173L30.265 213.645Q30.265 213.099 30.047 213.099Q29.756 213.099 29.600 213.370Q29.445 213.642 29.445 213.960L29.445 215.173L29.623 215.173Q29.804 215.194 29.838 215.375L29.838 215.454Q29.794 215.641 29.623 215.662L28.908 215.662Q28.734 215.641 28.690 215.454L28.690 215.375Q28.734 215.194 28.908 215.173L28.984 215.173L28.984 213.645Q28.984 213.099 28.768 213.099Q28.478 213.099 28.322 213.372Q28.167 213.645 28.167 213.960L28.167 215.173L28.341 215.173Q28.522 215.194 28.556 215.375L28.556 215.454Q28.512 215.645 28.341 215.662L27.527 215.662Q27.346 215.641 27.312 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M139.01 33.564h85.359V16.493H139.01Z\"\u002F>\u003Cg transform=\"translate(165.476 -188.494)\">\u003Cpath d=\"M-5.819 215.454L-5.819 215.375Q-5.774 215.194-5.603 215.173L-4.831 215.173L-4.831 213.136L-5.579 213.136Q-5.754 213.116-5.798 212.924L-5.798 212.849Q-5.754 212.664-5.579 212.644L-4.831 212.644L-4.831 212.247Q-4.831 211.841-4.475 211.595Q-4.120 211.349-3.700 211.349Q-3.426 211.349-3.213 211.454Q-2.999 211.560-2.999 211.807Q-2.999 211.950-3.095 212.053Q-3.190 212.155-3.334 212.155Q-3.464 212.155-3.570 212.063Q-3.676 211.971-3.676 211.841L-3.747 211.841Q-3.881 211.841-4 211.894Q-4.120 211.947-4.195 212.047Q-4.270 212.148-4.270 212.275L-4.270 212.644L-3.368 212.644Q-3.197 212.661-3.153 212.849L-3.153 212.924Q-3.197 213.116-3.368 213.136L-4.270 213.136L-4.270 215.173L-3.501 215.173Q-3.330 215.194-3.286 215.375L-3.286 215.454Q-3.330 215.641-3.501 215.662L-5.603 215.662Q-5.774 215.641-5.819 215.454M0.689 214.360L-1.447 214.360Q-1.399 214.602-1.227 214.797Q-1.054 214.992-0.811 215.100Q-0.569 215.207-0.319 215.207Q0.094 215.207 0.289 214.954Q0.296 214.944 0.346 214.852Q0.395 214.760 0.438 214.722Q0.481 214.684 0.563 214.674L0.689 214.674Q0.857 214.691 0.908 214.879L0.908 214.927Q0.850 215.190 0.648 215.363Q0.446 215.536 0.173 215.616Q-0.100 215.696-0.367 215.696Q-0.791 215.696-1.175 215.496Q-1.560 215.296-1.794 214.946Q-2.028 214.596-2.028 214.165L-2.028 214.114Q-2.028 213.704-1.813 213.351Q-1.598 212.999-1.240 212.794Q-0.883 212.589-0.473 212.589Q-0.032 212.589 0.277 212.784Q0.587 212.979 0.747 213.319Q0.908 213.659 0.908 214.100L0.908 214.151Q0.857 214.339 0.689 214.360M-1.440 213.878L0.334 213.878Q0.293 213.519 0.084 213.298Q-0.124 213.078-0.473 213.078Q-0.818 213.078-1.087 213.307Q-1.355 213.536-1.440 213.878M4.404 214.360L2.268 214.360Q2.316 214.602 2.489 214.797Q2.661 214.992 2.904 215.100Q3.147 215.207 3.396 215.207Q3.810 215.207 4.005 214.954Q4.011 214.944 4.061 214.852Q4.110 214.760 4.153 214.722Q4.196 214.684 4.278 214.674L4.404 214.674Q4.572 214.691 4.623 214.879L4.623 214.927Q4.565 215.190 4.363 215.363Q4.162 215.536 3.888 215.616Q3.615 215.696 3.348 215.696Q2.924 215.696 2.540 215.496Q2.155 215.296 1.921 214.946Q1.687 214.596 1.687 214.165L1.687 214.114Q1.687 213.704 1.902 213.351Q2.118 212.999 2.475 212.794Q2.832 212.589 3.242 212.589Q3.683 212.589 3.993 212.784Q4.302 212.979 4.463 213.319Q4.623 213.659 4.623 214.100L4.623 214.151Q4.572 214.339 4.404 214.360M2.275 213.878L4.049 213.878Q4.008 213.519 3.799 213.298Q3.591 213.078 3.242 213.078Q2.897 213.078 2.629 213.307Q2.360 213.536 2.275 213.878M6.677 215.696Q6.271 215.696 5.951 215.477Q5.631 215.259 5.452 214.905Q5.273 214.551 5.273 214.151Q5.273 213.850 5.382 213.570Q5.491 213.290 5.695 213.071Q5.898 212.852 6.165 212.731Q6.431 212.610 6.742 212.610Q7.190 212.610 7.546 212.890L7.546 211.875L7.176 211.875Q6.992 211.854 6.958 211.666L6.958 211.588Q6.992 211.407 7.176 211.386L7.887 211.386Q8.062 211.407 8.106 211.588L8.106 215.173L8.479 215.173Q8.660 215.194 8.694 215.375L8.694 215.454Q8.660 215.641 8.479 215.662L7.764 215.662Q7.590 215.641 7.546 215.454L7.546 215.341Q7.375 215.508 7.146 215.602Q6.917 215.696 6.677 215.696M6.712 215.207Q7.026 215.207 7.246 214.972Q7.467 214.736 7.546 214.408L7.546 213.680Q7.494 213.516 7.383 213.384Q7.272 213.252 7.117 213.175Q6.961 213.099 6.790 213.099Q6.520 213.099 6.301 213.247Q6.083 213.396 5.956 213.645Q5.830 213.895 5.830 214.158Q5.830 214.551 6.079 214.879Q6.329 215.207 6.712 215.207M11.821 213.792L9.422 213.792Q9.313 213.782 9.237 213.707Q9.162 213.632 9.162 213.519Q9.162 213.406 9.237 213.334Q9.313 213.263 9.422 213.252L11.821 213.252Q11.931 213.263 12.003 213.334Q12.074 213.406 12.074 213.519Q12.074 213.632 12.003 213.707Q11.931 213.782 11.821 213.792M12.758 215.454L12.758 215.375Q12.802 215.194 12.973 215.173L13.746 215.173L13.746 213.136L12.997 213.136Q12.823 213.116 12.778 212.924L12.778 212.849Q12.823 212.664 12.997 212.644L13.746 212.644L13.746 212.247Q13.746 211.841 14.101 211.595Q14.457 211.349 14.877 211.349Q15.151 211.349 15.364 211.454Q15.578 211.560 15.578 211.807Q15.578 211.950 15.482 212.053Q15.386 212.155 15.243 212.155Q15.113 212.155 15.007 212.063Q14.901 211.971 14.901 211.841L14.829 211.841Q14.696 211.841 14.576 211.894Q14.457 211.947 14.381 212.047Q14.306 212.148 14.306 212.275L14.306 212.644L15.209 212.644Q15.380 212.661 15.424 212.849L15.424 212.924Q15.380 213.116 15.209 213.136L14.306 213.136L14.306 215.173L15.075 215.173Q15.246 215.194 15.291 215.375L15.291 215.454Q15.246 215.641 15.075 215.662L12.973 215.662Q12.802 215.641 12.758 215.454M18.049 215.696Q17.635 215.696 17.299 215.483Q16.962 215.269 16.767 214.910Q16.572 214.551 16.572 214.151Q16.572 213.850 16.682 213.568Q16.791 213.287 16.993 213.064Q17.194 212.842 17.463 212.716Q17.731 212.589 18.049 212.589Q18.367 212.589 18.640 212.717Q18.914 212.846 19.109 213.061Q19.303 213.276 19.414 213.557Q19.526 213.837 19.526 214.151Q19.526 214.551 19.329 214.912Q19.132 215.272 18.796 215.484Q18.459 215.696 18.049 215.696M18.049 215.207Q18.456 215.207 18.710 214.862Q18.965 214.517 18.965 214.093Q18.965 213.837 18.847 213.603Q18.729 213.369 18.519 213.223Q18.309 213.078 18.049 213.078Q17.782 213.078 17.574 213.223Q17.365 213.369 17.247 213.603Q17.130 213.837 17.130 214.093Q17.130 214.514 17.386 214.860Q17.642 215.207 18.049 215.207M20.103 215.454L20.103 215.375Q20.154 215.194 20.322 215.173L20.944 215.173L20.944 213.136L20.322 213.136Q20.151 213.116 20.103 212.924L20.103 212.849Q20.154 212.664 20.322 212.644L21.286 212.644Q21.460 212.661 21.505 212.849L21.505 213.136Q21.734 212.887 22.045 212.748Q22.356 212.610 22.694 212.610Q22.950 212.610 23.155 212.728Q23.360 212.846 23.360 213.078Q23.360 213.225 23.265 213.328Q23.169 213.430 23.022 213.430Q22.889 213.430 22.788 213.333Q22.687 213.235 22.687 213.099Q22.359 213.099 22.084 213.275Q21.809 213.451 21.657 213.743Q21.505 214.035 21.505 214.367L21.505 215.173L22.332 215.173Q22.513 215.194 22.547 215.375L22.547 215.454Q22.513 215.641 22.332 215.662L20.322 215.662Q20.154 215.641 20.103 215.454M24.505 215.467L24.099 213.136L23.959 213.136Q23.777 213.116 23.743 212.924L23.743 212.849Q23.777 212.664 23.959 212.644L24.981 212.644Q25.165 212.664 25.199 212.849L25.199 212.924Q25.165 213.116 24.981 213.136L24.567 213.136Q24.666 213.700 24.734 214.090Q24.803 214.479 24.847 214.758Q24.892 215.037 24.892 215.101Q24.899 214.951 25.148 214.079Q25.182 213.980 25.268 213.915Q25.353 213.850 25.459 213.850L25.527 213.850Q25.633 213.850 25.719 213.915Q25.804 213.980 25.835 214.079Q25.931 214.414 26.003 214.698Q26.074 214.982 26.074 215.101Q26.085 214.849 26.389 213.136L25.975 213.136Q25.794 213.116 25.760 212.924L25.760 212.849Q25.794 212.664 25.975 212.644L27.004 212.644Q27.172 212.664 27.223 212.849L27.223 212.924Q27.175 213.116 27.004 213.136L26.857 213.136L26.450 215.467Q26.430 215.570 26.353 215.633Q26.276 215.696 26.170 215.696L26.047 215.696Q25.941 215.696 25.857 215.633Q25.774 215.570 25.736 215.467Q25.695 215.310 25.632 215.086Q25.568 214.862 25.531 214.679Q25.493 214.496 25.493 214.408Q25.486 214.654 25.240 215.467Q25.216 215.563 25.131 215.630Q25.046 215.696 24.940 215.696L24.786 215.696Q24.680 215.696 24.603 215.633Q24.526 215.570 24.505 215.467M27.694 214.688Q27.694 214.298 28.057 214.073Q28.419 213.847 28.892 213.760Q29.366 213.673 29.810 213.666Q29.810 213.478 29.692 213.345Q29.574 213.211 29.393 213.145Q29.212 213.078 29.027 213.078Q28.727 213.078 28.587 213.099L28.587 213.150Q28.587 213.297 28.482 213.398Q28.378 213.498 28.234 213.498Q28.081 213.498 27.980 213.391Q27.879 213.283 27.879 213.136Q27.879 212.781 28.212 212.685Q28.546 212.589 29.034 212.589Q29.270 212.589 29.504 212.658Q29.738 212.726 29.935 212.858Q30.131 212.989 30.251 213.182Q30.371 213.375 30.371 213.618L30.371 215.122Q30.371 215.173 30.832 215.173Q31.003 215.190 31.047 215.375L31.047 215.454Q31.003 215.641 30.832 215.662L30.706 215.662Q30.405 215.662 30.205 215.621Q30.005 215.580 29.879 215.416Q29.475 215.696 28.857 215.696Q28.563 215.696 28.296 215.573Q28.029 215.450 27.862 215.221Q27.694 214.992 27.694 214.688M28.255 214.695Q28.255 214.934 28.467 215.071Q28.679 215.207 28.928 215.207Q29.120 215.207 29.323 215.156Q29.526 215.105 29.668 214.984Q29.810 214.862 29.810 214.667L29.810 214.151Q29.564 214.151 29.200 214.201Q28.836 214.250 28.546 214.372Q28.255 214.493 28.255 214.695M31.249 215.454L31.249 215.375Q31.300 215.194 31.468 215.173L32.090 215.173L32.090 213.136L31.468 213.136Q31.297 213.116 31.249 212.924L31.249 212.849Q31.300 212.664 31.468 212.644L32.432 212.644Q32.606 212.661 32.651 212.849L32.651 213.136Q32.880 212.887 33.191 212.748Q33.502 212.610 33.840 212.610Q34.096 212.610 34.301 212.728Q34.506 212.846 34.506 213.078Q34.506 213.225 34.411 213.328Q34.315 213.430 34.168 213.430Q34.035 213.430 33.934 213.333Q33.833 213.235 33.833 213.099Q33.505 213.099 33.230 213.275Q32.955 213.451 32.803 213.743Q32.651 214.035 32.651 214.367L32.651 215.173L33.478 215.173Q33.659 215.194 33.693 215.375L33.693 215.454Q33.659 215.641 33.478 215.662L31.468 215.662Q31.300 215.641 31.249 215.454M36.400 215.696Q35.993 215.696 35.674 215.477Q35.354 215.259 35.175 214.905Q34.995 214.551 34.995 214.151Q34.995 213.850 35.105 213.570Q35.214 213.290 35.417 213.071Q35.621 212.852 35.887 212.731Q36.154 212.610 36.465 212.610Q36.913 212.610 37.268 212.890L37.268 211.875L36.899 211.875Q36.714 211.854 36.680 211.666L36.680 211.588Q36.714 211.407 36.899 211.386L37.610 211.386Q37.784 211.407 37.829 211.588L37.829 215.173L38.201 215.173Q38.382 215.194 38.417 215.375L38.417 215.454Q38.382 215.641 38.201 215.662L37.487 215.662Q37.313 215.641 37.268 215.454L37.268 215.341Q37.097 215.508 36.868 215.602Q36.639 215.696 36.400 215.696M36.434 215.207Q36.749 215.207 36.969 214.972Q37.190 214.736 37.268 214.408L37.268 213.680Q37.217 213.516 37.106 213.384Q36.995 213.252 36.839 213.175Q36.684 213.099 36.513 213.099Q36.243 213.099 36.024 213.247Q35.805 213.396 35.679 213.645Q35.552 213.895 35.552 214.158Q35.552 214.551 35.802 214.879Q36.051 215.207 36.434 215.207\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-soft-neutral)\">\u003Cpath d=\"M139.01 3.689h85.359v-14.227H139.01Z\"\u002F>\u003Cg fill=\"currentColor\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(169.194 -216.947)\">\u003Cpath d=\"M-5.744 214.688Q-5.744 214.298-5.381 214.073Q-5.019 213.847-4.546 213.760Q-4.072 213.673-3.628 213.666Q-3.628 213.478-3.746 213.345Q-3.864 213.211-4.045 213.145Q-4.226 213.078-4.411 213.078Q-4.711 213.078-4.851 213.099L-4.851 213.150Q-4.851 213.297-4.956 213.398Q-5.060 213.498-5.203 213.498Q-5.357 213.498-5.458 213.391Q-5.559 213.283-5.559 213.136Q-5.559 212.781-5.226 212.685Q-4.892 212.589-4.404 212.589Q-4.168 212.589-3.934 212.658Q-3.700 212.726-3.503 212.858Q-3.307 212.989-3.187 213.182Q-3.067 213.375-3.067 213.618L-3.067 215.122Q-3.067 215.173-2.606 215.173Q-2.435 215.190-2.391 215.375L-2.391 215.454Q-2.435 215.641-2.606 215.662L-2.732 215.662Q-3.033 215.662-3.233 215.621Q-3.433 215.580-3.559 215.416Q-3.963 215.696-4.581 215.696Q-4.875 215.696-5.142 215.573Q-5.409 215.450-5.576 215.221Q-5.744 214.992-5.744 214.688M-5.183 214.695Q-5.183 214.934-4.971 215.071Q-4.759 215.207-4.510 215.207Q-4.318 215.207-4.115 215.156Q-3.912 215.105-3.770 214.984Q-3.628 214.862-3.628 214.667L-3.628 214.151Q-3.874 214.151-4.238 214.201Q-4.602 214.250-4.892 214.372Q-5.183 214.493-5.183 214.695M-0.753 215.696Q-1.160 215.696-1.480 215.477Q-1.799 215.259-1.979 214.905Q-2.158 214.551-2.158 214.151Q-2.158 213.850-2.049 213.570Q-1.939 213.290-1.736 213.071Q-1.533 212.852-1.266 212.731Q-0.999 212.610-0.688 212.610Q-0.241 212.610 0.115 212.890L0.115 211.875L-0.254 211.875Q-0.439 211.854-0.473 211.666L-0.473 211.588Q-0.439 211.407-0.254 211.386L0.457 211.386Q0.631 211.407 0.675 211.588L0.675 215.173L1.048 215.173Q1.229 215.194 1.263 215.375L1.263 215.454Q1.229 215.641 1.048 215.662L0.334 215.662Q0.159 215.641 0.115 215.454L0.115 215.341Q-0.056 215.508-0.285 215.602Q-0.514 215.696-0.753 215.696M-0.719 215.207Q-0.405 215.207-0.184 214.972Q0.036 214.736 0.115 214.408L0.115 213.680Q0.064 213.516-0.047 213.384Q-0.159 213.252-0.314 213.175Q-0.470 213.099-0.641 213.099Q-0.911 213.099-1.129 213.247Q-1.348 213.396-1.474 213.645Q-1.601 213.895-1.601 214.158Q-1.601 214.551-1.351 214.879Q-1.102 215.207-0.719 215.207M2.962 215.696Q2.555 215.696 2.236 215.477Q1.916 215.259 1.737 214.905Q1.557 214.551 1.557 214.151Q1.557 213.850 1.667 213.570Q1.776 213.290 1.979 213.071Q2.183 212.852 2.449 212.731Q2.716 212.610 3.027 212.610Q3.475 212.610 3.830 212.890L3.830 211.875L3.461 211.875Q3.276 211.854 3.242 211.666L3.242 211.588Q3.276 211.407 3.461 211.386L4.172 211.386Q4.346 211.407 4.391 211.588L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L4.049 215.662Q3.875 215.641 3.830 215.454L3.830 215.341Q3.659 215.508 3.430 215.602Q3.201 215.696 2.962 215.696M2.996 215.207Q3.311 215.207 3.531 214.972Q3.752 214.736 3.830 214.408L3.830 213.680Q3.779 213.516 3.668 213.384Q3.557 213.252 3.401 213.175Q3.246 213.099 3.075 213.099Q2.805 213.099 2.586 213.247Q2.367 213.396 2.241 213.645Q2.114 213.895 2.114 214.158Q2.114 214.551 2.364 214.879Q2.613 215.207 2.996 215.207\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(169.194 -216.947)\">\u003Cpath d=\"M9.839 215.730Q9.579 215.730 9.383 215.580Q9.186 215.430 9.078 215.189Q8.971 214.948 8.971 214.702L8.971 214.654Q8.971 214.428 9.051 214.221Q9.131 214.015 9.272 213.878L9.672 213.478Q9.477 212.921 9.477 212.350L9.477 212.302Q9.477 212.070 9.571 211.839Q9.665 211.608 9.844 211.461Q10.024 211.314 10.266 211.314Q10.509 211.314 10.666 211.465Q10.823 211.615 10.892 211.844Q10.960 212.073 10.960 212.302L10.960 212.350Q10.960 212.586 10.849 212.810Q10.738 213.034 10.593 213.208Q10.447 213.382 10.218 213.611Q10.376 213.970 10.693 214.466Q10.881 214.114 11.155 213.379L11.254 213.122Q11.131 213.092 11.093 212.924L11.093 212.849Q11.138 212.664 11.309 212.644L12.030 212.644Q12.204 212.661 12.249 212.849L12.249 212.924Q12.204 213.116 12.030 213.136L11.743 213.136L11.575 213.577Q11.240 214.473 10.994 214.886Q11.145 215.050 11.271 215.146Q11.398 215.242 11.555 215.242Q11.661 215.242 11.709 215.122Q11.756 215.002 11.756 214.872Q11.811 214.667 11.989 214.667Q12.167 214.667 12.221 214.872L12.221 214.920Q12.221 215.238 12.038 215.484Q11.856 215.730 11.555 215.730Q11.138 215.730 10.721 215.276Q10.321 215.730 9.839 215.730M9.839 215.242Q10.147 215.242 10.420 214.900Q10.058 214.339 9.877 213.967Q9.777 214.059 9.716 214.129Q9.654 214.199 9.612 214.271Q9.569 214.343 9.550 214.440Q9.531 214.537 9.531 214.654Q9.531 214.845 9.605 215.043Q9.678 215.242 9.839 215.242M10.037 213.099Q10.235 212.883 10.367 212.695Q10.499 212.507 10.499 212.323Q10.499 212.159 10.446 211.983Q10.393 211.807 10.266 211.807Q10.106 211.807 10.022 211.979Q9.938 212.152 9.938 212.336Q9.938 212.719 10.037 213.099\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(169.194 -216.947)\">\u003Cpath d=\"M16.276 215.454L16.276 215.375Q16.313 215.194 16.494 215.173L16.863 215.173L16.863 213.136L16.494 213.136Q16.313 213.116 16.276 212.924L16.276 212.849Q16.317 212.664 16.494 212.644L17.209 212.644Q17.380 212.664 17.424 212.849L17.424 212.924L17.417 212.945Q17.615 212.787 17.855 212.699Q18.094 212.610 18.350 212.610Q18.654 212.610 18.863 212.733Q19.071 212.856 19.172 213.081Q19.273 213.307 19.273 213.618L19.273 215.173L19.646 215.173Q19.827 215.194 19.861 215.375L19.861 215.454Q19.827 215.641 19.646 215.662L18.425 215.662Q18.255 215.641 18.210 215.454L18.210 215.375Q18.255 215.190 18.425 215.173L18.713 215.173L18.713 213.645Q18.713 213.375 18.634 213.237Q18.555 213.099 18.299 213.099Q18.063 213.099 17.863 213.213Q17.663 213.328 17.544 213.527Q17.424 213.727 17.424 213.960L17.424 215.173L17.797 215.173Q17.978 215.194 18.012 215.375L18.012 215.454Q17.978 215.641 17.797 215.662L16.494 215.662Q16.313 215.641 16.276 215.454M21.785 215.696Q21.372 215.696 21.035 215.483Q20.698 215.269 20.504 214.910Q20.309 214.551 20.309 214.151Q20.309 213.850 20.418 213.568Q20.527 213.287 20.729 213.064Q20.931 212.842 21.199 212.716Q21.467 212.589 21.785 212.589Q22.103 212.589 22.377 212.717Q22.650 212.846 22.845 213.061Q23.040 213.276 23.151 213.557Q23.262 213.837 23.262 214.151Q23.262 214.551 23.065 214.912Q22.869 215.272 22.532 215.484Q22.195 215.696 21.785 215.696M21.785 215.207Q22.192 215.207 22.447 214.862Q22.701 214.517 22.701 214.093Q22.701 213.837 22.583 213.603Q22.465 213.369 22.255 213.223Q22.045 213.078 21.785 213.078Q21.519 213.078 21.310 213.223Q21.102 213.369 20.984 213.603Q20.866 213.837 20.866 214.093Q20.866 214.514 21.122 214.860Q21.379 215.207 21.785 215.207M23.839 215.454L23.839 215.375Q23.891 215.194 24.058 215.173L24.680 215.173L24.680 213.136L24.058 213.136Q23.887 213.116 23.839 212.924L23.839 212.849Q23.891 212.664 24.058 212.644L25.022 212.644Q25.196 212.661 25.241 212.849L25.241 213.136Q25.470 212.887 25.781 212.748Q26.092 212.610 26.430 212.610Q26.687 212.610 26.892 212.728Q27.097 212.846 27.097 213.078Q27.097 213.225 27.001 213.328Q26.905 213.430 26.758 213.430Q26.625 213.430 26.524 213.333Q26.423 213.235 26.423 213.099Q26.095 213.099 25.820 213.275Q25.545 213.451 25.393 213.743Q25.241 214.035 25.241 214.367L25.241 215.173L26.068 215.173Q26.249 215.194 26.283 215.375L26.283 215.454Q26.249 215.641 26.068 215.662L24.058 215.662Q23.891 215.641 23.839 215.454M27.312 215.454L27.312 215.375Q27.357 215.190 27.527 215.173L27.702 215.173L27.702 213.136L27.527 213.136Q27.346 213.116 27.312 212.924L27.312 212.849Q27.357 212.661 27.527 212.644L27.948 212.644Q28.115 212.664 28.167 212.849Q28.447 212.610 28.809 212.610Q28.977 212.610 29.124 212.705Q29.271 212.801 29.336 212.952Q29.489 212.784 29.684 212.697Q29.879 212.610 30.091 212.610Q30.457 212.610 30.592 212.909Q30.727 213.208 30.727 213.618L30.727 215.173L30.901 215.173Q31.086 215.194 31.120 215.375L31.120 215.454Q31.075 215.641 30.901 215.662L30.187 215.662Q30.016 215.641 29.971 215.454L29.971 215.375Q30.016 215.194 30.187 215.173L30.265 215.173L30.265 213.645Q30.265 213.099 30.047 213.099Q29.756 213.099 29.600 213.370Q29.445 213.642 29.445 213.960L29.445 215.173L29.623 215.173Q29.804 215.194 29.838 215.375L29.838 215.454Q29.794 215.641 29.623 215.662L28.908 215.662Q28.734 215.641 28.690 215.454L28.690 215.375Q28.734 215.194 28.908 215.173L28.984 215.173L28.984 213.645Q28.984 213.099 28.768 213.099Q28.478 213.099 28.322 213.372Q28.167 213.645 28.167 213.960L28.167 215.173L28.341 215.173Q28.522 215.194 28.556 215.375L28.556 215.454Q28.512 215.645 28.341 215.662L27.527 215.662Q27.346 215.641 27.312 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M139.01-29.032h85.359v-17.071H139.01Z\"\u002F>\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(158.038 -251.09)\">\u003Cpath d=\"M-5.706 215.454L-5.706 215.375Q-5.662 215.194-5.491 215.173L-4.523 215.173L-4.523 211.875L-5.491 211.875Q-5.662 211.854-5.706 211.666L-5.706 211.588Q-5.662 211.407-5.491 211.386L-4.182 211.386Q-4.014 211.407-3.963 211.588L-3.963 215.173L-2.999 215.173Q-2.825 215.194-2.780 215.375L-2.780 215.454Q-2.825 215.641-2.999 215.662L-5.491 215.662Q-5.662 215.641-5.706 215.454M-1.844 215.454L-1.844 215.375Q-1.799 215.194-1.628 215.173L-0.719 215.173L-0.719 213.136L-1.570 213.136Q-1.745 213.116-1.789 212.924L-1.789 212.849Q-1.745 212.664-1.570 212.644L-0.374 212.644Q-0.203 212.661-0.159 212.849L-0.159 215.173L0.641 215.173Q0.812 215.194 0.857 215.375L0.857 215.454Q0.812 215.641 0.641 215.662L-1.628 215.662Q-1.799 215.641-1.844 215.454M-0.941 211.789L-0.941 211.742Q-0.941 211.591-0.822 211.485Q-0.702 211.379-0.548 211.379Q-0.398 211.379-0.278 211.485Q-0.159 211.591-0.159 211.742L-0.159 211.789Q-0.159 211.943-0.278 212.049Q-0.398 212.155-0.548 212.155Q-0.702 212.155-0.822 212.049Q-0.941 211.943-0.941 211.789M1.393 215.454L1.393 215.375Q1.431 215.194 1.612 215.173L1.981 215.173L1.981 213.136L1.612 213.136Q1.431 213.116 1.393 212.924L1.393 212.849Q1.434 212.664 1.612 212.644L2.326 212.644Q2.497 212.664 2.542 212.849L2.542 212.924L2.535 212.945Q2.733 212.787 2.972 212.699Q3.212 212.610 3.468 212.610Q3.772 212.610 3.981 212.733Q4.189 212.856 4.290 213.081Q4.391 213.307 4.391 213.618L4.391 215.173L4.763 215.173Q4.944 215.194 4.979 215.375L4.979 215.454Q4.944 215.641 4.763 215.662L3.543 215.662Q3.372 215.641 3.328 215.454L3.328 215.375Q3.372 215.190 3.543 215.173L3.830 215.173L3.830 213.645Q3.830 213.375 3.752 213.237Q3.673 213.099 3.417 213.099Q3.181 213.099 2.981 213.213Q2.781 213.328 2.661 213.527Q2.542 213.727 2.542 213.960L2.542 215.173L2.914 215.173Q3.095 215.194 3.130 215.375L3.130 215.454Q3.095 215.641 2.914 215.662L1.612 215.662Q1.431 215.641 1.393 215.454M8.120 214.360L5.984 214.360Q6.031 214.602 6.204 214.797Q6.377 214.992 6.619 215.100Q6.862 215.207 7.111 215.207Q7.525 215.207 7.720 214.954Q7.727 214.944 7.776 214.852Q7.826 214.760 7.869 214.722Q7.911 214.684 7.993 214.674L8.120 214.674Q8.287 214.691 8.338 214.879L8.338 214.927Q8.280 215.190 8.079 215.363Q7.877 215.536 7.604 215.616Q7.330 215.696 7.064 215.696Q6.640 215.696 6.255 215.496Q5.871 215.296 5.637 214.946Q5.402 214.596 5.402 214.165L5.402 214.114Q5.402 213.704 5.618 213.351Q5.833 212.999 6.190 212.794Q6.547 212.589 6.958 212.589Q7.399 212.589 7.708 212.784Q8.017 212.979 8.178 213.319Q8.338 213.659 8.338 214.100L8.338 214.151Q8.287 214.339 8.120 214.360M5.990 213.878L7.764 213.878Q7.723 213.519 7.515 213.298Q7.306 213.078 6.958 213.078Q6.612 213.078 6.344 213.307Q6.076 213.536 5.990 213.878M9.118 214.688Q9.118 214.298 9.480 214.073Q9.842 213.847 10.316 213.760Q10.789 213.673 11.234 213.666Q11.234 213.478 11.116 213.345Q10.998 213.211 10.817 213.145Q10.635 213.078 10.451 213.078Q10.150 213.078 10.010 213.099L10.010 213.150Q10.010 213.297 9.906 213.398Q9.801 213.498 9.658 213.498Q9.504 213.498 9.403 213.391Q9.302 213.283 9.302 213.136Q9.302 212.781 9.636 212.685Q9.969 212.589 10.458 212.589Q10.693 212.589 10.928 212.658Q11.162 212.726 11.358 212.858Q11.555 212.989 11.674 213.182Q11.794 213.375 11.794 213.618L11.794 215.122Q11.794 215.173 12.255 215.173Q12.426 215.190 12.471 215.375L12.471 215.454Q12.426 215.641 12.255 215.662L12.129 215.662Q11.828 215.662 11.628 215.621Q11.428 215.580 11.302 215.416Q10.899 215.696 10.280 215.696Q9.986 215.696 9.719 215.573Q9.453 215.450 9.285 215.221Q9.118 214.992 9.118 214.688M9.678 214.695Q9.678 214.934 9.890 215.071Q10.102 215.207 10.352 215.207Q10.543 215.207 10.746 215.156Q10.950 215.105 11.092 214.984Q11.234 214.862 11.234 214.667L11.234 214.151Q10.987 214.151 10.623 214.201Q10.259 214.250 9.969 214.372Q9.678 214.493 9.678 214.695M12.672 215.454L12.672 215.375Q12.724 215.194 12.891 215.173L13.513 215.173L13.513 213.136L12.891 213.136Q12.720 213.116 12.672 212.924L12.672 212.849Q12.724 212.664 12.891 212.644L13.855 212.644Q14.029 212.661 14.074 212.849L14.074 213.136Q14.303 212.887 14.614 212.748Q14.925 212.610 15.263 212.610Q15.520 212.610 15.725 212.728Q15.930 212.846 15.930 213.078Q15.930 213.225 15.834 213.328Q15.738 213.430 15.591 213.430Q15.458 213.430 15.357 213.333Q15.256 213.235 15.256 213.099Q14.928 213.099 14.653 213.275Q14.378 213.451 14.226 213.743Q14.074 214.035 14.074 214.367L14.074 215.173L14.901 215.173Q15.082 215.194 15.116 215.375L15.116 215.454Q15.082 215.641 14.901 215.662L12.891 215.662Q12.724 215.641 12.672 215.454\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(158.038 -251.09)\">\u003Cpath d=\"M21.522 214.855L21.522 213.792L20.459 213.792Q20.350 213.782 20.275 213.707Q20.200 213.632 20.200 213.519Q20.200 213.406 20.275 213.334Q20.350 213.263 20.459 213.252L21.522 213.252L21.522 212.183Q21.533 212.073 21.608 212.001Q21.683 211.930 21.796 211.930Q21.909 211.930 21.980 212.001Q22.052 212.073 22.062 212.183L22.062 213.252L23.125 213.252Q23.235 213.263 23.307 213.334Q23.378 213.406 23.378 213.519Q23.378 213.632 23.307 213.707Q23.235 213.782 23.125 213.792L22.062 213.792L22.062 214.855Q22.052 214.965 21.980 215.040Q21.909 215.115 21.796 215.115Q21.683 215.115 21.608 215.040Q21.533 214.965 21.522 214.855\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(158.038 -251.09)\">\u003Cpath d=\"M27.883 215.488L27.883 214.688Q27.907 214.507 28.091 214.486L28.238 214.486Q28.382 214.507 28.433 214.647Q28.611 215.207 29.246 215.207Q29.428 215.207 29.628 215.177Q29.828 215.146 29.974 215.045Q30.121 214.944 30.121 214.766Q30.121 214.582 29.927 214.483Q29.732 214.384 29.493 214.346L28.881 214.247Q27.883 214.062 27.883 213.430Q27.883 213.177 28.009 213.011Q28.136 212.846 28.346 212.752Q28.556 212.658 28.780 212.623Q29.004 212.589 29.246 212.589Q29.465 212.589 29.634 212.615Q29.804 212.641 29.947 212.709Q30.016 212.606 30.128 212.589L30.197 212.589Q30.282 212.600 30.337 212.654Q30.391 212.709 30.402 212.791L30.402 213.410Q30.391 213.492 30.337 213.550Q30.282 213.608 30.197 213.618L30.050 213.618Q29.968 213.608 29.910 213.550Q29.851 213.492 29.841 213.410Q29.841 213.078 29.233 213.078Q28.929 213.078 28.650 213.150Q28.371 213.222 28.371 213.437Q28.371 213.669 28.959 213.765L29.575 213.871Q29.998 213.943 30.304 214.160Q30.610 214.377 30.610 214.766Q30.610 215.108 30.403 215.320Q30.197 215.532 29.891 215.614Q29.585 215.696 29.246 215.696Q28.741 215.696 28.392 215.474Q28.330 215.583 28.288 215.633Q28.245 215.683 28.153 215.696L28.091 215.696Q27.903 215.676 27.883 215.488M32.941 215.696Q32.528 215.696 32.191 215.483Q31.854 215.269 31.660 214.910Q31.465 214.551 31.465 214.151Q31.465 213.850 31.574 213.568Q31.683 213.287 31.885 213.064Q32.087 212.842 32.355 212.716Q32.623 212.589 32.941 212.589Q33.259 212.589 33.533 212.717Q33.806 212.846 34.001 213.061Q34.196 213.276 34.307 213.557Q34.418 213.837 34.418 214.151Q34.418 214.551 34.221 214.912Q34.025 215.272 33.688 215.484Q33.351 215.696 32.941 215.696M32.941 215.207Q33.348 215.207 33.603 214.862Q33.857 214.517 33.857 214.093Q33.857 213.837 33.739 213.603Q33.621 213.369 33.411 213.223Q33.201 213.078 32.941 213.078Q32.675 213.078 32.466 213.223Q32.258 213.369 32.140 213.603Q32.022 213.837 32.022 214.093Q32.022 214.514 32.278 214.860Q32.535 215.207 32.941 215.207M35.081 215.454L35.081 215.375Q35.125 215.194 35.296 215.173L36.069 215.173L36.069 213.136L35.320 213.136Q35.146 213.116 35.101 212.924L35.101 212.849Q35.146 212.664 35.320 212.644L36.069 212.644L36.069 212.247Q36.069 211.841 36.424 211.595Q36.780 211.349 37.200 211.349Q37.474 211.349 37.687 211.454Q37.901 211.560 37.901 211.807Q37.901 211.950 37.805 212.053Q37.709 212.155 37.566 212.155Q37.436 212.155 37.330 212.063Q37.224 211.971 37.224 211.841L37.152 211.841Q37.019 211.841 36.899 211.894Q36.780 211.947 36.704 212.047Q36.629 212.148 36.629 212.275L36.629 212.644L37.532 212.644Q37.703 212.661 37.747 212.849L37.747 212.924Q37.703 213.116 37.532 213.136L36.629 213.136L36.629 215.173L37.398 215.173Q37.569 215.194 37.614 215.375L37.614 215.454Q37.569 215.641 37.398 215.662L35.296 215.662Q35.125 215.641 35.081 215.454M39.565 214.695L39.565 213.136L38.909 213.136Q38.735 213.116 38.690 212.924L38.690 212.849Q38.735 212.664 38.909 212.644L39.565 212.644L39.565 211.988Q39.610 211.807 39.784 211.783L39.911 211.783Q40.081 211.807 40.126 211.988L40.126 212.644L41.315 212.644Q41.483 212.661 41.534 212.849L41.534 212.924Q41.486 213.116 41.315 213.136L40.126 213.136L40.126 214.667Q40.126 215.207 40.628 215.207Q40.847 215.207 40.991 215.045Q41.134 214.883 41.134 214.667Q41.134 214.585 41.197 214.524Q41.261 214.462 41.349 214.452L41.476 214.452Q41.650 214.473 41.695 214.654L41.695 214.695Q41.695 214.978 41.534 215.209Q41.373 215.440 41.117 215.568Q40.861 215.696 40.580 215.696Q40.133 215.696 39.849 215.424Q39.565 215.153 39.565 214.695M42.183 215.454L42.183 215.375Q42.228 215.190 42.399 215.173L42.573 215.173L42.573 213.136L42.399 213.136Q42.218 213.116 42.183 212.924L42.183 212.849Q42.228 212.661 42.399 212.644L42.819 212.644Q42.987 212.664 43.038 212.849Q43.318 212.610 43.681 212.610Q43.848 212.610 43.995 212.705Q44.142 212.801 44.207 212.952Q44.361 212.784 44.556 212.697Q44.750 212.610 44.962 212.610Q45.328 212.610 45.463 212.909Q45.598 213.208 45.598 213.618L45.598 215.173L45.772 215.173Q45.957 215.194 45.991 215.375L45.991 215.454Q45.947 215.641 45.772 215.662L45.058 215.662Q44.887 215.641 44.843 215.454L44.843 215.375Q44.887 215.194 45.058 215.173L45.137 215.173L45.137 213.645Q45.137 213.099 44.918 213.099Q44.627 213.099 44.472 213.370Q44.316 213.642 44.316 213.960L44.316 215.173L44.494 215.173Q44.675 215.194 44.709 215.375L44.709 215.454Q44.665 215.641 44.494 215.662L43.780 215.662Q43.605 215.641 43.561 215.454L43.561 215.375Q43.605 215.194 43.780 215.173L43.855 215.173L43.855 213.645Q43.855 213.099 43.640 213.099Q43.349 213.099 43.193 213.372Q43.038 213.645 43.038 213.960L43.038 215.173L43.212 215.173Q43.393 215.194 43.428 215.375L43.428 215.454Q43.383 215.645 43.212 215.662L42.399 215.662Q42.218 215.641 42.183 215.454M46.302 214.688Q46.302 214.298 46.664 214.073Q47.027 213.847 47.500 213.760Q47.974 213.673 48.418 213.666Q48.418 213.478 48.300 213.345Q48.182 213.211 48.001 213.145Q47.820 213.078 47.635 213.078Q47.334 213.078 47.194 213.099L47.194 213.150Q47.194 213.297 47.090 213.398Q46.986 213.498 46.842 213.498Q46.688 213.498 46.588 213.391Q46.487 213.283 46.487 213.136Q46.487 212.781 46.820 212.685Q47.153 212.589 47.642 212.589Q47.878 212.589 48.112 212.658Q48.346 212.726 48.543 212.858Q48.739 212.989 48.859 213.182Q48.978 213.375 48.978 213.618L48.978 215.122Q48.978 215.173 49.440 215.173Q49.611 215.190 49.655 215.375L49.655 215.454Q49.611 215.641 49.440 215.662L49.313 215.662Q49.013 215.662 48.813 215.621Q48.613 215.580 48.486 215.416Q48.083 215.696 47.464 215.696Q47.170 215.696 46.904 215.573Q46.637 215.450 46.470 215.221Q46.302 214.992 46.302 214.688M46.863 214.695Q46.863 214.934 47.075 215.071Q47.287 215.207 47.536 215.207Q47.727 215.207 47.931 215.156Q48.134 215.105 48.276 214.984Q48.418 214.862 48.418 214.667L48.418 214.151Q48.172 214.151 47.808 214.201Q47.444 214.250 47.153 214.372Q46.863 214.493 46.863 214.695M49.888 215.454L49.888 215.375Q49.922 215.194 50.103 215.173L50.458 215.173L51.272 214.107L50.510 213.136L50.144 213.136Q49.973 213.119 49.929 212.924L49.929 212.849Q49.973 212.664 50.144 212.644L51.159 212.644Q51.333 212.664 51.378 212.849L51.378 212.924Q51.333 213.116 51.159 213.136L51.063 213.136L51.497 213.710L51.914 213.136L51.812 213.136Q51.638 213.116 51.593 212.924L51.593 212.849Q51.638 212.664 51.812 212.644L52.827 212.644Q52.998 212.661 53.042 212.849L53.042 212.924Q52.998 213.116 52.827 213.136L52.468 213.136L51.726 214.107L52.567 215.173L52.923 215.173Q53.097 215.194 53.141 215.375L53.141 215.454Q53.107 215.641 52.923 215.662L51.914 215.662Q51.733 215.641 51.699 215.454L51.699 215.375Q51.733 215.194 51.914 215.173L52.027 215.173L51.497 214.425L50.985 215.173L51.111 215.173Q51.292 215.194 51.327 215.375L51.327 215.454Q51.292 215.641 51.111 215.662L50.103 215.662Q49.932 215.645 49.888 215.454\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(150.6 -280.32)\">\u003Cpath d=\"M-4.243 215.696Q-4.657 215.696-4.993 215.483Q-5.330 215.269-5.525 214.910Q-5.720 214.551-5.720 214.151Q-5.720 213.850-5.610 213.568Q-5.501 213.287-5.299 213.064Q-5.098 212.842-4.829 212.716Q-4.561 212.589-4.243 212.589Q-3.925 212.589-3.652 212.717Q-3.378 212.846-3.183 213.061Q-2.989 213.276-2.878 213.557Q-2.766 213.837-2.766 214.151Q-2.766 214.551-2.963 214.912Q-3.160 215.272-3.496 215.484Q-3.833 215.696-4.243 215.696M-4.243 215.207Q-3.836 215.207-3.582 214.862Q-3.327 214.517-3.327 214.093Q-3.327 213.837-3.445 213.603Q-3.563 213.369-3.773 213.223Q-3.983 213.078-4.243 213.078Q-4.510 213.078-4.718 213.223Q-4.927 213.369-5.045 213.603Q-5.162 213.837-5.162 214.093Q-5.162 214.514-4.906 214.860Q-4.650 215.207-4.243 215.207M-1.734 214.913L-1.734 213.136L-2.103 213.136Q-2.285 213.116-2.322 212.924L-2.322 212.849Q-2.281 212.664-2.103 212.644L-1.389 212.644Q-1.218 212.664-1.174 212.849L-1.174 214.886Q-1.174 215.091-1.025 215.149Q-0.876 215.207-0.627 215.207Q-0.446 215.207-0.275 215.141Q-0.104 215.074 0.005 214.943Q0.115 214.811 0.115 214.626L0.115 213.136L-0.254 213.136Q-0.439 213.116-0.473 212.924L-0.473 212.849Q-0.439 212.664-0.254 212.644L0.457 212.644Q0.631 212.664 0.675 212.849L0.675 215.173L1.048 215.173Q1.229 215.194 1.263 215.375L1.263 215.454Q1.229 215.641 1.048 215.662L0.334 215.662Q0.159 215.641 0.115 215.467Q-0.237 215.696-0.682 215.696Q-0.887 215.696-1.075 215.660Q-1.263 215.624-1.408 215.536Q-1.553 215.447-1.644 215.291Q-1.734 215.136-1.734 214.913M2.381 214.695L2.381 213.136L1.725 213.136Q1.550 213.116 1.506 212.924L1.506 212.849Q1.550 212.664 1.725 212.644L2.381 212.644L2.381 211.988Q2.425 211.807 2.600 211.783L2.726 211.783Q2.897 211.807 2.942 211.988L2.942 212.644L4.131 212.644Q4.298 212.661 4.350 212.849L4.350 212.924Q4.302 213.116 4.131 213.136L2.942 213.136L2.942 214.667Q2.942 215.207 3.444 215.207Q3.663 215.207 3.806 215.045Q3.950 214.883 3.950 214.667Q3.950 214.585 4.013 214.524Q4.076 214.462 4.165 214.452L4.292 214.452Q4.466 214.473 4.510 214.654L4.510 214.695Q4.510 214.978 4.350 215.209Q4.189 215.440 3.933 215.568Q3.676 215.696 3.396 215.696Q2.948 215.696 2.665 215.424Q2.381 215.153 2.381 214.695M5.109 217.012L5.109 216.937Q5.146 216.745 5.327 216.725L5.696 216.725L5.696 213.136L5.327 213.136Q5.146 213.116 5.109 212.924L5.109 212.849Q5.150 212.664 5.327 212.644L6.042 212.644Q6.213 212.661 6.257 212.849L6.257 212.911Q6.442 212.764 6.672 212.687Q6.903 212.610 7.139 212.610Q7.436 212.610 7.696 212.736Q7.956 212.863 8.144 213.083Q8.332 213.304 8.432 213.577Q8.533 213.850 8.533 214.151Q8.533 214.558 8.335 214.917Q8.137 215.276 7.798 215.486Q7.460 215.696 7.050 215.696Q6.595 215.696 6.257 215.375L6.257 216.725L6.630 216.725Q6.811 216.745 6.845 216.937L6.845 217.012Q6.811 217.197 6.630 217.217L5.327 217.217Q5.150 217.197 5.109 217.012M7.012 215.207Q7.282 215.207 7.501 215.059Q7.720 214.910 7.846 214.664Q7.973 214.418 7.973 214.151Q7.973 213.898 7.863 213.654Q7.754 213.410 7.551 213.254Q7.347 213.099 7.084 213.099Q6.804 213.099 6.575 213.261Q6.346 213.423 6.257 213.686L6.257 214.432Q6.336 214.753 6.529 214.980Q6.722 215.207 7.012 215.207M9.412 214.913L9.412 213.136L9.043 213.136Q8.861 213.116 8.824 212.924L8.824 212.849Q8.865 212.664 9.043 212.644L9.757 212.644Q9.928 212.664 9.972 212.849L9.972 214.886Q9.972 215.091 10.121 215.149Q10.270 215.207 10.519 215.207Q10.700 215.207 10.871 215.141Q11.042 215.074 11.151 214.943Q11.261 214.811 11.261 214.626L11.261 213.136L10.892 213.136Q10.707 213.116 10.673 212.924L10.673 212.849Q10.707 212.664 10.892 212.644L11.603 212.644Q11.777 212.664 11.821 212.849L11.821 215.173L12.194 215.173Q12.375 215.194 12.409 215.375L12.409 215.454Q12.375 215.641 12.194 215.662L11.480 215.662Q11.305 215.641 11.261 215.467Q10.909 215.696 10.464 215.696Q10.259 215.696 10.071 215.660Q9.883 215.624 9.738 215.536Q9.593 215.447 9.502 215.291Q9.412 215.136 9.412 214.913M13.527 214.695L13.527 213.136L12.871 213.136Q12.696 213.116 12.652 212.924L12.652 212.849Q12.696 212.664 12.871 212.644L13.527 212.644L13.527 211.988Q13.571 211.807 13.746 211.783L13.872 211.783Q14.043 211.807 14.088 211.988L14.088 212.644L15.277 212.644Q15.444 212.661 15.496 212.849L15.496 212.924Q15.448 213.116 15.277 213.136L14.088 213.136L14.088 214.667Q14.088 215.207 14.590 215.207Q14.809 215.207 14.952 215.045Q15.096 214.883 15.096 214.667Q15.096 214.585 15.159 214.524Q15.222 214.462 15.311 214.452L15.438 214.452Q15.612 214.473 15.656 214.654L15.656 214.695Q15.656 214.978 15.496 215.209Q15.335 215.440 15.079 215.568Q14.822 215.696 14.542 215.696Q14.094 215.696 13.811 215.424Q13.527 215.153 13.527 214.695\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(150.6 -280.32)\">\u003Cpath d=\"M19.995 217.012L19.995 216.937Q20.032 216.745 20.213 216.725L20.582 216.725L20.582 213.136L20.213 213.136Q20.032 213.116 19.995 212.924L19.995 212.849Q20.036 212.664 20.213 212.644L20.928 212.644Q21.099 212.661 21.143 212.849L21.143 212.911Q21.328 212.764 21.558 212.687Q21.789 212.610 22.025 212.610Q22.322 212.610 22.582 212.736Q22.842 212.863 23.030 213.083Q23.218 213.304 23.318 213.577Q23.419 213.850 23.419 214.151Q23.419 214.558 23.221 214.917Q23.023 215.276 22.684 215.486Q22.346 215.696 21.936 215.696Q21.481 215.696 21.143 215.375L21.143 216.725L21.516 216.725Q21.697 216.745 21.731 216.937L21.731 217.012Q21.697 217.197 21.516 217.217L20.213 217.217Q20.036 217.197 19.995 217.012M21.898 215.207Q22.168 215.207 22.387 215.059Q22.606 214.910 22.732 214.664Q22.859 214.418 22.859 214.151Q22.859 213.898 22.749 213.654Q22.640 213.410 22.437 213.254Q22.233 213.099 21.970 213.099Q21.690 213.099 21.461 213.261Q21.232 213.423 21.143 213.686L21.143 214.432Q21.222 214.753 21.415 214.980Q21.608 215.207 21.898 215.207M23.843 215.454L23.843 215.375Q23.894 215.194 24.062 215.173L24.684 215.173L24.684 213.136L24.062 213.136Q23.891 213.116 23.843 212.924L23.843 212.849Q23.894 212.664 24.062 212.644L25.026 212.644Q25.200 212.661 25.245 212.849L25.245 213.136Q25.474 212.887 25.785 212.748Q26.096 212.610 26.434 212.610Q26.690 212.610 26.895 212.728Q27.100 212.846 27.100 213.078Q27.100 213.225 27.005 213.328Q26.909 213.430 26.762 213.430Q26.629 213.430 26.528 213.333Q26.427 213.235 26.427 213.099Q26.099 213.099 25.824 213.275Q25.549 213.451 25.397 213.743Q25.245 214.035 25.245 214.367L25.245 215.173L26.072 215.173Q26.253 215.194 26.287 215.375L26.287 215.454Q26.253 215.641 26.072 215.662L24.062 215.662Q23.894 215.641 23.843 215.454M29.220 215.696Q28.806 215.696 28.469 215.483Q28.133 215.269 27.938 214.910Q27.743 214.551 27.743 214.151Q27.743 213.850 27.852 213.568Q27.962 213.287 28.163 213.064Q28.365 212.842 28.633 212.716Q28.902 212.589 29.220 212.589Q29.537 212.589 29.811 212.717Q30.084 212.846 30.279 213.061Q30.474 213.276 30.585 213.557Q30.696 213.837 30.696 214.151Q30.696 214.551 30.500 214.912Q30.303 215.272 29.966 215.484Q29.630 215.696 29.220 215.696M29.220 215.207Q29.626 215.207 29.881 214.862Q30.136 214.517 30.136 214.093Q30.136 213.837 30.018 213.603Q29.900 213.369 29.690 213.223Q29.479 213.078 29.220 213.078Q28.953 213.078 28.745 213.223Q28.536 213.369 28.418 213.603Q28.300 213.837 28.300 214.093Q28.300 214.514 28.557 214.860Q28.813 215.207 29.220 215.207M31.728 215.454L31.728 211.875L31.359 211.875Q31.178 211.854 31.141 211.666L31.141 211.588Q31.178 211.407 31.359 211.386L32.074 211.386Q32.245 211.407 32.289 211.588L32.289 212.911Q32.474 212.764 32.704 212.687Q32.935 212.610 33.171 212.610Q33.468 212.610 33.728 212.736Q33.988 212.863 34.176 213.083Q34.364 213.304 34.464 213.577Q34.565 213.850 34.565 214.151Q34.565 214.558 34.367 214.917Q34.169 215.276 33.830 215.486Q33.492 215.696 33.082 215.696Q32.627 215.696 32.289 215.375L32.289 215.454Q32.245 215.645 32.074 215.662L31.947 215.662Q31.780 215.641 31.728 215.454M33.044 215.207Q33.314 215.207 33.533 215.059Q33.752 214.910 33.878 214.664Q34.005 214.418 34.005 214.151Q34.005 213.898 33.895 213.654Q33.786 213.410 33.583 213.254Q33.379 213.099 33.116 213.099Q32.836 213.099 32.607 213.261Q32.378 213.423 32.289 213.686L32.289 214.432Q32.368 214.753 32.561 214.980Q32.754 215.207 33.044 215.207M35.150 214.688Q35.150 214.298 35.512 214.073Q35.874 213.847 36.348 213.760Q36.821 213.673 37.266 213.666Q37.266 213.478 37.148 213.345Q37.030 213.211 36.849 213.145Q36.667 213.078 36.483 213.078Q36.182 213.078 36.042 213.099L36.042 213.150Q36.042 213.297 35.938 213.398Q35.833 213.498 35.690 213.498Q35.536 213.498 35.435 213.391Q35.334 213.283 35.334 213.136Q35.334 212.781 35.668 212.685Q36.001 212.589 36.490 212.589Q36.725 212.589 36.960 212.658Q37.194 212.726 37.390 212.858Q37.587 212.989 37.706 213.182Q37.826 213.375 37.826 213.618L37.826 215.122Q37.826 215.173 38.287 215.173Q38.458 215.190 38.503 215.375L38.503 215.454Q38.458 215.641 38.287 215.662L38.161 215.662Q37.860 215.662 37.660 215.621Q37.460 215.580 37.334 215.416Q36.931 215.696 36.312 215.696Q36.018 215.696 35.751 215.573Q35.485 215.450 35.317 215.221Q35.150 214.992 35.150 214.688M35.710 214.695Q35.710 214.934 35.922 215.071Q36.134 215.207 36.384 215.207Q36.575 215.207 36.778 215.156Q36.982 215.105 37.124 214.984Q37.266 214.862 37.266 214.667L37.266 214.151Q37.019 214.151 36.655 214.201Q36.291 214.250 36.001 214.372Q35.710 214.493 35.710 214.695M39.159 215.454L39.159 211.875L38.790 211.875Q38.609 211.854 38.571 211.666L38.571 211.588Q38.609 211.407 38.790 211.386L39.504 211.386Q39.675 211.407 39.720 211.588L39.720 212.911Q39.904 212.764 40.135 212.687Q40.366 212.610 40.601 212.610Q40.899 212.610 41.159 212.736Q41.418 212.863 41.606 213.083Q41.794 213.304 41.895 213.577Q41.996 213.850 41.996 214.151Q41.996 214.558 41.798 214.917Q41.600 215.276 41.261 215.486Q40.923 215.696 40.513 215.696Q40.058 215.696 39.720 215.375L39.720 215.454Q39.675 215.645 39.504 215.662L39.378 215.662Q39.210 215.641 39.159 215.454M40.475 215.207Q40.745 215.207 40.964 215.059Q41.183 214.910 41.309 214.664Q41.435 214.418 41.435 214.151Q41.435 213.898 41.326 213.654Q41.217 213.410 41.013 213.254Q40.810 213.099 40.547 213.099Q40.266 213.099 40.037 213.261Q39.808 213.423 39.720 213.686L39.720 214.432Q39.798 214.753 39.991 214.980Q40.184 215.207 40.475 215.207M42.765 215.454L42.765 215.375Q42.809 215.194 42.980 215.173L43.890 215.173L43.890 213.136L43.038 213.136Q42.864 213.116 42.820 212.924L42.820 212.849Q42.864 212.664 43.038 212.644L44.235 212.644Q44.406 212.661 44.450 212.849L44.450 215.173L45.250 215.173Q45.421 215.194 45.465 215.375L45.465 215.454Q45.421 215.641 45.250 215.662L42.980 215.662Q42.809 215.641 42.765 215.454M43.667 211.789L43.667 211.742Q43.667 211.591 43.787 211.485Q43.907 211.379 44.060 211.379Q44.211 211.379 44.330 211.485Q44.450 211.591 44.450 211.742L44.450 211.789Q44.450 211.943 44.330 212.049Q44.211 212.155 44.060 212.155Q43.907 212.155 43.787 212.049Q43.667 211.943 43.667 211.789M46.333 215.454L46.333 215.375Q46.378 215.194 46.549 215.173L47.516 215.173L47.516 211.875L46.549 211.875Q46.378 211.854 46.333 211.666L46.333 211.588Q46.378 211.407 46.549 211.386L47.858 211.386Q48.025 211.407 48.077 211.588L48.077 215.173L49.040 215.173Q49.215 215.194 49.259 215.375L49.259 215.454Q49.215 215.641 49.040 215.662L46.549 215.662Q46.378 215.641 46.333 215.454M50.196 215.454L50.196 215.375Q50.240 215.194 50.411 215.173L51.320 215.173L51.320 213.136L50.469 213.136Q50.295 213.116 50.250 212.924L50.250 212.849Q50.295 212.664 50.469 212.644L51.665 212.644Q51.836 212.661 51.881 212.849L51.881 215.173L52.681 215.173Q52.851 215.194 52.896 215.375L52.896 215.454Q52.851 215.641 52.681 215.662L50.411 215.662Q50.240 215.641 50.196 215.454M51.098 211.789L51.098 211.742Q51.098 211.591 51.218 211.485Q51.337 211.379 51.491 211.379Q51.641 211.379 51.761 211.485Q51.881 211.591 51.881 211.742L51.881 211.789Q51.881 211.943 51.761 212.049Q51.641 212.155 51.491 212.155Q51.337 212.155 51.218 212.049Q51.098 211.943 51.098 211.789M54.420 214.695L54.420 213.136L53.764 213.136Q53.590 213.116 53.545 212.924L53.545 212.849Q53.590 212.664 53.764 212.644L54.420 212.644L54.420 211.988Q54.465 211.807 54.639 211.783L54.766 211.783Q54.936 211.807 54.981 211.988L54.981 212.644L56.170 212.644Q56.338 212.661 56.389 212.849L56.389 212.924Q56.341 213.116 56.170 213.136L54.981 213.136L54.981 214.667Q54.981 215.207 55.483 215.207Q55.702 215.207 55.846 215.045Q55.989 214.883 55.989 214.667Q55.989 214.585 56.052 214.524Q56.116 214.462 56.204 214.452L56.331 214.452Q56.505 214.473 56.550 214.654L56.550 214.695Q56.550 214.978 56.389 215.209Q56.228 215.440 55.972 215.568Q55.716 215.696 55.435 215.696Q54.988 215.696 54.704 215.424Q54.420 215.153 54.420 214.695M57.626 215.454L57.626 215.375Q57.671 215.194 57.842 215.173L58.751 215.173L58.751 213.136L57.900 213.136Q57.725 213.116 57.681 212.924L57.681 212.849Q57.725 212.664 57.900 212.644L59.096 212.644Q59.267 212.661 59.311 212.849L59.311 215.173L60.111 215.173Q60.282 215.194 60.327 215.375L60.327 215.454Q60.282 215.641 60.111 215.662L57.842 215.662Q57.671 215.641 57.626 215.454M58.529 211.789L58.529 211.742Q58.529 211.591 58.648 211.485Q58.768 211.379 58.922 211.379Q59.072 211.379 59.192 211.485Q59.311 211.591 59.311 211.742L59.311 211.789Q59.311 211.943 59.192 212.049Q59.072 212.155 58.922 212.155Q58.768 212.155 58.648 212.049Q58.529 211.943 58.529 211.789M63.874 214.360L61.738 214.360Q61.786 214.602 61.959 214.797Q62.131 214.992 62.374 215.100Q62.617 215.207 62.866 215.207Q63.280 215.207 63.475 214.954Q63.481 214.944 63.531 214.852Q63.580 214.760 63.623 214.722Q63.666 214.684 63.748 214.674L63.874 214.674Q64.042 214.691 64.093 214.879L64.093 214.927Q64.035 215.190 63.833 215.363Q63.632 215.536 63.358 215.616Q63.085 215.696 62.818 215.696Q62.394 215.696 62.010 215.496Q61.625 215.296 61.391 214.946Q61.157 214.596 61.157 214.165L61.157 214.114Q61.157 213.704 61.372 213.351Q61.588 212.999 61.945 212.794Q62.302 212.589 62.712 212.589Q63.153 212.589 63.463 212.784Q63.772 212.979 63.933 213.319Q64.093 213.659 64.093 214.100L64.093 214.151Q64.042 214.339 63.874 214.360M61.745 213.878L63.519 213.878Q63.478 213.519 63.269 213.298Q63.061 213.078 62.712 213.078Q62.367 213.078 62.099 213.307Q61.830 213.536 61.745 213.878M65.030 215.488L65.030 214.688Q65.054 214.507 65.238 214.486L65.385 214.486Q65.529 214.507 65.580 214.647Q65.758 215.207 66.393 215.207Q66.575 215.207 66.775 215.177Q66.975 215.146 67.121 215.045Q67.268 214.944 67.268 214.766Q67.268 214.582 67.074 214.483Q66.879 214.384 66.640 214.346L66.028 214.247Q65.030 214.062 65.030 213.430Q65.030 213.177 65.156 213.011Q65.283 212.846 65.493 212.752Q65.703 212.658 65.927 212.623Q66.151 212.589 66.393 212.589Q66.612 212.589 66.781 212.615Q66.951 212.641 67.094 212.709Q67.162 212.606 67.275 212.589L67.344 212.589Q67.429 212.600 67.484 212.654Q67.538 212.709 67.549 212.791L67.549 213.410Q67.538 213.492 67.484 213.550Q67.429 213.608 67.344 213.618L67.197 213.618Q67.115 213.608 67.057 213.550Q66.998 213.492 66.988 213.410Q66.988 213.078 66.380 213.078Q66.076 213.078 65.797 213.150Q65.518 213.222 65.518 213.437Q65.518 213.669 66.106 213.765L66.722 213.871Q67.145 213.943 67.451 214.160Q67.757 214.377 67.757 214.766Q67.757 215.108 67.550 215.320Q67.344 215.532 67.038 215.614Q66.732 215.696 66.393 215.696Q65.888 215.696 65.539 215.474Q65.477 215.583 65.435 215.633Q65.392 215.683 65.300 215.696L65.238 215.696Q65.050 215.676 65.030 215.488\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 206.926v-8.381\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 195.945-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 178.473v-22.407\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 153.466-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 135.594v-9.604\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 123.39-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 108.764v-12.45\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 93.715-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 75.843v-9.604\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 63.64-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 49.013V36.564\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 33.964-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69 16.093V6.489\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69 3.889-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69-10.738v-15.494\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69-28.832-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M181.69-46.303v-10.668\"\u002F>\u003Cpath stroke=\"none\" d=\"m181.69-59.57-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(246.804 -240.196)\">\u003Cpath d=\"M-5.925 215.454L-5.925 215.375Q-5.880 215.194-5.706 215.173L-5.470 215.173L-5.470 211.875L-5.706 211.875Q-5.880 211.854-5.925 211.666L-5.925 211.588Q-5.880 211.407-5.706 211.386L-5.022 211.386Q-4.910 211.386-4.817 211.451Q-4.725 211.516-4.691 211.615Q-4.448 212.306-4.308 212.699Q-4.168 213.092-3.946 213.721Q-3.724 214.350-3.602 214.708Q-3.481 215.067-3.481 215.101L-3.481 211.875L-3.720 211.875Q-3.891 211.854-3.935 211.666L-3.935 211.588Q-3.891 211.407-3.720 211.386L-2.780 211.386Q-2.609 211.407-2.565 211.588L-2.565 211.666Q-2.609 211.854-2.780 211.875L-3.019 211.875L-3.019 215.454Q-3.064 215.641-3.235 215.662L-3.467 215.662Q-3.577 215.662-3.667 215.597Q-3.758 215.532-3.795 215.430Q-4.055 214.688-4.381 213.770Q-4.708 212.852-4.857 212.425Q-5.005 211.998-5.009 211.947L-5.009 215.173L-4.769 215.173Q-4.602 215.194-4.551 215.375L-4.551 215.454Q-4.602 215.641-4.769 215.662L-5.706 215.662Q-5.880 215.641-5.925 215.454\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(246.804 -240.196)\">\u003Cpath d=\"M1.732 215.454L1.732 215.375Q1.777 215.194 1.947 215.173L2.915 215.173L2.915 211.875L1.947 211.875Q1.777 211.854 1.732 211.666L1.732 211.588Q1.777 211.407 1.947 211.386L3.256 211.386Q3.424 211.407 3.475 211.588L3.475 215.173L4.439 215.173Q4.613 215.194 4.658 215.375L4.658 215.454Q4.613 215.641 4.439 215.662L1.947 215.662Q1.777 215.641 1.732 215.454M5.410 214.688Q5.410 214.298 5.772 214.073Q6.134 213.847 6.608 213.760Q7.081 213.673 7.526 213.666Q7.526 213.478 7.408 213.345Q7.290 213.211 7.109 213.145Q6.927 213.078 6.743 213.078Q6.442 213.078 6.302 213.099L6.302 213.150Q6.302 213.297 6.198 213.398Q6.093 213.498 5.950 213.498Q5.796 213.498 5.695 213.391Q5.594 213.283 5.594 213.136Q5.594 212.781 5.928 212.685Q6.261 212.589 6.750 212.589Q6.985 212.589 7.220 212.658Q7.454 212.726 7.650 212.858Q7.847 212.989 7.966 213.182Q8.086 213.375 8.086 213.618L8.086 215.122Q8.086 215.173 8.547 215.173Q8.718 215.190 8.763 215.375L8.763 215.454Q8.718 215.641 8.547 215.662L8.421 215.662Q8.120 215.662 7.920 215.621Q7.720 215.580 7.594 215.416Q7.191 215.696 6.572 215.696Q6.278 215.696 6.011 215.573Q5.745 215.450 5.577 215.221Q5.410 214.992 5.410 214.688M5.970 214.695Q5.970 214.934 6.182 215.071Q6.394 215.207 6.644 215.207Q6.835 215.207 7.038 215.156Q7.242 215.105 7.384 214.984Q7.526 214.862 7.526 214.667L7.526 214.151Q7.279 214.151 6.915 214.201Q6.551 214.250 6.261 214.372Q5.970 214.493 5.970 214.695M9.070 216.643Q9.070 216.547 9.115 216.467Q9.159 216.387 9.240 216.342Q9.320 216.298 9.412 216.298Q9.508 216.298 9.588 216.342Q9.669 216.387 9.713 216.467Q9.757 216.547 9.757 216.643L9.631 216.643Q9.631 216.763 9.652 216.763Q9.877 216.763 10.041 216.595Q10.205 216.428 10.280 216.195L10.465 215.662L9.470 213.136L9.183 213.136Q9.012 213.116 8.964 212.924L8.964 212.849Q9.016 212.664 9.183 212.644L10.198 212.644Q10.369 212.664 10.414 212.849L10.414 212.924Q10.369 213.116 10.198 213.136L9.966 213.136Q10.260 213.878 10.474 214.450Q10.687 215.023 10.687 215.101L10.694 215.101Q10.694 215.050 10.774 214.794Q10.855 214.537 11.024 214.027Q11.193 213.516 11.316 213.136L11.073 213.136Q10.889 213.116 10.855 212.924L10.855 212.849Q10.899 212.661 11.073 212.644L12.082 212.644Q12.263 212.664 12.297 212.849L12.297 212.924Q12.263 213.116 12.082 213.136L11.801 213.136L10.773 216.195Q10.626 216.633 10.340 216.942Q10.055 217.251 9.652 217.251Q9.412 217.251 9.241 217.067Q9.070 216.882 9.070 216.643M15.558 214.360L13.422 214.360Q13.469 214.602 13.642 214.797Q13.815 214.992 14.057 215.100Q14.300 215.207 14.549 215.207Q14.963 215.207 15.158 214.954Q15.165 214.944 15.214 214.852Q15.264 214.760 15.307 214.722Q15.349 214.684 15.431 214.674L15.558 214.674Q15.725 214.691 15.777 214.879L15.777 214.927Q15.718 215.190 15.517 215.363Q15.315 215.536 15.042 215.616Q14.768 215.696 14.502 215.696Q14.078 215.696 13.693 215.496Q13.309 215.296 13.075 214.946Q12.840 214.596 12.840 214.165L12.840 214.114Q12.840 213.704 13.056 213.351Q13.271 212.999 13.628 212.794Q13.985 212.589 14.396 212.589Q14.837 212.589 15.146 212.784Q15.455 212.979 15.616 213.319Q15.777 213.659 15.777 214.100L15.777 214.151Q15.725 214.339 15.558 214.360M13.428 213.878L15.202 213.878Q15.161 213.519 14.953 213.298Q14.744 213.078 14.396 213.078Q14.050 213.078 13.782 213.307Q13.514 213.536 13.428 213.878M16.395 215.454L16.395 215.375Q16.446 215.194 16.614 215.173L17.236 215.173L17.236 213.136L16.614 213.136Q16.443 213.116 16.395 212.924L16.395 212.849Q16.446 212.664 16.614 212.644L17.578 212.644Q17.752 212.661 17.797 212.849L17.797 213.136Q18.026 212.887 18.337 212.748Q18.648 212.610 18.986 212.610Q19.242 212.610 19.447 212.728Q19.652 212.846 19.652 213.078Q19.652 213.225 19.557 213.328Q19.461 213.430 19.314 213.430Q19.181 213.430 19.080 213.333Q18.979 213.235 18.979 213.099Q18.651 213.099 18.376 213.275Q18.101 213.451 17.949 213.743Q17.797 214.035 17.797 214.367L17.797 215.173L18.624 215.173Q18.805 215.194 18.839 215.375L18.839 215.454Q18.805 215.641 18.624 215.662L16.614 215.662Q16.446 215.641 16.395 215.454M20.428 215.488L20.428 214.688Q20.452 214.507 20.637 214.486L20.784 214.486Q20.927 214.507 20.979 214.647Q21.156 215.207 21.792 215.207Q21.973 215.207 22.173 215.177Q22.373 215.146 22.520 215.045Q22.667 214.944 22.667 214.766Q22.667 214.582 22.472 214.483Q22.277 214.384 22.038 214.346L21.426 214.247Q20.428 214.062 20.428 213.430Q20.428 213.177 20.555 213.011Q20.681 212.846 20.891 212.752Q21.102 212.658 21.326 212.623Q21.549 212.589 21.792 212.589Q22.011 212.589 22.180 212.615Q22.349 212.641 22.493 212.709Q22.561 212.606 22.674 212.589L22.742 212.589Q22.828 212.600 22.882 212.654Q22.937 212.709 22.947 212.791L22.947 213.410Q22.937 213.492 22.882 213.550Q22.828 213.608 22.742 213.618L22.595 213.618Q22.513 213.608 22.455 213.550Q22.397 213.492 22.387 213.410Q22.387 213.078 21.778 213.078Q21.474 213.078 21.196 213.150Q20.917 213.222 20.917 213.437Q20.917 213.669 21.505 213.765L22.120 213.871Q22.544 213.943 22.850 214.160Q23.156 214.377 23.156 214.766Q23.156 215.108 22.949 215.320Q22.742 215.532 22.436 215.614Q22.131 215.696 21.792 215.696Q21.286 215.696 20.938 215.474Q20.876 215.583 20.833 215.633Q20.791 215.683 20.698 215.696L20.637 215.696Q20.449 215.676 20.428 215.488\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(246.804 -240.196)\">\u003Cpath d=\"M30.094 216.223Q29.629 215.953 29.279 215.525Q28.929 215.098 28.744 214.579Q28.559 214.059 28.559 213.519Q28.559 212.979 28.742 212.464Q28.925 211.950 29.272 211.530Q29.619 211.109 30.087 210.826Q30.149 210.805 30.176 210.805L30.255 210.805Q30.340 210.815 30.398 210.873Q30.456 210.932 30.456 211.020Q30.456 211.147 30.368 211.202Q29.974 211.454 29.689 211.818Q29.404 212.183 29.262 212.613Q29.120 213.044 29.120 213.519Q29.120 213.874 29.204 214.213Q29.287 214.551 29.443 214.845Q29.599 215.139 29.826 215.387Q30.053 215.635 30.357 215.836Q30.456 215.905 30.456 216.024Q30.456 216.110 30.398 216.171Q30.340 216.233 30.255 216.243L30.176 216.243Q30.125 216.243 30.094 216.223M32.716 215.696Q32.309 215.696 31.989 215.477Q31.670 215.259 31.490 214.905Q31.311 214.551 31.311 214.151Q31.311 213.850 31.420 213.570Q31.530 213.290 31.733 213.071Q31.936 212.852 32.203 212.731Q32.470 212.610 32.781 212.610Q33.228 212.610 33.584 212.890L33.584 211.875L33.215 211.875Q33.030 211.854 32.996 211.666L32.996 211.588Q33.030 211.407 33.215 211.386L33.926 211.386Q34.100 211.407 34.144 211.588L34.144 215.173L34.517 215.173Q34.698 215.194 34.732 215.375L34.732 215.454Q34.698 215.641 34.517 215.662L33.803 215.662Q33.628 215.641 33.584 215.454L33.584 215.341Q33.413 215.508 33.184 215.602Q32.955 215.696 32.716 215.696M32.750 215.207Q33.064 215.207 33.285 214.972Q33.505 214.736 33.584 214.408L33.584 213.680Q33.533 213.516 33.422 213.384Q33.310 213.252 33.155 213.175Q32.999 213.099 32.828 213.099Q32.558 213.099 32.340 213.247Q32.121 213.396 31.995 213.645Q31.868 213.895 31.868 214.158Q31.868 214.551 32.118 214.879Q32.367 215.207 32.750 215.207M37.873 214.360L35.737 214.360Q35.785 214.602 35.958 214.797Q36.130 214.992 36.373 215.100Q36.616 215.207 36.865 215.207Q37.279 215.207 37.474 214.954Q37.480 214.944 37.530 214.852Q37.579 214.760 37.622 214.722Q37.665 214.684 37.747 214.674L37.873 214.674Q38.041 214.691 38.092 214.879L38.092 214.927Q38.034 215.190 37.832 215.363Q37.631 215.536 37.357 215.616Q37.084 215.696 36.817 215.696Q36.393 215.696 36.009 215.496Q35.624 215.296 35.390 214.946Q35.156 214.596 35.156 214.165L35.156 214.114Q35.156 213.704 35.371 213.351Q35.587 212.999 35.944 212.794Q36.301 212.589 36.711 212.589Q37.152 212.589 37.462 212.784Q37.771 212.979 37.932 213.319Q38.092 213.659 38.092 214.100L38.092 214.151Q38.041 214.339 37.873 214.360M35.744 213.878L37.518 213.878Q37.477 213.519 37.268 213.298Q37.060 213.078 36.711 213.078Q36.366 213.078 36.098 213.307Q35.829 213.536 35.744 213.878M39.005 214.151Q39.005 213.731 39.218 213.369Q39.432 213.006 39.796 212.798Q40.160 212.589 40.580 212.589Q41.066 212.589 41.397 212.685Q41.729 212.781 41.729 213.136Q41.729 213.283 41.630 213.391Q41.531 213.498 41.380 213.498Q41.230 213.498 41.126 213.398Q41.021 213.297 41.021 213.150L41.021 213.099Q40.881 213.078 40.587 213.078Q40.300 213.078 40.066 213.227Q39.832 213.375 39.699 213.623Q39.565 213.871 39.565 214.151Q39.565 214.432 39.716 214.678Q39.866 214.924 40.116 215.066Q40.365 215.207 40.652 215.207Q40.926 215.207 41.037 215.117Q41.148 215.026 41.250 214.860Q41.353 214.695 41.455 214.681L41.602 214.681Q41.695 214.691 41.751 214.751Q41.808 214.811 41.808 214.900Q41.808 214.941 41.790 214.975Q41.695 215.231 41.517 215.389Q41.339 215.546 41.098 215.621Q40.857 215.696 40.580 215.696Q40.157 215.696 39.793 215.488Q39.429 215.279 39.217 214.927Q39.005 214.575 39.005 214.151M44.087 215.696Q43.674 215.696 43.337 215.483Q43 215.269 42.806 214.910Q42.611 214.551 42.611 214.151Q42.611 213.850 42.720 213.568Q42.829 213.287 43.031 213.064Q43.233 212.842 43.501 212.716Q43.769 212.589 44.087 212.589Q44.405 212.589 44.679 212.717Q44.952 212.846 45.147 213.061Q45.342 213.276 45.453 213.557Q45.564 213.837 45.564 214.151Q45.564 214.551 45.367 214.912Q45.171 215.272 44.834 215.484Q44.497 215.696 44.087 215.696M44.087 215.207Q44.494 215.207 44.749 214.862Q45.003 214.517 45.003 214.093Q45.003 213.837 44.885 213.603Q44.767 213.369 44.557 213.223Q44.347 213.078 44.087 213.078Q43.821 213.078 43.612 213.223Q43.404 213.369 43.286 213.603Q43.168 213.837 43.168 214.093Q43.168 214.514 43.424 214.860Q43.681 215.207 44.087 215.207M47.577 215.696Q47.170 215.696 46.851 215.477Q46.531 215.259 46.352 214.905Q46.172 214.551 46.172 214.151Q46.172 213.850 46.282 213.570Q46.391 213.290 46.594 213.071Q46.798 212.852 47.064 212.731Q47.331 212.610 47.642 212.610Q48.090 212.610 48.445 212.890L48.445 211.875L48.076 211.875Q47.891 211.854 47.857 211.666L47.857 211.588Q47.891 211.407 48.076 211.386L48.787 211.386Q48.961 211.407 49.006 211.588L49.006 215.173L49.378 215.173Q49.559 215.194 49.594 215.375L49.594 215.454Q49.559 215.641 49.378 215.662L48.664 215.662Q48.490 215.641 48.445 215.454L48.445 215.341Q48.274 215.508 48.045 215.602Q47.816 215.696 47.577 215.696M47.611 215.207Q47.926 215.207 48.146 214.972Q48.367 214.736 48.445 214.408L48.445 213.680Q48.394 213.516 48.283 213.384Q48.172 213.252 48.016 213.175Q47.861 213.099 47.690 213.099Q47.420 213.099 47.201 213.247Q46.982 213.396 46.856 213.645Q46.729 213.895 46.729 214.158Q46.729 214.551 46.979 214.879Q47.228 215.207 47.611 215.207M52.735 214.360L50.599 214.360Q50.646 214.602 50.819 214.797Q50.992 214.992 51.234 215.100Q51.477 215.207 51.726 215.207Q52.140 215.207 52.335 214.954Q52.342 214.944 52.391 214.852Q52.441 214.760 52.484 214.722Q52.526 214.684 52.608 214.674L52.735 214.674Q52.902 214.691 52.953 214.879L52.953 214.927Q52.895 215.190 52.694 215.363Q52.492 215.536 52.219 215.616Q51.945 215.696 51.679 215.696Q51.255 215.696 50.870 215.496Q50.486 215.296 50.252 214.946Q50.017 214.596 50.017 214.165L50.017 214.114Q50.017 213.704 50.233 213.351Q50.448 212.999 50.805 212.794Q51.162 212.589 51.573 212.589Q52.014 212.589 52.323 212.784Q52.632 212.979 52.793 213.319Q52.953 213.659 52.953 214.100L52.953 214.151Q52.902 214.339 52.735 214.360M50.605 213.878L52.379 213.878Q52.338 213.519 52.130 213.298Q51.921 213.078 51.573 213.078Q51.227 213.078 50.959 213.307Q50.691 213.536 50.605 213.878M53.572 215.454L53.572 215.375Q53.623 215.194 53.791 215.173L54.413 215.173L54.413 213.136L53.791 213.136Q53.620 213.116 53.572 212.924L53.572 212.849Q53.623 212.664 53.791 212.644L54.755 212.644Q54.929 212.661 54.974 212.849L54.974 213.136Q55.203 212.887 55.514 212.748Q55.825 212.610 56.163 212.610Q56.419 212.610 56.624 212.728Q56.829 212.846 56.829 213.078Q56.829 213.225 56.734 213.328Q56.638 213.430 56.491 213.430Q56.358 213.430 56.257 213.333Q56.156 213.235 56.156 213.099Q55.828 213.099 55.553 213.275Q55.278 213.451 55.126 213.743Q54.974 214.035 54.974 214.367L54.974 215.173L55.801 215.173Q55.982 215.194 56.016 215.375L56.016 215.454Q55.982 215.641 55.801 215.662L53.791 215.662Q53.623 215.641 53.572 215.454M58.002 216.243L57.927 216.243Q57.834 216.233 57.775 216.170Q57.715 216.106 57.715 216.024Q57.715 215.901 57.807 215.843Q58.101 215.655 58.337 215.402Q58.573 215.149 58.733 214.845Q58.894 214.541 58.973 214.209Q59.051 213.878 59.051 213.519Q59.051 213.047 58.908 212.617Q58.764 212.186 58.485 211.824Q58.207 211.461 57.821 211.208Q57.715 211.137 57.715 211.020Q57.715 210.935 57.775 210.875Q57.834 210.815 57.927 210.805L58.002 210.805Q58.050 210.805 58.080 210.826Q58.419 211.020 58.716 211.325Q59.014 211.629 59.207 211.974Q59.400 212.319 59.506 212.709Q59.612 213.099 59.612 213.519Q59.612 213.943 59.506 214.338Q59.400 214.732 59.203 215.079Q59.007 215.426 58.723 215.718Q58.439 216.011 58.087 216.223Q58.026 216.243 58.002 216.243\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M46.539 47.79c32.72 0 52.637 36.989 79.913 36.989\"\u002F>\u003Cpath stroke=\"none\" d=\"m129.052 84.779-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003Cg fill=\"var(--tk-good)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(69.46 -154.888)\">\u003Cpath d=\"M-5.954 215.424L-5.954 215.334Q-5.904 215.127-5.708 215.103L-5.244 215.103L-5.244 211.334L-5.708 211.334Q-5.904 211.310-5.954 211.096L-5.954 211.006Q-5.904 210.799-5.708 210.775L-4.962 210.775Q-4.767 210.795-4.716 211.006L-4.716 213.830L-3.572 212.775L-3.869 212.775Q-4.076 212.752-4.115 212.533L-4.115 212.447Q-4.076 212.236-3.869 212.213L-2.419 212.213Q-2.216 212.236-2.169 212.447L-2.169 212.533Q-2.212 212.752-2.419 212.775L-2.787 212.775L-3.732 213.639L-2.579 215.103L-2.244 215.103Q-2.037 215.127-1.994 215.334L-1.994 215.424Q-2.037 215.639-2.244 215.662L-3.412 215.662Q-3.607 215.639-3.658 215.424L-3.658 215.334Q-3.607 215.127-3.412 215.103L-3.251 215.103L-4.115 213.998L-4.716 214.549L-4.716 215.103L-4.251 215.103Q-4.060 215.127-4.001 215.334L-4.001 215.424Q-4.060 215.639-4.251 215.662L-5.708 215.662Q-5.904 215.639-5.954 215.424M1.659 214.174L-0.783 214.174Q-0.728 214.451-0.531 214.674Q-0.333 214.896-0.056 215.019Q0.221 215.142 0.506 215.142Q0.979 215.142 1.202 214.853Q1.210 214.842 1.266 214.736Q1.323 214.631 1.372 214.588Q1.421 214.545 1.514 214.533L1.659 214.533Q1.850 214.553 1.909 214.767L1.909 214.822Q1.842 215.123 1.612 215.320Q1.381 215.517 1.069 215.609Q0.756 215.701 0.452 215.701Q-0.033 215.701-0.472 215.473Q-0.912 215.244-1.179 214.844Q-1.447 214.443-1.447 213.951L-1.447 213.892Q-1.447 213.424-1.201 213.021Q-0.954 212.619-0.546 212.385Q-0.138 212.150 0.331 212.150Q0.835 212.150 1.188 212.373Q1.542 212.596 1.725 212.984Q1.909 213.373 1.909 213.877L1.909 213.935Q1.850 214.150 1.659 214.174M-0.775 213.623L1.253 213.623Q1.206 213.213 0.967 212.961Q0.729 212.709 0.331 212.709Q-0.064 212.709-0.370 212.971Q-0.677 213.232-0.775 213.623M2.737 216.783Q2.737 216.674 2.788 216.582Q2.838 216.490 2.930 216.439Q3.022 216.389 3.128 216.389Q3.237 216.389 3.329 216.439Q3.421 216.490 3.471 216.582Q3.522 216.674 3.522 216.783L3.378 216.783Q3.378 216.920 3.401 216.920Q3.659 216.920 3.846 216.728Q4.034 216.537 4.120 216.271L4.331 215.662L3.194 212.775L2.866 212.775Q2.671 212.752 2.616 212.533L2.616 212.447Q2.674 212.236 2.866 212.213L4.026 212.213Q4.221 212.236 4.272 212.447L4.272 212.533Q4.221 212.752 4.026 212.775L3.760 212.775Q4.096 213.623 4.340 214.277Q4.585 214.932 4.585 215.021L4.592 215.021Q4.592 214.963 4.684 214.670Q4.776 214.377 4.969 213.793Q5.163 213.209 5.303 212.775L5.026 212.775Q4.815 212.752 4.776 212.533L4.776 212.447Q4.827 212.232 5.026 212.213L6.178 212.213Q6.385 212.236 6.424 212.447L6.424 212.533Q6.385 212.752 6.178 212.775L5.858 212.775L4.682 216.271Q4.514 216.771 4.188 217.125Q3.862 217.478 3.401 217.478Q3.128 217.478 2.932 217.267Q2.737 217.057 2.737 216.783M7.225 215.463L7.225 214.549Q7.253 214.342 7.463 214.318L7.631 214.318Q7.796 214.342 7.854 214.502Q8.057 215.142 8.784 215.142Q8.991 215.142 9.219 215.107Q9.448 215.072 9.616 214.957Q9.784 214.842 9.784 214.639Q9.784 214.428 9.561 214.314Q9.338 214.201 9.065 214.158L8.366 214.045Q7.225 213.834 7.225 213.111Q7.225 212.822 7.370 212.633Q7.514 212.443 7.755 212.336Q7.995 212.228 8.251 212.189Q8.506 212.150 8.784 212.150Q9.034 212.150 9.227 212.180Q9.421 212.209 9.585 212.287Q9.663 212.170 9.792 212.150L9.870 212.150Q9.967 212.162 10.030 212.225Q10.092 212.287 10.104 212.381L10.104 213.088Q10.092 213.182 10.030 213.248Q9.967 213.314 9.870 213.326L9.702 213.326Q9.608 213.314 9.542 213.248Q9.475 213.182 9.463 213.088Q9.463 212.709 8.768 212.709Q8.421 212.709 8.102 212.791Q7.784 212.873 7.784 213.119Q7.784 213.385 8.456 213.494L9.159 213.615Q9.643 213.697 9.993 213.945Q10.342 214.193 10.342 214.639Q10.342 215.029 10.106 215.271Q9.870 215.514 9.520 215.607Q9.171 215.701 8.784 215.701Q8.206 215.701 7.807 215.447Q7.737 215.572 7.688 215.629Q7.639 215.685 7.534 215.701L7.463 215.701Q7.249 215.678 7.225 215.463M12.604 216.775Q12.491 216.775 12.401 216.685Q12.311 216.596 12.311 216.486Q12.311 216.310 12.503 216.236Q12.721 216.185 12.893 216.027Q13.065 215.869 13.131 215.646Q13.108 215.646 13.077 215.662L13.014 215.662Q12.784 215.662 12.618 215.500Q12.452 215.338 12.452 215.103Q12.452 214.869 12.616 214.709Q12.780 214.549 13.014 214.549Q13.225 214.549 13.389 214.670Q13.553 214.791 13.643 214.984Q13.733 215.178 13.733 215.389Q13.733 215.865 13.434 216.254Q13.135 216.642 12.671 216.767Q12.647 216.775 12.604 216.775\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(69.46 -154.888)\">\u003Cpath d=\"M21.057 215.439L20.171 212.775L19.850 212.775Q19.651 212.752 19.600 212.533L19.600 212.447Q19.651 212.236 19.850 212.213L21.010 212.213Q21.206 212.232 21.256 212.447L21.256 212.533Q21.206 212.752 21.010 212.775L20.729 212.775L21.522 215.150L22.311 212.775L22.034 212.775Q21.835 212.752 21.784 212.533L21.784 212.447Q21.835 212.236 22.034 212.213L23.194 212.213Q23.389 212.236 23.440 212.447L23.440 212.533Q23.389 212.752 23.194 212.775L22.874 212.775L21.987 215.439Q21.944 215.553 21.842 215.627Q21.741 215.701 21.616 215.701L21.424 215.701Q21.307 215.701 21.204 215.629Q21.100 215.557 21.057 215.439M24.053 214.549Q24.053 214.103 24.467 213.846Q24.881 213.588 25.422 213.488Q25.963 213.389 26.471 213.381Q26.471 213.166 26.337 213.014Q26.202 212.861 25.995 212.785Q25.788 212.709 25.577 212.709Q25.233 212.709 25.073 212.732L25.073 212.791Q25.073 212.959 24.954 213.074Q24.835 213.189 24.671 213.189Q24.495 213.189 24.380 213.066Q24.264 212.943 24.264 212.775Q24.264 212.369 24.645 212.260Q25.026 212.150 25.585 212.150Q25.854 212.150 26.122 212.228Q26.389 212.307 26.614 212.457Q26.838 212.607 26.975 212.828Q27.112 213.049 27.112 213.326L27.112 215.045Q27.112 215.103 27.639 215.103Q27.835 215.123 27.885 215.334L27.885 215.424Q27.835 215.639 27.639 215.662L27.495 215.662Q27.151 215.662 26.922 215.615Q26.694 215.568 26.549 215.381Q26.088 215.701 25.381 215.701Q25.046 215.701 24.741 215.560Q24.436 215.420 24.245 215.158Q24.053 214.896 24.053 214.549M24.694 214.557Q24.694 214.830 24.936 214.986Q25.178 215.142 25.463 215.142Q25.682 215.142 25.915 215.084Q26.147 215.025 26.309 214.887Q26.471 214.748 26.471 214.525L26.471 213.935Q26.190 213.935 25.774 213.992Q25.358 214.049 25.026 214.187Q24.694 214.326 24.694 214.557M28.342 215.424L28.342 215.334Q28.393 215.127 28.588 215.103L29.694 215.103L29.694 211.334L28.588 211.334Q28.393 211.310 28.342 211.096L28.342 211.006Q28.393 210.799 28.588 210.775L30.085 210.775Q30.276 210.799 30.335 211.006L30.335 215.103L31.436 215.103Q31.635 215.127 31.686 215.334L31.686 215.424Q31.635 215.639 31.436 215.662L28.588 215.662Q28.393 215.639 28.342 215.424M32.881 214.807L32.881 212.775L32.460 212.775Q32.253 212.752 32.210 212.533L32.210 212.447Q32.256 212.236 32.460 212.213L33.276 212.213Q33.471 212.236 33.522 212.447L33.522 214.775Q33.522 215.010 33.692 215.076Q33.862 215.142 34.147 215.142Q34.354 215.142 34.549 215.066Q34.745 214.990 34.870 214.840Q34.995 214.689 34.995 214.478L34.995 212.775L34.573 212.775Q34.362 212.752 34.323 212.533L34.323 212.447Q34.362 212.236 34.573 212.213L35.385 212.213Q35.585 212.236 35.635 212.447L35.635 215.103L36.061 215.103Q36.268 215.127 36.307 215.334L36.307 215.424Q36.268 215.639 36.061 215.662L35.245 215.662Q35.046 215.639 34.995 215.439Q34.592 215.701 34.085 215.701Q33.850 215.701 33.635 215.660Q33.421 215.619 33.255 215.517Q33.088 215.416 32.985 215.238Q32.881 215.060 32.881 214.807M39.897 214.174L37.456 214.174Q37.510 214.451 37.708 214.674Q37.905 214.896 38.182 215.019Q38.460 215.142 38.745 215.142Q39.217 215.142 39.440 214.853Q39.448 214.842 39.505 214.736Q39.561 214.631 39.610 214.588Q39.659 214.545 39.753 214.533L39.897 214.533Q40.088 214.553 40.147 214.767L40.147 214.822Q40.081 215.123 39.850 215.320Q39.620 215.517 39.307 215.609Q38.995 215.701 38.690 215.701Q38.206 215.701 37.766 215.473Q37.327 215.244 37.059 214.844Q36.792 214.443 36.792 213.951L36.792 213.892Q36.792 213.424 37.038 213.021Q37.284 212.619 37.692 212.385Q38.100 212.150 38.569 212.150Q39.073 212.150 39.426 212.373Q39.780 212.596 39.963 212.984Q40.147 213.373 40.147 213.877L40.147 213.935Q40.088 214.150 39.897 214.174M37.463 213.623L39.491 213.623Q39.444 213.213 39.206 212.961Q38.967 212.709 38.569 212.709Q38.174 212.709 37.868 212.971Q37.561 213.232 37.463 213.623M41.217 215.463L41.217 214.549Q41.245 214.342 41.456 214.318L41.624 214.318Q41.788 214.342 41.846 214.502Q42.049 215.142 42.776 215.142Q42.983 215.142 43.212 215.107Q43.440 215.072 43.608 214.957Q43.776 214.842 43.776 214.639Q43.776 214.428 43.553 214.314Q43.331 214.201 43.057 214.158L42.358 214.045Q41.217 213.834 41.217 213.111Q41.217 212.822 41.362 212.633Q41.506 212.443 41.747 212.336Q41.987 212.228 42.243 212.189Q42.499 212.150 42.776 212.150Q43.026 212.150 43.219 212.180Q43.413 212.209 43.577 212.287Q43.655 212.170 43.784 212.150L43.862 212.150Q43.960 212.162 44.022 212.225Q44.085 212.287 44.096 212.381L44.096 213.088Q44.085 213.182 44.022 213.248Q43.960 213.314 43.862 213.326L43.694 213.326Q43.600 213.314 43.534 213.248Q43.467 213.182 43.456 213.088Q43.456 212.709 42.760 212.709Q42.413 212.709 42.094 212.791Q41.776 212.873 41.776 213.119Q41.776 213.385 42.448 213.494L43.151 213.615Q43.635 213.697 43.985 213.945Q44.335 214.193 44.335 214.639Q44.335 215.029 44.098 215.271Q43.862 215.514 43.512 215.607Q43.163 215.701 42.776 215.701Q42.198 215.701 41.799 215.447Q41.729 215.572 41.680 215.629Q41.631 215.685 41.526 215.701L41.456 215.701Q41.241 215.678 41.217 215.463\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">The full encoder–decoder Transformer. The encoder (left) reads the source; its output feeds cross-attention (green) in every decoder layer, which masks self-attention and reads out through linear-plus-softmax.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:371.858px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 278.894 178.965\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M-33.272-30.388v-26.176h26.176v26.176Zm26.176-26.176\"\u002F>\u003Cpath stroke=\"none\" d=\"M-7.096-30.388v-26.176h26.177v26.176Zm26.177-26.176\"\u002F>\u003Cpath stroke=\"none\" d=\"M19.08-30.388v-26.176h26.177v26.176ZM45.257-30.388v-26.176h26.177v26.176ZM71.434-30.388v-26.176H97.61v26.176ZM97.61-30.388v-26.176h26.177v26.176Zm26.177-26.176\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M-33.272-4.211v-26.177h26.176V-4.21ZM-7.096-4.211v-26.177h26.177V-4.21Zm26.177-26.177\"\u002F>\u003Cpath stroke=\"none\" d=\"M19.08-4.211v-26.177h26.177V-4.21ZM45.257-4.211v-26.177h26.177V-4.21ZM71.434-4.211v-26.177H97.61V-4.21ZM97.61-4.211v-26.177h26.177V-4.21Zm26.177-26.177\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M-33.272 21.965V-4.21h26.176v26.176ZM-7.096 21.965V-4.21h26.177v26.176ZM19.081-4.21\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M19.08 21.965V-4.21h26.177v26.176ZM45.258-4.21\"\u002F>\u003Cpath stroke=\"none\" d=\"M45.257 21.965V-4.21h26.177v26.176ZM71.434 21.965V-4.21H97.61v26.176ZM97.61 21.965V-4.21h26.177v26.176ZM123.787-4.21\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M-33.272 48.142V21.965h26.176v26.177ZM-7.096 48.142V21.965h26.177v26.177Zm26.177-26.177\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M19.08 48.142V21.965h26.177v26.177ZM45.257 48.142V21.965h26.177v26.177Zm26.177-26.177\"\u002F>\u003Cpath stroke=\"none\" d=\"M71.434 48.142V21.965H97.61v26.177ZM97.61 48.142V21.965h26.177v26.177Zm26.177-26.177\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M-33.272 74.318V48.142h26.176v26.176ZM-7.096 74.318V48.142h26.177v26.176Zm26.177-26.176\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M19.08 74.318V48.142h26.177v26.176ZM45.257 74.318V48.142h26.177v26.176ZM71.434 74.318V48.142H97.61v26.176ZM97.61 48.142\"\u002F>\u003Cpath stroke=\"none\" d=\"M97.61 74.318V48.142h26.177v26.176Zm26.177-26.176\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M-33.272 100.495V74.318h26.176v26.177ZM-7.096 100.495V74.318h26.177v26.177Zm26.177-26.177\"\u002F>\u003Cpath fill=\"var(--tk-soft-accent)\" stroke=\"none\" d=\"M19.08 100.495V74.318h26.177v26.177ZM45.257 100.495V74.318h26.177v26.177ZM71.434 100.495V74.318H97.61v26.177ZM97.61 100.495V74.318h26.177v26.177Zm26.177-26.177\"\u002F>\u003Cpath fill=\"none\" d=\"M-33.272 100.495h157.059m-157.06-28.453h157.06M-33.273 43.59h157.06m-157.06-28.452h157.06m-157.06-28.453h157.06M-33.273-41.77h157.06m-157.06 142.264v-157.06m28.453 157.06v-157.06m28.453 157.06v-157.06m28.453 157.06v-157.06m28.453 157.06v-157.06m28.452 157.06v-157.06m14.796 0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(3.876 -164.57)\">\u003Cpath d=\"M-31.361 100.495L-32.944 100.495L-32.944 100.215Q-32.715 100.215-32.566 100.181Q-32.418 100.146-32.418 100.006L-32.418 96.387Q-32.418 96.117-32.525 96.055Q-32.633 95.994-32.944 95.994L-32.944 95.713L-31.864 95.638L-31.864 98.926L-30.879 98.157Q-30.674 98.020-30.674 97.870Q-30.674 97.826-30.715 97.791Q-30.756 97.757-30.801 97.757L-30.801 97.477L-29.437 97.477L-29.437 97.757Q-29.926 97.757-30.445 98.157L-31.002 98.591L-30.025 99.815Q-29.823 100.061-29.690 100.138Q-29.557 100.215-29.270 100.215L-29.270 100.495L-30.702 100.495L-30.702 100.215Q-30.514 100.215-30.514 100.102Q-30.514 100.006-30.668 99.815L-31.402 98.906L-31.884 99.285L-31.884 100.006Q-31.884 100.143-31.736 100.179Q-31.587 100.215-31.361 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.876 -164.57)\">\u003Cpath d=\"M-29.013 98.960Q-29.013 98.639-28.888 98.350Q-28.763 98.061-28.537 97.838Q-28.312 97.614-28.016 97.494Q-27.721 97.374-27.403 97.374Q-27.075 97.374-26.813 97.474Q-26.552 97.573-26.376 97.755Q-26.200 97.938-26.106 98.196Q-26.012 98.454-26.012 98.786Q-26.012 98.878-26.094 98.899L-28.349 98.899L-28.349 98.960Q-28.349 99.548-28.066 99.931Q-27.782 100.314-27.215 100.314Q-26.893 100.314-26.625 100.121Q-26.357 99.928-26.268 99.613Q-26.261 99.572-26.186 99.558L-26.094 99.558Q-26.012 99.582-26.012 99.654Q-26.012 99.661-26.018 99.688Q-26.131 100.085-26.502 100.324Q-26.873 100.563-27.297 100.563Q-27.734 100.563-28.134 100.355Q-28.534 100.146-28.773 99.779Q-29.013 99.412-29.013 98.960M-28.343 98.690L-26.528 98.690Q-26.528 98.413-26.625 98.161Q-26.723 97.908-26.921 97.752Q-27.119 97.597-27.403 97.597Q-27.680 97.597-27.893 97.755Q-28.107 97.914-28.225 98.169Q-28.343 98.424-28.343 98.690M-25.089 101.630Q-24.959 101.698-24.822 101.698Q-24.651 101.698-24.501 101.609Q-24.350 101.520-24.239 101.375Q-24.128 101.230-24.050 101.062L-23.786 100.495L-24.955 97.969Q-25.031 97.822-25.161 97.790Q-25.290 97.757-25.523 97.757L-25.523 97.477L-24.002 97.477L-24.002 97.757Q-24.350 97.757-24.350 97.904Q-24.347 97.925-24.345 97.942Q-24.344 97.959-24.344 97.969L-23.486 99.828L-22.713 98.157Q-22.679 98.089-22.679 98.010Q-22.679 97.897-22.763 97.827Q-22.847 97.757-22.959 97.757L-22.959 97.477L-21.763 97.477L-21.763 97.757Q-21.982 97.757-22.154 97.861Q-22.327 97.966-22.419 98.157L-23.756 101.062Q-23.927 101.432-24.197 101.678Q-24.467 101.924-24.822 101.924Q-25.092 101.924-25.311 101.758Q-25.530 101.592-25.530 101.329Q-25.530 101.192-25.437 101.103Q-25.345 101.015-25.205 101.015Q-25.068 101.015-24.979 101.103Q-24.890 101.192-24.890 101.329Q-24.890 101.432-24.943 101.510Q-24.996 101.589-25.089 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(3.876 -164.57)\">\u003Cpath d=\"M-15.509 100.495L-18.039 100.495L-18.039 100.215Q-17.071 100.215-17.071 100.006L-17.071 96.387Q-17.464 96.575-18.086 96.575L-18.086 96.294Q-17.669 96.294-17.305 96.193Q-16.941 96.093-16.685 95.847L-16.559 95.847Q-16.494 95.864-16.477 95.932L-16.477 100.006Q-16.477 100.215-15.509 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(30.053 -164.57)\">\u003Cpath d=\"M-31.361 100.495L-32.944 100.495L-32.944 100.215Q-32.715 100.215-32.566 100.181Q-32.418 100.146-32.418 100.006L-32.418 96.387Q-32.418 96.117-32.525 96.055Q-32.633 95.994-32.944 95.994L-32.944 95.713L-31.864 95.638L-31.864 98.926L-30.879 98.157Q-30.674 98.020-30.674 97.870Q-30.674 97.826-30.715 97.791Q-30.756 97.757-30.801 97.757L-30.801 97.477L-29.437 97.477L-29.437 97.757Q-29.926 97.757-30.445 98.157L-31.002 98.591L-30.025 99.815Q-29.823 100.061-29.690 100.138Q-29.557 100.215-29.270 100.215L-29.270 100.495L-30.702 100.495L-30.702 100.215Q-30.514 100.215-30.514 100.102Q-30.514 100.006-30.668 99.815L-31.402 98.906L-31.884 99.285L-31.884 100.006Q-31.884 100.143-31.736 100.179Q-31.587 100.215-31.361 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(30.053 -164.57)\">\u003Cpath d=\"M-29.013 98.960Q-29.013 98.639-28.888 98.350Q-28.763 98.061-28.537 97.838Q-28.312 97.614-28.016 97.494Q-27.721 97.374-27.403 97.374Q-27.075 97.374-26.813 97.474Q-26.552 97.573-26.376 97.755Q-26.200 97.938-26.106 98.196Q-26.012 98.454-26.012 98.786Q-26.012 98.878-26.094 98.899L-28.349 98.899L-28.349 98.960Q-28.349 99.548-28.066 99.931Q-27.782 100.314-27.215 100.314Q-26.893 100.314-26.625 100.121Q-26.357 99.928-26.268 99.613Q-26.261 99.572-26.186 99.558L-26.094 99.558Q-26.012 99.582-26.012 99.654Q-26.012 99.661-26.018 99.688Q-26.131 100.085-26.502 100.324Q-26.873 100.563-27.297 100.563Q-27.734 100.563-28.134 100.355Q-28.534 100.146-28.773 99.779Q-29.013 99.412-29.013 98.960M-28.343 98.690L-26.528 98.690Q-26.528 98.413-26.625 98.161Q-26.723 97.908-26.921 97.752Q-27.119 97.597-27.403 97.597Q-27.680 97.597-27.893 97.755Q-28.107 97.914-28.225 98.169Q-28.343 98.424-28.343 98.690M-25.089 101.630Q-24.959 101.698-24.822 101.698Q-24.651 101.698-24.501 101.609Q-24.350 101.520-24.239 101.375Q-24.128 101.230-24.050 101.062L-23.786 100.495L-24.955 97.969Q-25.031 97.822-25.161 97.790Q-25.290 97.757-25.523 97.757L-25.523 97.477L-24.002 97.477L-24.002 97.757Q-24.350 97.757-24.350 97.904Q-24.347 97.925-24.345 97.942Q-24.344 97.959-24.344 97.969L-23.486 99.828L-22.713 98.157Q-22.679 98.089-22.679 98.010Q-22.679 97.897-22.763 97.827Q-22.847 97.757-22.959 97.757L-22.959 97.477L-21.763 97.477L-21.763 97.757Q-21.982 97.757-22.154 97.861Q-22.327 97.966-22.419 98.157L-23.756 101.062Q-23.927 101.432-24.197 101.678Q-24.467 101.924-24.822 101.924Q-25.092 101.924-25.311 101.758Q-25.530 101.592-25.530 101.329Q-25.530 101.192-25.437 101.103Q-25.345 101.015-25.205 101.015Q-25.068 101.015-24.979 101.103Q-24.890 101.192-24.890 101.329Q-24.890 101.432-24.943 101.510Q-24.996 101.589-25.089 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(30.053 -164.57)\">\u003Cpath d=\"M-15.509 100.495L-18.394 100.495L-18.394 100.293Q-18.394 100.263-18.367 100.235L-17.119 99.018Q-17.047 98.943-17.005 98.901Q-16.962 98.858-16.883 98.779Q-16.470 98.366-16.239 98.008Q-16.008 97.651-16.008 97.227Q-16.008 96.995-16.087 96.792Q-16.166 96.588-16.307 96.438Q-16.449 96.287-16.644 96.207Q-16.839 96.127-17.071 96.127Q-17.382 96.127-17.640 96.286Q-17.898 96.445-18.028 96.722L-18.008 96.722Q-17.840 96.722-17.733 96.833Q-17.625 96.944-17.625 97.108Q-17.625 97.265-17.734 97.378Q-17.844 97.491-18.008 97.491Q-18.168 97.491-18.281 97.378Q-18.394 97.265-18.394 97.108Q-18.394 96.732-18.186 96.445Q-17.977 96.158-17.642 96.002Q-17.307 95.847-16.952 95.847Q-16.528 95.847-16.148 96.005Q-15.769 96.164-15.535 96.481Q-15.301 96.797-15.301 97.227Q-15.301 97.538-15.441 97.807Q-15.581 98.075-15.786 98.280Q-15.991 98.485-16.354 98.767Q-16.716 99.049-16.825 99.145L-17.680 99.873L-17.037 99.873Q-16.774 99.873-16.485 99.871Q-16.196 99.870-15.978 99.861Q-15.759 99.852-15.742 99.835Q-15.680 99.770-15.643 99.603Q-15.605 99.435-15.567 99.193L-15.301 99.193\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(56.23 -164.57)\">\u003Cpath d=\"M-31.361 100.495L-32.944 100.495L-32.944 100.215Q-32.715 100.215-32.566 100.181Q-32.418 100.146-32.418 100.006L-32.418 96.387Q-32.418 96.117-32.525 96.055Q-32.633 95.994-32.944 95.994L-32.944 95.713L-31.864 95.638L-31.864 98.926L-30.879 98.157Q-30.674 98.020-30.674 97.870Q-30.674 97.826-30.715 97.791Q-30.756 97.757-30.801 97.757L-30.801 97.477L-29.437 97.477L-29.437 97.757Q-29.926 97.757-30.445 98.157L-31.002 98.591L-30.025 99.815Q-29.823 100.061-29.690 100.138Q-29.557 100.215-29.270 100.215L-29.270 100.495L-30.702 100.495L-30.702 100.215Q-30.514 100.215-30.514 100.102Q-30.514 100.006-30.668 99.815L-31.402 98.906L-31.884 99.285L-31.884 100.006Q-31.884 100.143-31.736 100.179Q-31.587 100.215-31.361 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(56.23 -164.57)\">\u003Cpath d=\"M-29.013 98.960Q-29.013 98.639-28.888 98.350Q-28.763 98.061-28.537 97.838Q-28.312 97.614-28.016 97.494Q-27.721 97.374-27.403 97.374Q-27.075 97.374-26.813 97.474Q-26.552 97.573-26.376 97.755Q-26.200 97.938-26.106 98.196Q-26.012 98.454-26.012 98.786Q-26.012 98.878-26.094 98.899L-28.349 98.899L-28.349 98.960Q-28.349 99.548-28.066 99.931Q-27.782 100.314-27.215 100.314Q-26.893 100.314-26.625 100.121Q-26.357 99.928-26.268 99.613Q-26.261 99.572-26.186 99.558L-26.094 99.558Q-26.012 99.582-26.012 99.654Q-26.012 99.661-26.018 99.688Q-26.131 100.085-26.502 100.324Q-26.873 100.563-27.297 100.563Q-27.734 100.563-28.134 100.355Q-28.534 100.146-28.773 99.779Q-29.013 99.412-29.013 98.960M-28.343 98.690L-26.528 98.690Q-26.528 98.413-26.625 98.161Q-26.723 97.908-26.921 97.752Q-27.119 97.597-27.403 97.597Q-27.680 97.597-27.893 97.755Q-28.107 97.914-28.225 98.169Q-28.343 98.424-28.343 98.690M-25.089 101.630Q-24.959 101.698-24.822 101.698Q-24.651 101.698-24.501 101.609Q-24.350 101.520-24.239 101.375Q-24.128 101.230-24.050 101.062L-23.786 100.495L-24.955 97.969Q-25.031 97.822-25.161 97.790Q-25.290 97.757-25.523 97.757L-25.523 97.477L-24.002 97.477L-24.002 97.757Q-24.350 97.757-24.350 97.904Q-24.347 97.925-24.345 97.942Q-24.344 97.959-24.344 97.969L-23.486 99.828L-22.713 98.157Q-22.679 98.089-22.679 98.010Q-22.679 97.897-22.763 97.827Q-22.847 97.757-22.959 97.757L-22.959 97.477L-21.763 97.477L-21.763 97.757Q-21.982 97.757-22.154 97.861Q-22.327 97.966-22.419 98.157L-23.756 101.062Q-23.927 101.432-24.197 101.678Q-24.467 101.924-24.822 101.924Q-25.092 101.924-25.311 101.758Q-25.530 101.592-25.530 101.329Q-25.530 101.192-25.437 101.103Q-25.345 101.015-25.205 101.015Q-25.068 101.015-24.979 101.103Q-24.890 101.192-24.890 101.329Q-24.890 101.432-24.943 101.510Q-24.996 101.589-25.089 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(56.23 -164.57)\">\u003Cpath d=\"M-18.039 99.948Q-17.919 100.105-17.728 100.204Q-17.536 100.304-17.321 100.343Q-17.106 100.382-16.883 100.382Q-16.586 100.382-16.391 100.227Q-16.196 100.071-16.106 99.817Q-16.015 99.562-16.015 99.278Q-16.015 98.984-16.107 98.733Q-16.200 98.482-16.398 98.326Q-16.596 98.171-16.890 98.171L-17.406 98.171Q-17.434 98.171-17.459 98.145Q-17.485 98.120-17.485 98.096L-17.485 98.024Q-17.485 97.993-17.459 97.971Q-17.434 97.949-17.406 97.949L-16.965 97.918Q-16.603 97.918-16.383 97.561Q-16.162 97.203-16.162 96.814Q-16.162 96.486-16.357 96.282Q-16.552 96.079-16.883 96.079Q-17.170 96.079-17.423 96.163Q-17.676 96.246-17.840 96.434Q-17.693 96.434-17.593 96.549Q-17.492 96.663-17.492 96.814Q-17.492 96.964-17.598 97.074Q-17.704 97.183-17.861 97.183Q-18.022 97.183-18.131 97.074Q-18.240 96.964-18.240 96.814Q-18.240 96.489-18.032 96.270Q-17.823 96.052-17.507 95.949Q-17.191 95.847-16.883 95.847Q-16.565 95.847-16.237 95.951Q-15.909 96.055-15.682 96.277Q-15.455 96.499-15.455 96.814Q-15.455 97.248-15.742 97.573Q-16.029 97.897-16.463 98.044Q-16.152 98.109-15.872 98.275Q-15.591 98.441-15.414 98.699Q-15.236 98.957-15.236 99.278Q-15.236 99.688-15.480 99.998Q-15.725 100.307-16.106 100.471Q-16.487 100.635-16.883 100.635Q-17.252 100.635-17.610 100.522Q-17.967 100.410-18.211 100.160Q-18.456 99.911-18.456 99.541Q-18.456 99.370-18.339 99.258Q-18.223 99.145-18.052 99.145Q-17.943 99.145-17.852 99.196Q-17.762 99.247-17.707 99.340Q-17.652 99.432-17.652 99.541Q-17.652 99.709-17.765 99.828Q-17.878 99.948-18.039 99.948\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(82.406 -164.57)\">\u003Cpath d=\"M-31.361 100.495L-32.944 100.495L-32.944 100.215Q-32.715 100.215-32.566 100.181Q-32.418 100.146-32.418 100.006L-32.418 96.387Q-32.418 96.117-32.525 96.055Q-32.633 95.994-32.944 95.994L-32.944 95.713L-31.864 95.638L-31.864 98.926L-30.879 98.157Q-30.674 98.020-30.674 97.870Q-30.674 97.826-30.715 97.791Q-30.756 97.757-30.801 97.757L-30.801 97.477L-29.437 97.477L-29.437 97.757Q-29.926 97.757-30.445 98.157L-31.002 98.591L-30.025 99.815Q-29.823 100.061-29.690 100.138Q-29.557 100.215-29.270 100.215L-29.270 100.495L-30.702 100.495L-30.702 100.215Q-30.514 100.215-30.514 100.102Q-30.514 100.006-30.668 99.815L-31.402 98.906L-31.884 99.285L-31.884 100.006Q-31.884 100.143-31.736 100.179Q-31.587 100.215-31.361 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(82.406 -164.57)\">\u003Cpath d=\"M-29.013 98.960Q-29.013 98.639-28.888 98.350Q-28.763 98.061-28.537 97.838Q-28.312 97.614-28.016 97.494Q-27.721 97.374-27.403 97.374Q-27.075 97.374-26.813 97.474Q-26.552 97.573-26.376 97.755Q-26.200 97.938-26.106 98.196Q-26.012 98.454-26.012 98.786Q-26.012 98.878-26.094 98.899L-28.349 98.899L-28.349 98.960Q-28.349 99.548-28.066 99.931Q-27.782 100.314-27.215 100.314Q-26.893 100.314-26.625 100.121Q-26.357 99.928-26.268 99.613Q-26.261 99.572-26.186 99.558L-26.094 99.558Q-26.012 99.582-26.012 99.654Q-26.012 99.661-26.018 99.688Q-26.131 100.085-26.502 100.324Q-26.873 100.563-27.297 100.563Q-27.734 100.563-28.134 100.355Q-28.534 100.146-28.773 99.779Q-29.013 99.412-29.013 98.960M-28.343 98.690L-26.528 98.690Q-26.528 98.413-26.625 98.161Q-26.723 97.908-26.921 97.752Q-27.119 97.597-27.403 97.597Q-27.680 97.597-27.893 97.755Q-28.107 97.914-28.225 98.169Q-28.343 98.424-28.343 98.690M-25.089 101.630Q-24.959 101.698-24.822 101.698Q-24.651 101.698-24.501 101.609Q-24.350 101.520-24.239 101.375Q-24.128 101.230-24.050 101.062L-23.786 100.495L-24.955 97.969Q-25.031 97.822-25.161 97.790Q-25.290 97.757-25.523 97.757L-25.523 97.477L-24.002 97.477L-24.002 97.757Q-24.350 97.757-24.350 97.904Q-24.347 97.925-24.345 97.942Q-24.344 97.959-24.344 97.969L-23.486 99.828L-22.713 98.157Q-22.679 98.089-22.679 98.010Q-22.679 97.897-22.763 97.827Q-22.847 97.757-22.959 97.757L-22.959 97.477L-21.763 97.477L-21.763 97.757Q-21.982 97.757-22.154 97.861Q-22.327 97.966-22.419 98.157L-23.756 101.062Q-23.927 101.432-24.197 101.678Q-24.467 101.924-24.822 101.924Q-25.092 101.924-25.311 101.758Q-25.530 101.592-25.530 101.329Q-25.530 101.192-25.437 101.103Q-25.345 101.015-25.205 101.015Q-25.068 101.015-24.979 101.103Q-24.890 101.192-24.890 101.329Q-24.890 101.432-24.943 101.510Q-24.996 101.589-25.089 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(82.406 -164.57)\">\u003Cpath d=\"M-16.518 99.347L-18.562 99.347L-18.562 99.066L-16.231 95.894Q-16.196 95.847-16.131 95.847L-15.995 95.847Q-15.950 95.847-15.923 95.874Q-15.896 95.901-15.896 95.946L-15.896 99.066L-15.133 99.066L-15.133 99.347L-15.896 99.347L-15.896 100.006Q-15.896 100.215-15.140 100.215L-15.140 100.495L-17.273 100.495L-17.273 100.215Q-16.518 100.215-16.518 100.006L-16.518 99.347M-16.470 96.622L-18.261 99.066L-16.470 99.066\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(108.582 -164.57)\">\u003Cpath d=\"M-31.361 100.495L-32.944 100.495L-32.944 100.215Q-32.715 100.215-32.566 100.181Q-32.418 100.146-32.418 100.006L-32.418 96.387Q-32.418 96.117-32.525 96.055Q-32.633 95.994-32.944 95.994L-32.944 95.713L-31.864 95.638L-31.864 98.926L-30.879 98.157Q-30.674 98.020-30.674 97.870Q-30.674 97.826-30.715 97.791Q-30.756 97.757-30.801 97.757L-30.801 97.477L-29.437 97.477L-29.437 97.757Q-29.926 97.757-30.445 98.157L-31.002 98.591L-30.025 99.815Q-29.823 100.061-29.690 100.138Q-29.557 100.215-29.270 100.215L-29.270 100.495L-30.702 100.495L-30.702 100.215Q-30.514 100.215-30.514 100.102Q-30.514 100.006-30.668 99.815L-31.402 98.906L-31.884 99.285L-31.884 100.006Q-31.884 100.143-31.736 100.179Q-31.587 100.215-31.361 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(108.582 -164.57)\">\u003Cpath d=\"M-29.013 98.960Q-29.013 98.639-28.888 98.350Q-28.763 98.061-28.537 97.838Q-28.312 97.614-28.016 97.494Q-27.721 97.374-27.403 97.374Q-27.075 97.374-26.813 97.474Q-26.552 97.573-26.376 97.755Q-26.200 97.938-26.106 98.196Q-26.012 98.454-26.012 98.786Q-26.012 98.878-26.094 98.899L-28.349 98.899L-28.349 98.960Q-28.349 99.548-28.066 99.931Q-27.782 100.314-27.215 100.314Q-26.893 100.314-26.625 100.121Q-26.357 99.928-26.268 99.613Q-26.261 99.572-26.186 99.558L-26.094 99.558Q-26.012 99.582-26.012 99.654Q-26.012 99.661-26.018 99.688Q-26.131 100.085-26.502 100.324Q-26.873 100.563-27.297 100.563Q-27.734 100.563-28.134 100.355Q-28.534 100.146-28.773 99.779Q-29.013 99.412-29.013 98.960M-28.343 98.690L-26.528 98.690Q-26.528 98.413-26.625 98.161Q-26.723 97.908-26.921 97.752Q-27.119 97.597-27.403 97.597Q-27.680 97.597-27.893 97.755Q-28.107 97.914-28.225 98.169Q-28.343 98.424-28.343 98.690M-25.089 101.630Q-24.959 101.698-24.822 101.698Q-24.651 101.698-24.501 101.609Q-24.350 101.520-24.239 101.375Q-24.128 101.230-24.050 101.062L-23.786 100.495L-24.955 97.969Q-25.031 97.822-25.161 97.790Q-25.290 97.757-25.523 97.757L-25.523 97.477L-24.002 97.477L-24.002 97.757Q-24.350 97.757-24.350 97.904Q-24.347 97.925-24.345 97.942Q-24.344 97.959-24.344 97.969L-23.486 99.828L-22.713 98.157Q-22.679 98.089-22.679 98.010Q-22.679 97.897-22.763 97.827Q-22.847 97.757-22.959 97.757L-22.959 97.477L-21.763 97.477L-21.763 97.757Q-21.982 97.757-22.154 97.861Q-22.327 97.966-22.419 98.157L-23.756 101.062Q-23.927 101.432-24.197 101.678Q-24.467 101.924-24.822 101.924Q-25.092 101.924-25.311 101.758Q-25.530 101.592-25.530 101.329Q-25.530 101.192-25.437 101.103Q-25.345 101.015-25.205 101.015Q-25.068 101.015-24.979 101.103Q-24.890 101.192-24.890 101.329Q-24.890 101.432-24.943 101.510Q-24.996 101.589-25.089 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(108.582 -164.57)\">\u003Cpath d=\"M-18.028 99.733L-18.059 99.733Q-17.922 100.030-17.625 100.206Q-17.328 100.382-17 100.382Q-16.637 100.382-16.410 100.204Q-16.183 100.027-16.089 99.738Q-15.995 99.449-15.995 99.087Q-15.995 98.772-16.049 98.487Q-16.104 98.202-16.277 97.996Q-16.449 97.791-16.764 97.791Q-17.037 97.791-17.220 97.858Q-17.403 97.925-17.507 98.014Q-17.611 98.102-17.707 98.212Q-17.803 98.321-17.847 98.331L-17.926 98.331Q-17.998 98.314-18.015 98.243L-18.015 95.925Q-18.015 95.891-17.991 95.869Q-17.967 95.847-17.933 95.847L-17.905 95.847Q-17.618 95.963-17.350 96.017Q-17.082 96.072-16.805 96.072Q-16.528 96.072-16.258 96.017Q-15.988 95.963-15.708 95.847L-15.684 95.847Q-15.649 95.847-15.626 95.870Q-15.602 95.894-15.602 95.925L-15.602 95.994Q-15.602 96.021-15.622 96.041Q-15.896 96.356-16.280 96.532Q-16.665 96.708-17.078 96.708Q-17.417 96.708-17.734 96.622L-17.734 97.904Q-17.338 97.569-16.764 97.569Q-16.360 97.569-16.024 97.779Q-15.687 97.990-15.494 98.342Q-15.301 98.694-15.301 99.094Q-15.301 99.425-15.441 99.711Q-15.581 99.996-15.825 100.206Q-16.070 100.416-16.372 100.526Q-16.675 100.635-16.993 100.635Q-17.352 100.635-17.678 100.471Q-18.004 100.307-18.199 100.015Q-18.394 99.723-18.394 99.360Q-18.394 99.210-18.288 99.104Q-18.182 98.998-18.028 98.998Q-17.875 98.998-17.770 99.102Q-17.666 99.206-17.666 99.360Q-17.666 99.517-17.770 99.625Q-17.875 99.733-18.028 99.733\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(134.759 -164.57)\">\u003Cpath d=\"M-31.361 100.495L-32.944 100.495L-32.944 100.215Q-32.715 100.215-32.566 100.181Q-32.418 100.146-32.418 100.006L-32.418 96.387Q-32.418 96.117-32.525 96.055Q-32.633 95.994-32.944 95.994L-32.944 95.713L-31.864 95.638L-31.864 98.926L-30.879 98.157Q-30.674 98.020-30.674 97.870Q-30.674 97.826-30.715 97.791Q-30.756 97.757-30.801 97.757L-30.801 97.477L-29.437 97.477L-29.437 97.757Q-29.926 97.757-30.445 98.157L-31.002 98.591L-30.025 99.815Q-29.823 100.061-29.690 100.138Q-29.557 100.215-29.270 100.215L-29.270 100.495L-30.702 100.495L-30.702 100.215Q-30.514 100.215-30.514 100.102Q-30.514 100.006-30.668 99.815L-31.402 98.906L-31.884 99.285L-31.884 100.006Q-31.884 100.143-31.736 100.179Q-31.587 100.215-31.361 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(134.759 -164.57)\">\u003Cpath d=\"M-29.013 98.960Q-29.013 98.639-28.888 98.350Q-28.763 98.061-28.537 97.838Q-28.312 97.614-28.016 97.494Q-27.721 97.374-27.403 97.374Q-27.075 97.374-26.813 97.474Q-26.552 97.573-26.376 97.755Q-26.200 97.938-26.106 98.196Q-26.012 98.454-26.012 98.786Q-26.012 98.878-26.094 98.899L-28.349 98.899L-28.349 98.960Q-28.349 99.548-28.066 99.931Q-27.782 100.314-27.215 100.314Q-26.893 100.314-26.625 100.121Q-26.357 99.928-26.268 99.613Q-26.261 99.572-26.186 99.558L-26.094 99.558Q-26.012 99.582-26.012 99.654Q-26.012 99.661-26.018 99.688Q-26.131 100.085-26.502 100.324Q-26.873 100.563-27.297 100.563Q-27.734 100.563-28.134 100.355Q-28.534 100.146-28.773 99.779Q-29.013 99.412-29.013 98.960M-28.343 98.690L-26.528 98.690Q-26.528 98.413-26.625 98.161Q-26.723 97.908-26.921 97.752Q-27.119 97.597-27.403 97.597Q-27.680 97.597-27.893 97.755Q-28.107 97.914-28.225 98.169Q-28.343 98.424-28.343 98.690M-25.089 101.630Q-24.959 101.698-24.822 101.698Q-24.651 101.698-24.501 101.609Q-24.350 101.520-24.239 101.375Q-24.128 101.230-24.050 101.062L-23.786 100.495L-24.955 97.969Q-25.031 97.822-25.161 97.790Q-25.290 97.757-25.523 97.757L-25.523 97.477L-24.002 97.477L-24.002 97.757Q-24.350 97.757-24.350 97.904Q-24.347 97.925-24.345 97.942Q-24.344 97.959-24.344 97.969L-23.486 99.828L-22.713 98.157Q-22.679 98.089-22.679 98.010Q-22.679 97.897-22.763 97.827Q-22.847 97.757-22.959 97.757L-22.959 97.477L-21.763 97.477L-21.763 97.757Q-21.982 97.757-22.154 97.861Q-22.327 97.966-22.419 98.157L-23.756 101.062Q-23.927 101.432-24.197 101.678Q-24.467 101.924-24.822 101.924Q-25.092 101.924-25.311 101.758Q-25.530 101.592-25.530 101.329Q-25.530 101.192-25.437 101.103Q-25.345 101.015-25.205 101.015Q-25.068 101.015-24.979 101.103Q-24.890 101.192-24.890 101.329Q-24.890 101.432-24.943 101.510Q-24.996 101.589-25.089 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(134.759 -164.57)\">\u003Cpath d=\"M-16.846 100.635Q-17.304 100.635-17.622 100.420Q-17.939 100.204-18.121 99.852Q-18.302 99.500-18.379 99.080Q-18.456 98.660-18.456 98.232Q-18.456 97.648-18.203 97.092Q-17.950 96.537-17.480 96.192Q-17.010 95.847-16.412 95.847Q-16.002 95.847-15.718 96.045Q-15.434 96.243-15.434 96.646Q-15.434 96.742-15.480 96.821Q-15.526 96.899-15.607 96.944Q-15.687 96.988-15.776 96.988Q-15.923 96.988-16.024 96.891Q-16.125 96.793-16.125 96.646Q-16.125 96.516-16.034 96.409Q-15.943 96.301-15.810 96.301Q-15.998 96.079-16.412 96.079Q-16.726 96.079-17 96.243Q-17.273 96.407-17.440 96.681Q-17.628 96.971-17.693 97.337Q-17.758 97.703-17.758 98.157Q-17.608 97.863-17.343 97.685Q-17.078 97.508-16.764 97.508Q-16.333 97.508-15.984 97.714Q-15.636 97.921-15.436 98.277Q-15.236 98.632-15.236 99.059Q-15.236 99.504-15.453 99.864Q-15.670 100.225-16.043 100.430Q-16.415 100.635-16.846 100.635M-16.846 100.382Q-16.470 100.382-16.266 100.199Q-16.063 100.016-16 99.733Q-15.937 99.449-15.937 99.059Q-15.937 98.673-15.991 98.393Q-16.046 98.113-16.241 97.921Q-16.436 97.730-16.805 97.730Q-17.095 97.730-17.307 97.906Q-17.519 98.082-17.627 98.355Q-17.734 98.629-17.734 98.912L-17.734 99.053L-17.734 99.094Q-17.734 99.599-17.523 99.991Q-17.311 100.382-16.846 100.382\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-32.331 -142.396)\">\u003Cpath d=\"M-31.334 100.563Q-31.765 100.563-32.141 100.351Q-32.517 100.140-32.737 99.779Q-32.958 99.418-32.958 98.984Q-32.958 98.540-32.720 98.179Q-32.482 97.819-32.096 97.614Q-31.710 97.409-31.269 97.409Q-30.951 97.409-30.668 97.564Q-30.384 97.720-30.199 97.996L-29.953 97.409L-29.717 97.409L-29.717 101.363Q-29.717 101.500-29.567 101.536Q-29.417 101.572-29.191 101.572L-29.191 101.852L-30.821 101.852L-30.821 101.572Q-30.596 101.572-30.447 101.537Q-30.298 101.503-30.298 101.363L-30.298 100.102Q-30.497 100.321-30.768 100.442Q-31.040 100.563-31.334 100.563M-31.283 100.341Q-30.951 100.341-30.679 100.136Q-30.408 99.931-30.268 99.606L-30.268 98.472Q-30.326 98.249-30.457 98.067Q-30.589 97.884-30.779 97.773Q-30.968 97.662-31.194 97.662Q-31.522 97.662-31.773 97.858Q-32.024 98.055-32.158 98.362Q-32.291 98.670-32.291 98.991Q-32.291 99.292-32.175 99.608Q-32.059 99.924-31.830 100.133Q-31.601 100.341-31.283 100.341M-28.183 99.661L-28.183 98.157Q-28.183 97.887-28.290 97.826Q-28.398 97.764-28.709 97.764L-28.709 97.484L-27.602 97.409L-27.602 99.641L-27.602 99.661Q-27.602 99.941-27.550 100.085Q-27.499 100.228-27.357 100.285Q-27.215 100.341-26.928 100.341Q-26.675 100.341-26.470 100.201Q-26.265 100.061-26.149 99.835Q-26.033 99.610-26.033 99.360L-26.033 98.157Q-26.033 97.887-26.140 97.826Q-26.248 97.764-26.559 97.764L-26.559 97.484L-25.452 97.409L-25.452 99.822Q-25.452 100.013-25.399 100.095Q-25.346 100.177-25.245 100.196Q-25.144 100.215-24.929 100.215L-24.929 100.495L-26.005 100.563L-26.005 99.999Q-26.115 100.181-26.260 100.304Q-26.405 100.427-26.592 100.495Q-26.778 100.563-26.980 100.563Q-28.183 100.563-28.183 99.661M-24.382 98.960Q-24.382 98.639-24.257 98.350Q-24.132 98.061-23.907 97.838Q-23.681 97.614-23.386 97.494Q-23.090 97.374-22.772 97.374Q-22.444 97.374-22.182 97.474Q-21.921 97.573-21.745 97.755Q-21.569 97.938-21.475 98.196Q-21.381 98.454-21.381 98.786Q-21.381 98.878-21.463 98.899L-23.719 98.899L-23.719 98.960Q-23.719 99.548-23.435 99.931Q-23.151 100.314-22.584 100.314Q-22.263 100.314-21.994 100.121Q-21.726 99.928-21.637 99.613Q-21.630 99.572-21.555 99.558L-21.463 99.558Q-21.381 99.582-21.381 99.654Q-21.381 99.661-21.388 99.688Q-21.501 100.085-21.871 100.324Q-22.242 100.563-22.666 100.563Q-23.104 100.563-23.503 100.355Q-23.903 100.146-24.143 99.779Q-24.382 99.412-24.382 98.960M-23.712 98.690L-21.897 98.690Q-21.897 98.413-21.994 98.161Q-22.092 97.908-22.290 97.752Q-22.488 97.597-22.772 97.597Q-23.049 97.597-23.262 97.755Q-23.476 97.914-23.594 98.169Q-23.712 98.424-23.712 98.690M-19.043 100.495L-20.779 100.495L-20.779 100.215Q-20.550 100.215-20.402 100.181Q-20.253 100.146-20.253 100.006L-20.253 98.157Q-20.253 97.887-20.361 97.826Q-20.468 97.764-20.779 97.764L-20.779 97.484L-19.751 97.409L-19.751 98.116Q-19.621 97.808-19.378 97.609Q-19.135 97.409-18.817 97.409Q-18.599 97.409-18.428 97.533Q-18.257 97.658-18.257 97.870Q-18.257 98.007-18.356 98.106Q-18.455 98.205-18.588 98.205Q-18.725 98.205-18.824 98.106Q-18.923 98.007-18.923 97.870Q-18.923 97.730-18.824 97.631Q-19.115 97.631-19.315 97.827Q-19.515 98.024-19.607 98.318Q-19.699 98.612-19.699 98.892L-19.699 100.006Q-19.699 100.215-19.043 100.215L-19.043 100.495M-17.337 101.630Q-17.208 101.698-17.071 101.698Q-16.900 101.698-16.750 101.609Q-16.599 101.520-16.488 101.375Q-16.377 101.230-16.298 101.062L-16.035 100.495L-17.204 97.969Q-17.279 97.822-17.409 97.790Q-17.539 97.757-17.772 97.757L-17.772 97.477L-16.251 97.477L-16.251 97.757Q-16.599 97.757-16.599 97.904Q-16.596 97.925-16.594 97.942Q-16.592 97.959-16.592 97.969L-15.734 99.828L-14.962 98.157Q-14.928 98.089-14.928 98.010Q-14.928 97.897-15.012 97.827Q-15.095 97.757-15.208 97.757L-15.208 97.477L-14.012 97.477L-14.012 97.757Q-14.230 97.757-14.403 97.861Q-14.576 97.966-14.668 98.157L-16.004 101.062Q-16.175 101.432-16.445 101.678Q-16.715 101.924-17.071 101.924Q-17.341 101.924-17.560 101.758Q-17.778 101.592-17.778 101.329Q-17.778 101.192-17.686 101.103Q-17.594 101.015-17.454 101.015Q-17.317 101.015-17.228 101.103Q-17.139 101.192-17.139 101.329Q-17.139 101.432-17.192 101.510Q-17.245 101.589-17.337 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.331 -142.396)\">\u003Cpath d=\"M-7.752 100.495L-10.282 100.495L-10.282 100.215Q-9.314 100.215-9.314 100.006L-9.314 96.387Q-9.707 96.575-10.329 96.575L-10.329 96.294Q-9.912 96.294-9.548 96.193Q-9.184 96.093-8.928 95.847L-8.802 95.847Q-8.737 95.864-8.720 95.932L-8.720 100.006Q-8.720 100.215-7.752 100.215\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-32.331 -116.22)\">\u003Cpath d=\"M-31.334 100.563Q-31.765 100.563-32.141 100.351Q-32.517 100.140-32.737 99.779Q-32.958 99.418-32.958 98.984Q-32.958 98.540-32.720 98.179Q-32.482 97.819-32.096 97.614Q-31.710 97.409-31.269 97.409Q-30.951 97.409-30.668 97.564Q-30.384 97.720-30.199 97.996L-29.953 97.409L-29.717 97.409L-29.717 101.363Q-29.717 101.500-29.567 101.536Q-29.417 101.572-29.191 101.572L-29.191 101.852L-30.821 101.852L-30.821 101.572Q-30.596 101.572-30.447 101.537Q-30.298 101.503-30.298 101.363L-30.298 100.102Q-30.497 100.321-30.768 100.442Q-31.040 100.563-31.334 100.563M-31.283 100.341Q-30.951 100.341-30.679 100.136Q-30.408 99.931-30.268 99.606L-30.268 98.472Q-30.326 98.249-30.457 98.067Q-30.589 97.884-30.779 97.773Q-30.968 97.662-31.194 97.662Q-31.522 97.662-31.773 97.858Q-32.024 98.055-32.158 98.362Q-32.291 98.670-32.291 98.991Q-32.291 99.292-32.175 99.608Q-32.059 99.924-31.830 100.133Q-31.601 100.341-31.283 100.341M-28.183 99.661L-28.183 98.157Q-28.183 97.887-28.290 97.826Q-28.398 97.764-28.709 97.764L-28.709 97.484L-27.602 97.409L-27.602 99.641L-27.602 99.661Q-27.602 99.941-27.550 100.085Q-27.499 100.228-27.357 100.285Q-27.215 100.341-26.928 100.341Q-26.675 100.341-26.470 100.201Q-26.265 100.061-26.149 99.835Q-26.033 99.610-26.033 99.360L-26.033 98.157Q-26.033 97.887-26.140 97.826Q-26.248 97.764-26.559 97.764L-26.559 97.484L-25.452 97.409L-25.452 99.822Q-25.452 100.013-25.399 100.095Q-25.346 100.177-25.245 100.196Q-25.144 100.215-24.929 100.215L-24.929 100.495L-26.005 100.563L-26.005 99.999Q-26.115 100.181-26.260 100.304Q-26.405 100.427-26.592 100.495Q-26.778 100.563-26.980 100.563Q-28.183 100.563-28.183 99.661M-24.382 98.960Q-24.382 98.639-24.257 98.350Q-24.132 98.061-23.907 97.838Q-23.681 97.614-23.386 97.494Q-23.090 97.374-22.772 97.374Q-22.444 97.374-22.182 97.474Q-21.921 97.573-21.745 97.755Q-21.569 97.938-21.475 98.196Q-21.381 98.454-21.381 98.786Q-21.381 98.878-21.463 98.899L-23.719 98.899L-23.719 98.960Q-23.719 99.548-23.435 99.931Q-23.151 100.314-22.584 100.314Q-22.263 100.314-21.994 100.121Q-21.726 99.928-21.637 99.613Q-21.630 99.572-21.555 99.558L-21.463 99.558Q-21.381 99.582-21.381 99.654Q-21.381 99.661-21.388 99.688Q-21.501 100.085-21.871 100.324Q-22.242 100.563-22.666 100.563Q-23.104 100.563-23.503 100.355Q-23.903 100.146-24.143 99.779Q-24.382 99.412-24.382 98.960M-23.712 98.690L-21.897 98.690Q-21.897 98.413-21.994 98.161Q-22.092 97.908-22.290 97.752Q-22.488 97.597-22.772 97.597Q-23.049 97.597-23.262 97.755Q-23.476 97.914-23.594 98.169Q-23.712 98.424-23.712 98.690M-19.043 100.495L-20.779 100.495L-20.779 100.215Q-20.550 100.215-20.402 100.181Q-20.253 100.146-20.253 100.006L-20.253 98.157Q-20.253 97.887-20.361 97.826Q-20.468 97.764-20.779 97.764L-20.779 97.484L-19.751 97.409L-19.751 98.116Q-19.621 97.808-19.378 97.609Q-19.135 97.409-18.817 97.409Q-18.599 97.409-18.428 97.533Q-18.257 97.658-18.257 97.870Q-18.257 98.007-18.356 98.106Q-18.455 98.205-18.588 98.205Q-18.725 98.205-18.824 98.106Q-18.923 98.007-18.923 97.870Q-18.923 97.730-18.824 97.631Q-19.115 97.631-19.315 97.827Q-19.515 98.024-19.607 98.318Q-19.699 98.612-19.699 98.892L-19.699 100.006Q-19.699 100.215-19.043 100.215L-19.043 100.495M-17.337 101.630Q-17.208 101.698-17.071 101.698Q-16.900 101.698-16.750 101.609Q-16.599 101.520-16.488 101.375Q-16.377 101.230-16.298 101.062L-16.035 100.495L-17.204 97.969Q-17.279 97.822-17.409 97.790Q-17.539 97.757-17.772 97.757L-17.772 97.477L-16.251 97.477L-16.251 97.757Q-16.599 97.757-16.599 97.904Q-16.596 97.925-16.594 97.942Q-16.592 97.959-16.592 97.969L-15.734 99.828L-14.962 98.157Q-14.928 98.089-14.928 98.010Q-14.928 97.897-15.012 97.827Q-15.095 97.757-15.208 97.757L-15.208 97.477L-14.012 97.477L-14.012 97.757Q-14.230 97.757-14.403 97.861Q-14.576 97.966-14.668 98.157L-16.004 101.062Q-16.175 101.432-16.445 101.678Q-16.715 101.924-17.071 101.924Q-17.341 101.924-17.560 101.758Q-17.778 101.592-17.778 101.329Q-17.778 101.192-17.686 101.103Q-17.594 101.015-17.454 101.015Q-17.317 101.015-17.228 101.103Q-17.139 101.192-17.139 101.329Q-17.139 101.432-17.192 101.510Q-17.245 101.589-17.337 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.331 -116.22)\">\u003Cpath d=\"M-7.752 100.495L-10.637 100.495L-10.637 100.293Q-10.637 100.263-10.610 100.235L-9.362 99.018Q-9.290 98.943-9.248 98.901Q-9.205 98.858-9.126 98.779Q-8.713 98.366-8.482 98.008Q-8.251 97.651-8.251 97.227Q-8.251 96.995-8.330 96.792Q-8.409 96.588-8.550 96.438Q-8.692 96.287-8.887 96.207Q-9.082 96.127-9.314 96.127Q-9.625 96.127-9.883 96.286Q-10.141 96.445-10.271 96.722L-10.251 96.722Q-10.083 96.722-9.976 96.833Q-9.868 96.944-9.868 97.108Q-9.868 97.265-9.977 97.378Q-10.087 97.491-10.251 97.491Q-10.411 97.491-10.524 97.378Q-10.637 97.265-10.637 97.108Q-10.637 96.732-10.429 96.445Q-10.220 96.158-9.885 96.002Q-9.550 95.847-9.195 95.847Q-8.771 95.847-8.391 96.005Q-8.012 96.164-7.778 96.481Q-7.544 96.797-7.544 97.227Q-7.544 97.538-7.684 97.807Q-7.824 98.075-8.029 98.280Q-8.234 98.485-8.597 98.767Q-8.959 99.049-9.068 99.145L-9.923 99.873L-9.280 99.873Q-9.017 99.873-8.728 99.871Q-8.439 99.870-8.221 99.861Q-8.002 99.852-7.985 99.835Q-7.923 99.770-7.886 99.603Q-7.848 99.435-7.810 99.193L-7.544 99.193\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-32.331 -90.043)\">\u003Cpath d=\"M-31.334 100.563Q-31.765 100.563-32.141 100.351Q-32.517 100.140-32.737 99.779Q-32.958 99.418-32.958 98.984Q-32.958 98.540-32.720 98.179Q-32.482 97.819-32.096 97.614Q-31.710 97.409-31.269 97.409Q-30.951 97.409-30.668 97.564Q-30.384 97.720-30.199 97.996L-29.953 97.409L-29.717 97.409L-29.717 101.363Q-29.717 101.500-29.567 101.536Q-29.417 101.572-29.191 101.572L-29.191 101.852L-30.821 101.852L-30.821 101.572Q-30.596 101.572-30.447 101.537Q-30.298 101.503-30.298 101.363L-30.298 100.102Q-30.497 100.321-30.768 100.442Q-31.040 100.563-31.334 100.563M-31.283 100.341Q-30.951 100.341-30.679 100.136Q-30.408 99.931-30.268 99.606L-30.268 98.472Q-30.326 98.249-30.457 98.067Q-30.589 97.884-30.779 97.773Q-30.968 97.662-31.194 97.662Q-31.522 97.662-31.773 97.858Q-32.024 98.055-32.158 98.362Q-32.291 98.670-32.291 98.991Q-32.291 99.292-32.175 99.608Q-32.059 99.924-31.830 100.133Q-31.601 100.341-31.283 100.341M-28.183 99.661L-28.183 98.157Q-28.183 97.887-28.290 97.826Q-28.398 97.764-28.709 97.764L-28.709 97.484L-27.602 97.409L-27.602 99.641L-27.602 99.661Q-27.602 99.941-27.550 100.085Q-27.499 100.228-27.357 100.285Q-27.215 100.341-26.928 100.341Q-26.675 100.341-26.470 100.201Q-26.265 100.061-26.149 99.835Q-26.033 99.610-26.033 99.360L-26.033 98.157Q-26.033 97.887-26.140 97.826Q-26.248 97.764-26.559 97.764L-26.559 97.484L-25.452 97.409L-25.452 99.822Q-25.452 100.013-25.399 100.095Q-25.346 100.177-25.245 100.196Q-25.144 100.215-24.929 100.215L-24.929 100.495L-26.005 100.563L-26.005 99.999Q-26.115 100.181-26.260 100.304Q-26.405 100.427-26.592 100.495Q-26.778 100.563-26.980 100.563Q-28.183 100.563-28.183 99.661M-24.382 98.960Q-24.382 98.639-24.257 98.350Q-24.132 98.061-23.907 97.838Q-23.681 97.614-23.386 97.494Q-23.090 97.374-22.772 97.374Q-22.444 97.374-22.182 97.474Q-21.921 97.573-21.745 97.755Q-21.569 97.938-21.475 98.196Q-21.381 98.454-21.381 98.786Q-21.381 98.878-21.463 98.899L-23.719 98.899L-23.719 98.960Q-23.719 99.548-23.435 99.931Q-23.151 100.314-22.584 100.314Q-22.263 100.314-21.994 100.121Q-21.726 99.928-21.637 99.613Q-21.630 99.572-21.555 99.558L-21.463 99.558Q-21.381 99.582-21.381 99.654Q-21.381 99.661-21.388 99.688Q-21.501 100.085-21.871 100.324Q-22.242 100.563-22.666 100.563Q-23.104 100.563-23.503 100.355Q-23.903 100.146-24.143 99.779Q-24.382 99.412-24.382 98.960M-23.712 98.690L-21.897 98.690Q-21.897 98.413-21.994 98.161Q-22.092 97.908-22.290 97.752Q-22.488 97.597-22.772 97.597Q-23.049 97.597-23.262 97.755Q-23.476 97.914-23.594 98.169Q-23.712 98.424-23.712 98.690M-19.043 100.495L-20.779 100.495L-20.779 100.215Q-20.550 100.215-20.402 100.181Q-20.253 100.146-20.253 100.006L-20.253 98.157Q-20.253 97.887-20.361 97.826Q-20.468 97.764-20.779 97.764L-20.779 97.484L-19.751 97.409L-19.751 98.116Q-19.621 97.808-19.378 97.609Q-19.135 97.409-18.817 97.409Q-18.599 97.409-18.428 97.533Q-18.257 97.658-18.257 97.870Q-18.257 98.007-18.356 98.106Q-18.455 98.205-18.588 98.205Q-18.725 98.205-18.824 98.106Q-18.923 98.007-18.923 97.870Q-18.923 97.730-18.824 97.631Q-19.115 97.631-19.315 97.827Q-19.515 98.024-19.607 98.318Q-19.699 98.612-19.699 98.892L-19.699 100.006Q-19.699 100.215-19.043 100.215L-19.043 100.495M-17.337 101.630Q-17.208 101.698-17.071 101.698Q-16.900 101.698-16.750 101.609Q-16.599 101.520-16.488 101.375Q-16.377 101.230-16.298 101.062L-16.035 100.495L-17.204 97.969Q-17.279 97.822-17.409 97.790Q-17.539 97.757-17.772 97.757L-17.772 97.477L-16.251 97.477L-16.251 97.757Q-16.599 97.757-16.599 97.904Q-16.596 97.925-16.594 97.942Q-16.592 97.959-16.592 97.969L-15.734 99.828L-14.962 98.157Q-14.928 98.089-14.928 98.010Q-14.928 97.897-15.012 97.827Q-15.095 97.757-15.208 97.757L-15.208 97.477L-14.012 97.477L-14.012 97.757Q-14.230 97.757-14.403 97.861Q-14.576 97.966-14.668 98.157L-16.004 101.062Q-16.175 101.432-16.445 101.678Q-16.715 101.924-17.071 101.924Q-17.341 101.924-17.560 101.758Q-17.778 101.592-17.778 101.329Q-17.778 101.192-17.686 101.103Q-17.594 101.015-17.454 101.015Q-17.317 101.015-17.228 101.103Q-17.139 101.192-17.139 101.329Q-17.139 101.432-17.192 101.510Q-17.245 101.589-17.337 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.331 -90.043)\">\u003Cpath d=\"M-10.282 99.948Q-10.162 100.105-9.971 100.204Q-9.779 100.304-9.564 100.343Q-9.349 100.382-9.126 100.382Q-8.829 100.382-8.634 100.227Q-8.439 100.071-8.349 99.817Q-8.258 99.562-8.258 99.278Q-8.258 98.984-8.350 98.733Q-8.443 98.482-8.641 98.326Q-8.839 98.171-9.133 98.171L-9.649 98.171Q-9.677 98.171-9.702 98.145Q-9.728 98.120-9.728 98.096L-9.728 98.024Q-9.728 97.993-9.702 97.971Q-9.677 97.949-9.649 97.949L-9.208 97.918Q-8.846 97.918-8.626 97.561Q-8.405 97.203-8.405 96.814Q-8.405 96.486-8.600 96.282Q-8.795 96.079-9.126 96.079Q-9.413 96.079-9.666 96.163Q-9.919 96.246-10.083 96.434Q-9.936 96.434-9.836 96.549Q-9.735 96.663-9.735 96.814Q-9.735 96.964-9.841 97.074Q-9.947 97.183-10.104 97.183Q-10.265 97.183-10.374 97.074Q-10.483 96.964-10.483 96.814Q-10.483 96.489-10.275 96.270Q-10.066 96.052-9.750 95.949Q-9.434 95.847-9.126 95.847Q-8.808 95.847-8.480 95.951Q-8.152 96.055-7.925 96.277Q-7.698 96.499-7.698 96.814Q-7.698 97.248-7.985 97.573Q-8.272 97.897-8.706 98.044Q-8.395 98.109-8.115 98.275Q-7.834 98.441-7.657 98.699Q-7.479 98.957-7.479 99.278Q-7.479 99.688-7.723 99.998Q-7.968 100.307-8.349 100.471Q-8.730 100.635-9.126 100.635Q-9.495 100.635-9.853 100.522Q-10.210 100.410-10.454 100.160Q-10.699 99.911-10.699 99.541Q-10.699 99.370-10.582 99.258Q-10.466 99.145-10.295 99.145Q-10.186 99.145-10.095 99.196Q-10.005 99.247-9.950 99.340Q-9.895 99.432-9.895 99.541Q-9.895 99.709-10.008 99.828Q-10.121 99.948-10.282 99.948\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-32.331 -63.866)\">\u003Cpath d=\"M-31.334 100.563Q-31.765 100.563-32.141 100.351Q-32.517 100.140-32.737 99.779Q-32.958 99.418-32.958 98.984Q-32.958 98.540-32.720 98.179Q-32.482 97.819-32.096 97.614Q-31.710 97.409-31.269 97.409Q-30.951 97.409-30.668 97.564Q-30.384 97.720-30.199 97.996L-29.953 97.409L-29.717 97.409L-29.717 101.363Q-29.717 101.500-29.567 101.536Q-29.417 101.572-29.191 101.572L-29.191 101.852L-30.821 101.852L-30.821 101.572Q-30.596 101.572-30.447 101.537Q-30.298 101.503-30.298 101.363L-30.298 100.102Q-30.497 100.321-30.768 100.442Q-31.040 100.563-31.334 100.563M-31.283 100.341Q-30.951 100.341-30.679 100.136Q-30.408 99.931-30.268 99.606L-30.268 98.472Q-30.326 98.249-30.457 98.067Q-30.589 97.884-30.779 97.773Q-30.968 97.662-31.194 97.662Q-31.522 97.662-31.773 97.858Q-32.024 98.055-32.158 98.362Q-32.291 98.670-32.291 98.991Q-32.291 99.292-32.175 99.608Q-32.059 99.924-31.830 100.133Q-31.601 100.341-31.283 100.341M-28.183 99.661L-28.183 98.157Q-28.183 97.887-28.290 97.826Q-28.398 97.764-28.709 97.764L-28.709 97.484L-27.602 97.409L-27.602 99.641L-27.602 99.661Q-27.602 99.941-27.550 100.085Q-27.499 100.228-27.357 100.285Q-27.215 100.341-26.928 100.341Q-26.675 100.341-26.470 100.201Q-26.265 100.061-26.149 99.835Q-26.033 99.610-26.033 99.360L-26.033 98.157Q-26.033 97.887-26.140 97.826Q-26.248 97.764-26.559 97.764L-26.559 97.484L-25.452 97.409L-25.452 99.822Q-25.452 100.013-25.399 100.095Q-25.346 100.177-25.245 100.196Q-25.144 100.215-24.929 100.215L-24.929 100.495L-26.005 100.563L-26.005 99.999Q-26.115 100.181-26.260 100.304Q-26.405 100.427-26.592 100.495Q-26.778 100.563-26.980 100.563Q-28.183 100.563-28.183 99.661M-24.382 98.960Q-24.382 98.639-24.257 98.350Q-24.132 98.061-23.907 97.838Q-23.681 97.614-23.386 97.494Q-23.090 97.374-22.772 97.374Q-22.444 97.374-22.182 97.474Q-21.921 97.573-21.745 97.755Q-21.569 97.938-21.475 98.196Q-21.381 98.454-21.381 98.786Q-21.381 98.878-21.463 98.899L-23.719 98.899L-23.719 98.960Q-23.719 99.548-23.435 99.931Q-23.151 100.314-22.584 100.314Q-22.263 100.314-21.994 100.121Q-21.726 99.928-21.637 99.613Q-21.630 99.572-21.555 99.558L-21.463 99.558Q-21.381 99.582-21.381 99.654Q-21.381 99.661-21.388 99.688Q-21.501 100.085-21.871 100.324Q-22.242 100.563-22.666 100.563Q-23.104 100.563-23.503 100.355Q-23.903 100.146-24.143 99.779Q-24.382 99.412-24.382 98.960M-23.712 98.690L-21.897 98.690Q-21.897 98.413-21.994 98.161Q-22.092 97.908-22.290 97.752Q-22.488 97.597-22.772 97.597Q-23.049 97.597-23.262 97.755Q-23.476 97.914-23.594 98.169Q-23.712 98.424-23.712 98.690M-19.043 100.495L-20.779 100.495L-20.779 100.215Q-20.550 100.215-20.402 100.181Q-20.253 100.146-20.253 100.006L-20.253 98.157Q-20.253 97.887-20.361 97.826Q-20.468 97.764-20.779 97.764L-20.779 97.484L-19.751 97.409L-19.751 98.116Q-19.621 97.808-19.378 97.609Q-19.135 97.409-18.817 97.409Q-18.599 97.409-18.428 97.533Q-18.257 97.658-18.257 97.870Q-18.257 98.007-18.356 98.106Q-18.455 98.205-18.588 98.205Q-18.725 98.205-18.824 98.106Q-18.923 98.007-18.923 97.870Q-18.923 97.730-18.824 97.631Q-19.115 97.631-19.315 97.827Q-19.515 98.024-19.607 98.318Q-19.699 98.612-19.699 98.892L-19.699 100.006Q-19.699 100.215-19.043 100.215L-19.043 100.495M-17.337 101.630Q-17.208 101.698-17.071 101.698Q-16.900 101.698-16.750 101.609Q-16.599 101.520-16.488 101.375Q-16.377 101.230-16.298 101.062L-16.035 100.495L-17.204 97.969Q-17.279 97.822-17.409 97.790Q-17.539 97.757-17.772 97.757L-17.772 97.477L-16.251 97.477L-16.251 97.757Q-16.599 97.757-16.599 97.904Q-16.596 97.925-16.594 97.942Q-16.592 97.959-16.592 97.969L-15.734 99.828L-14.962 98.157Q-14.928 98.089-14.928 98.010Q-14.928 97.897-15.012 97.827Q-15.095 97.757-15.208 97.757L-15.208 97.477L-14.012 97.477L-14.012 97.757Q-14.230 97.757-14.403 97.861Q-14.576 97.966-14.668 98.157L-16.004 101.062Q-16.175 101.432-16.445 101.678Q-16.715 101.924-17.071 101.924Q-17.341 101.924-17.560 101.758Q-17.778 101.592-17.778 101.329Q-17.778 101.192-17.686 101.103Q-17.594 101.015-17.454 101.015Q-17.317 101.015-17.228 101.103Q-17.139 101.192-17.139 101.329Q-17.139 101.432-17.192 101.510Q-17.245 101.589-17.337 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.331 -63.866)\">\u003Cpath d=\"M-8.761 99.347L-10.805 99.347L-10.805 99.066L-8.474 95.894Q-8.439 95.847-8.374 95.847L-8.238 95.847Q-8.193 95.847-8.166 95.874Q-8.139 95.901-8.139 95.946L-8.139 99.066L-7.376 99.066L-7.376 99.347L-8.139 99.347L-8.139 100.006Q-8.139 100.215-7.383 100.215L-7.383 100.495L-9.516 100.495L-9.516 100.215Q-8.761 100.215-8.761 100.006L-8.761 99.347M-8.713 96.622L-10.504 99.066L-8.713 99.066\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-32.331 -37.69)\">\u003Cpath d=\"M-31.334 100.563Q-31.765 100.563-32.141 100.351Q-32.517 100.140-32.737 99.779Q-32.958 99.418-32.958 98.984Q-32.958 98.540-32.720 98.179Q-32.482 97.819-32.096 97.614Q-31.710 97.409-31.269 97.409Q-30.951 97.409-30.668 97.564Q-30.384 97.720-30.199 97.996L-29.953 97.409L-29.717 97.409L-29.717 101.363Q-29.717 101.500-29.567 101.536Q-29.417 101.572-29.191 101.572L-29.191 101.852L-30.821 101.852L-30.821 101.572Q-30.596 101.572-30.447 101.537Q-30.298 101.503-30.298 101.363L-30.298 100.102Q-30.497 100.321-30.768 100.442Q-31.040 100.563-31.334 100.563M-31.283 100.341Q-30.951 100.341-30.679 100.136Q-30.408 99.931-30.268 99.606L-30.268 98.472Q-30.326 98.249-30.457 98.067Q-30.589 97.884-30.779 97.773Q-30.968 97.662-31.194 97.662Q-31.522 97.662-31.773 97.858Q-32.024 98.055-32.158 98.362Q-32.291 98.670-32.291 98.991Q-32.291 99.292-32.175 99.608Q-32.059 99.924-31.830 100.133Q-31.601 100.341-31.283 100.341M-28.183 99.661L-28.183 98.157Q-28.183 97.887-28.290 97.826Q-28.398 97.764-28.709 97.764L-28.709 97.484L-27.602 97.409L-27.602 99.641L-27.602 99.661Q-27.602 99.941-27.550 100.085Q-27.499 100.228-27.357 100.285Q-27.215 100.341-26.928 100.341Q-26.675 100.341-26.470 100.201Q-26.265 100.061-26.149 99.835Q-26.033 99.610-26.033 99.360L-26.033 98.157Q-26.033 97.887-26.140 97.826Q-26.248 97.764-26.559 97.764L-26.559 97.484L-25.452 97.409L-25.452 99.822Q-25.452 100.013-25.399 100.095Q-25.346 100.177-25.245 100.196Q-25.144 100.215-24.929 100.215L-24.929 100.495L-26.005 100.563L-26.005 99.999Q-26.115 100.181-26.260 100.304Q-26.405 100.427-26.592 100.495Q-26.778 100.563-26.980 100.563Q-28.183 100.563-28.183 99.661M-24.382 98.960Q-24.382 98.639-24.257 98.350Q-24.132 98.061-23.907 97.838Q-23.681 97.614-23.386 97.494Q-23.090 97.374-22.772 97.374Q-22.444 97.374-22.182 97.474Q-21.921 97.573-21.745 97.755Q-21.569 97.938-21.475 98.196Q-21.381 98.454-21.381 98.786Q-21.381 98.878-21.463 98.899L-23.719 98.899L-23.719 98.960Q-23.719 99.548-23.435 99.931Q-23.151 100.314-22.584 100.314Q-22.263 100.314-21.994 100.121Q-21.726 99.928-21.637 99.613Q-21.630 99.572-21.555 99.558L-21.463 99.558Q-21.381 99.582-21.381 99.654Q-21.381 99.661-21.388 99.688Q-21.501 100.085-21.871 100.324Q-22.242 100.563-22.666 100.563Q-23.104 100.563-23.503 100.355Q-23.903 100.146-24.143 99.779Q-24.382 99.412-24.382 98.960M-23.712 98.690L-21.897 98.690Q-21.897 98.413-21.994 98.161Q-22.092 97.908-22.290 97.752Q-22.488 97.597-22.772 97.597Q-23.049 97.597-23.262 97.755Q-23.476 97.914-23.594 98.169Q-23.712 98.424-23.712 98.690M-19.043 100.495L-20.779 100.495L-20.779 100.215Q-20.550 100.215-20.402 100.181Q-20.253 100.146-20.253 100.006L-20.253 98.157Q-20.253 97.887-20.361 97.826Q-20.468 97.764-20.779 97.764L-20.779 97.484L-19.751 97.409L-19.751 98.116Q-19.621 97.808-19.378 97.609Q-19.135 97.409-18.817 97.409Q-18.599 97.409-18.428 97.533Q-18.257 97.658-18.257 97.870Q-18.257 98.007-18.356 98.106Q-18.455 98.205-18.588 98.205Q-18.725 98.205-18.824 98.106Q-18.923 98.007-18.923 97.870Q-18.923 97.730-18.824 97.631Q-19.115 97.631-19.315 97.827Q-19.515 98.024-19.607 98.318Q-19.699 98.612-19.699 98.892L-19.699 100.006Q-19.699 100.215-19.043 100.215L-19.043 100.495M-17.337 101.630Q-17.208 101.698-17.071 101.698Q-16.900 101.698-16.750 101.609Q-16.599 101.520-16.488 101.375Q-16.377 101.230-16.298 101.062L-16.035 100.495L-17.204 97.969Q-17.279 97.822-17.409 97.790Q-17.539 97.757-17.772 97.757L-17.772 97.477L-16.251 97.477L-16.251 97.757Q-16.599 97.757-16.599 97.904Q-16.596 97.925-16.594 97.942Q-16.592 97.959-16.592 97.969L-15.734 99.828L-14.962 98.157Q-14.928 98.089-14.928 98.010Q-14.928 97.897-15.012 97.827Q-15.095 97.757-15.208 97.757L-15.208 97.477L-14.012 97.477L-14.012 97.757Q-14.230 97.757-14.403 97.861Q-14.576 97.966-14.668 98.157L-16.004 101.062Q-16.175 101.432-16.445 101.678Q-16.715 101.924-17.071 101.924Q-17.341 101.924-17.560 101.758Q-17.778 101.592-17.778 101.329Q-17.778 101.192-17.686 101.103Q-17.594 101.015-17.454 101.015Q-17.317 101.015-17.228 101.103Q-17.139 101.192-17.139 101.329Q-17.139 101.432-17.192 101.510Q-17.245 101.589-17.337 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.331 -37.69)\">\u003Cpath d=\"M-10.271 99.733L-10.302 99.733Q-10.165 100.030-9.868 100.206Q-9.571 100.382-9.243 100.382Q-8.880 100.382-8.653 100.204Q-8.426 100.027-8.332 99.738Q-8.238 99.449-8.238 99.087Q-8.238 98.772-8.292 98.487Q-8.347 98.202-8.520 97.996Q-8.692 97.791-9.007 97.791Q-9.280 97.791-9.463 97.858Q-9.646 97.925-9.750 98.014Q-9.854 98.102-9.950 98.212Q-10.046 98.321-10.090 98.331L-10.169 98.331Q-10.241 98.314-10.258 98.243L-10.258 95.925Q-10.258 95.891-10.234 95.869Q-10.210 95.847-10.176 95.847L-10.148 95.847Q-9.861 95.963-9.593 96.017Q-9.325 96.072-9.048 96.072Q-8.771 96.072-8.501 96.017Q-8.231 95.963-7.951 95.847L-7.927 95.847Q-7.892 95.847-7.869 95.870Q-7.845 95.894-7.845 95.925L-7.845 95.994Q-7.845 96.021-7.865 96.041Q-8.139 96.356-8.523 96.532Q-8.908 96.708-9.321 96.708Q-9.660 96.708-9.977 96.622L-9.977 97.904Q-9.581 97.569-9.007 97.569Q-8.603 97.569-8.267 97.779Q-7.930 97.990-7.737 98.342Q-7.544 98.694-7.544 99.094Q-7.544 99.425-7.684 99.711Q-7.824 99.996-8.068 100.206Q-8.313 100.416-8.615 100.526Q-8.918 100.635-9.236 100.635Q-9.595 100.635-9.921 100.471Q-10.247 100.307-10.442 100.015Q-10.637 99.723-10.637 99.360Q-10.637 99.210-10.531 99.104Q-10.425 98.998-10.271 98.998Q-10.118 98.998-10.013 99.102Q-9.909 99.206-9.909 99.360Q-9.909 99.517-10.013 99.625Q-10.118 99.733-10.271 99.733\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-32.331 -11.513)\">\u003Cpath d=\"M-31.334 100.563Q-31.765 100.563-32.141 100.351Q-32.517 100.140-32.737 99.779Q-32.958 99.418-32.958 98.984Q-32.958 98.540-32.720 98.179Q-32.482 97.819-32.096 97.614Q-31.710 97.409-31.269 97.409Q-30.951 97.409-30.668 97.564Q-30.384 97.720-30.199 97.996L-29.953 97.409L-29.717 97.409L-29.717 101.363Q-29.717 101.500-29.567 101.536Q-29.417 101.572-29.191 101.572L-29.191 101.852L-30.821 101.852L-30.821 101.572Q-30.596 101.572-30.447 101.537Q-30.298 101.503-30.298 101.363L-30.298 100.102Q-30.497 100.321-30.768 100.442Q-31.040 100.563-31.334 100.563M-31.283 100.341Q-30.951 100.341-30.679 100.136Q-30.408 99.931-30.268 99.606L-30.268 98.472Q-30.326 98.249-30.457 98.067Q-30.589 97.884-30.779 97.773Q-30.968 97.662-31.194 97.662Q-31.522 97.662-31.773 97.858Q-32.024 98.055-32.158 98.362Q-32.291 98.670-32.291 98.991Q-32.291 99.292-32.175 99.608Q-32.059 99.924-31.830 100.133Q-31.601 100.341-31.283 100.341M-28.183 99.661L-28.183 98.157Q-28.183 97.887-28.290 97.826Q-28.398 97.764-28.709 97.764L-28.709 97.484L-27.602 97.409L-27.602 99.641L-27.602 99.661Q-27.602 99.941-27.550 100.085Q-27.499 100.228-27.357 100.285Q-27.215 100.341-26.928 100.341Q-26.675 100.341-26.470 100.201Q-26.265 100.061-26.149 99.835Q-26.033 99.610-26.033 99.360L-26.033 98.157Q-26.033 97.887-26.140 97.826Q-26.248 97.764-26.559 97.764L-26.559 97.484L-25.452 97.409L-25.452 99.822Q-25.452 100.013-25.399 100.095Q-25.346 100.177-25.245 100.196Q-25.144 100.215-24.929 100.215L-24.929 100.495L-26.005 100.563L-26.005 99.999Q-26.115 100.181-26.260 100.304Q-26.405 100.427-26.592 100.495Q-26.778 100.563-26.980 100.563Q-28.183 100.563-28.183 99.661M-24.382 98.960Q-24.382 98.639-24.257 98.350Q-24.132 98.061-23.907 97.838Q-23.681 97.614-23.386 97.494Q-23.090 97.374-22.772 97.374Q-22.444 97.374-22.182 97.474Q-21.921 97.573-21.745 97.755Q-21.569 97.938-21.475 98.196Q-21.381 98.454-21.381 98.786Q-21.381 98.878-21.463 98.899L-23.719 98.899L-23.719 98.960Q-23.719 99.548-23.435 99.931Q-23.151 100.314-22.584 100.314Q-22.263 100.314-21.994 100.121Q-21.726 99.928-21.637 99.613Q-21.630 99.572-21.555 99.558L-21.463 99.558Q-21.381 99.582-21.381 99.654Q-21.381 99.661-21.388 99.688Q-21.501 100.085-21.871 100.324Q-22.242 100.563-22.666 100.563Q-23.104 100.563-23.503 100.355Q-23.903 100.146-24.143 99.779Q-24.382 99.412-24.382 98.960M-23.712 98.690L-21.897 98.690Q-21.897 98.413-21.994 98.161Q-22.092 97.908-22.290 97.752Q-22.488 97.597-22.772 97.597Q-23.049 97.597-23.262 97.755Q-23.476 97.914-23.594 98.169Q-23.712 98.424-23.712 98.690M-19.043 100.495L-20.779 100.495L-20.779 100.215Q-20.550 100.215-20.402 100.181Q-20.253 100.146-20.253 100.006L-20.253 98.157Q-20.253 97.887-20.361 97.826Q-20.468 97.764-20.779 97.764L-20.779 97.484L-19.751 97.409L-19.751 98.116Q-19.621 97.808-19.378 97.609Q-19.135 97.409-18.817 97.409Q-18.599 97.409-18.428 97.533Q-18.257 97.658-18.257 97.870Q-18.257 98.007-18.356 98.106Q-18.455 98.205-18.588 98.205Q-18.725 98.205-18.824 98.106Q-18.923 98.007-18.923 97.870Q-18.923 97.730-18.824 97.631Q-19.115 97.631-19.315 97.827Q-19.515 98.024-19.607 98.318Q-19.699 98.612-19.699 98.892L-19.699 100.006Q-19.699 100.215-19.043 100.215L-19.043 100.495M-17.337 101.630Q-17.208 101.698-17.071 101.698Q-16.900 101.698-16.750 101.609Q-16.599 101.520-16.488 101.375Q-16.377 101.230-16.298 101.062L-16.035 100.495L-17.204 97.969Q-17.279 97.822-17.409 97.790Q-17.539 97.757-17.772 97.757L-17.772 97.477L-16.251 97.477L-16.251 97.757Q-16.599 97.757-16.599 97.904Q-16.596 97.925-16.594 97.942Q-16.592 97.959-16.592 97.969L-15.734 99.828L-14.962 98.157Q-14.928 98.089-14.928 98.010Q-14.928 97.897-15.012 97.827Q-15.095 97.757-15.208 97.757L-15.208 97.477L-14.012 97.477L-14.012 97.757Q-14.230 97.757-14.403 97.861Q-14.576 97.966-14.668 98.157L-16.004 101.062Q-16.175 101.432-16.445 101.678Q-16.715 101.924-17.071 101.924Q-17.341 101.924-17.560 101.758Q-17.778 101.592-17.778 101.329Q-17.778 101.192-17.686 101.103Q-17.594 101.015-17.454 101.015Q-17.317 101.015-17.228 101.103Q-17.139 101.192-17.139 101.329Q-17.139 101.432-17.192 101.510Q-17.245 101.589-17.337 101.630\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-32.331 -11.513)\">\u003Cpath d=\"M-9.089 100.635Q-9.547 100.635-9.865 100.420Q-10.182 100.204-10.364 99.852Q-10.545 99.500-10.622 99.080Q-10.699 98.660-10.699 98.232Q-10.699 97.648-10.446 97.092Q-10.193 96.537-9.723 96.192Q-9.253 95.847-8.655 95.847Q-8.245 95.847-7.961 96.045Q-7.677 96.243-7.677 96.646Q-7.677 96.742-7.723 96.821Q-7.769 96.899-7.850 96.944Q-7.930 96.988-8.019 96.988Q-8.166 96.988-8.267 96.891Q-8.368 96.793-8.368 96.646Q-8.368 96.516-8.277 96.409Q-8.186 96.301-8.053 96.301Q-8.241 96.079-8.655 96.079Q-8.969 96.079-9.243 96.243Q-9.516 96.407-9.683 96.681Q-9.871 96.971-9.936 97.337Q-10.001 97.703-10.001 98.157Q-9.851 97.863-9.586 97.685Q-9.321 97.508-9.007 97.508Q-8.576 97.508-8.227 97.714Q-7.879 97.921-7.679 98.277Q-7.479 98.632-7.479 99.059Q-7.479 99.504-7.696 99.864Q-7.913 100.225-8.286 100.430Q-8.658 100.635-9.089 100.635M-9.089 100.382Q-8.713 100.382-8.509 100.199Q-8.306 100.016-8.243 99.733Q-8.180 99.449-8.180 99.059Q-8.180 98.673-8.234 98.393Q-8.289 98.113-8.484 97.921Q-8.679 97.730-9.048 97.730Q-9.338 97.730-9.550 97.906Q-9.762 98.082-9.870 98.355Q-9.977 98.629-9.977 98.912L-9.977 99.053L-9.977 99.094Q-9.977 99.599-9.765 99.991Q-9.554 100.382-9.089 100.382\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\">\u003Cg fill=\"var(--tk-accent)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(171.062 -108.288)\">\u003Cpath d=\"M-33.146 100.287L-33.146 100.208Q-33.101 100.027-32.930 100.006L-32.523 100.006L-32.523 96.708L-32.930 96.708Q-33.101 96.687-33.146 96.499L-33.146 96.421Q-33.101 96.240-32.930 96.219L-32.277 96.219Q-32.106 96.236-32.062 96.421L-32.062 98.892L-31.061 97.969L-31.320 97.969Q-31.501 97.949-31.536 97.757L-31.536 97.682Q-31.501 97.497-31.320 97.477L-30.052 97.477Q-29.875 97.497-29.834 97.682L-29.834 97.757Q-29.871 97.949-30.052 97.969L-30.374 97.969L-31.201 98.724L-30.192 100.006L-29.898 100.006Q-29.717 100.027-29.680 100.208L-29.680 100.287Q-29.717 100.474-29.898 100.495L-30.920 100.495Q-31.091 100.474-31.136 100.287L-31.136 100.208Q-31.091 100.027-30.920 100.006L-30.780 100.006L-31.536 99.039L-32.062 99.521L-32.062 100.006L-31.655 100.006Q-31.488 100.027-31.437 100.208L-31.437 100.287Q-31.488 100.474-31.655 100.495L-32.930 100.495Q-33.101 100.474-33.146 100.287M-26.484 99.193L-28.620 99.193Q-28.572 99.435-28.400 99.630Q-28.227 99.825-27.984 99.933Q-27.742 100.040-27.492 100.040Q-27.079 100.040-26.884 99.787Q-26.877 99.777-26.827 99.685Q-26.778 99.593-26.735 99.555Q-26.692 99.517-26.610 99.507L-26.484 99.507Q-26.316 99.524-26.265 99.712L-26.265 99.760Q-26.323 100.023-26.525 100.196Q-26.727 100.369-27 100.449Q-27.273 100.529-27.540 100.529Q-27.964 100.529-28.348 100.329Q-28.733 100.129-28.967 99.779Q-29.201 99.429-29.201 98.998L-29.201 98.947Q-29.201 98.537-28.986 98.184Q-28.771 97.832-28.413 97.627Q-28.056 97.422-27.646 97.422Q-27.205 97.422-26.896 97.617Q-26.586 97.812-26.426 98.152Q-26.265 98.492-26.265 98.933L-26.265 98.984Q-26.316 99.172-26.484 99.193M-28.613 98.711L-26.839 98.711Q-26.880 98.352-27.089 98.131Q-27.297 97.911-27.646 97.911Q-27.991 97.911-28.260 98.140Q-28.528 98.369-28.613 98.711M-25.780 101.845L-25.780 101.770Q-25.742 101.578-25.561 101.558L-25.192 101.558L-25.192 97.969L-25.561 97.969Q-25.742 97.949-25.780 97.757L-25.780 97.682Q-25.739 97.497-25.561 97.477L-24.847 97.477Q-24.676 97.494-24.631 97.682L-24.631 97.744Q-24.447 97.597-24.216 97.520Q-23.985 97.443-23.750 97.443Q-23.452 97.443-23.192 97.569Q-22.933 97.696-22.745 97.916Q-22.557 98.137-22.456 98.410Q-22.355 98.683-22.355 98.984Q-22.355 99.391-22.553 99.750Q-22.751 100.109-23.090 100.319Q-23.428 100.529-23.838 100.529Q-24.293 100.529-24.631 100.208L-24.631 101.558L-24.259 101.558Q-24.078 101.578-24.043 101.770L-24.043 101.845Q-24.078 102.030-24.259 102.050L-25.561 102.050Q-25.739 102.030-25.780 101.845M-23.876 100.040Q-23.606 100.040-23.387 99.892Q-23.168 99.743-23.042 99.497Q-22.916 99.251-22.916 98.984Q-22.916 98.731-23.025 98.487Q-23.134 98.243-23.338 98.087Q-23.541 97.932-23.804 97.932Q-24.084 97.932-24.314 98.094Q-24.543 98.256-24.631 98.519L-24.631 99.265Q-24.553 99.586-24.360 99.813Q-24.167 100.040-23.876 100.040M-21.077 99.528L-21.077 97.969L-21.733 97.969Q-21.907 97.949-21.952 97.757L-21.952 97.682Q-21.907 97.497-21.733 97.477L-21.077 97.477L-21.077 96.821Q-21.032 96.640-20.858 96.616L-20.731 96.616Q-20.561 96.640-20.516 96.821L-20.516 97.477L-19.327 97.477Q-19.159 97.494-19.108 97.682L-19.108 97.757Q-19.156 97.949-19.327 97.969L-20.516 97.969L-20.516 99.500Q-20.516 100.040-20.014 100.040Q-19.795 100.040-19.651 99.878Q-19.508 99.716-19.508 99.500Q-19.508 99.418-19.445 99.357Q-19.381 99.295-19.293 99.285L-19.166 99.285Q-18.992 99.306-18.947 99.487L-18.947 99.528Q-18.947 99.811-19.108 100.042Q-19.269 100.273-19.525 100.401Q-19.781 100.529-20.062 100.529Q-20.509 100.529-20.793 100.257Q-21.077 99.986-21.077 99.528\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(171.062 -108.288)\">\u003Cpath d=\"M-11.954 101.056Q-12.419 100.786-12.769 100.358Q-13.119 99.931-13.304 99.412Q-13.489 98.892-13.489 98.352Q-13.489 97.812-13.306 97.297Q-13.123 96.783-12.776 96.363Q-12.429 95.942-11.961 95.659Q-11.899 95.638-11.872 95.638L-11.793 95.638Q-11.708 95.648-11.650 95.706Q-11.592 95.765-11.592 95.853Q-11.592 95.980-11.680 96.035Q-12.074 96.287-12.359 96.651Q-12.644 97.016-12.786 97.446Q-12.928 97.877-12.928 98.352Q-12.928 98.707-12.844 99.046Q-12.761 99.384-12.605 99.678Q-12.449 99.972-12.222 100.220Q-11.995 100.468-11.691 100.669Q-11.592 100.738-11.592 100.857Q-11.592 100.943-11.650 101.004Q-11.708 101.066-11.793 101.076L-11.872 101.076Q-11.923 101.076-11.954 101.056M-10.901 101.845L-10.901 101.770Q-10.864 101.578-10.682 101.558L-10.313 101.558L-10.313 97.969L-10.682 97.969Q-10.864 97.949-10.901 97.757L-10.901 97.682Q-10.860 97.497-10.682 97.477L-9.968 97.477Q-9.797 97.494-9.753 97.682L-9.753 97.744Q-9.568 97.597-9.337 97.520Q-9.107 97.443-8.871 97.443Q-8.574 97.443-8.314 97.569Q-8.054 97.696-7.866 97.916Q-7.678 98.137-7.577 98.410Q-7.476 98.683-7.476 98.984Q-7.476 99.391-7.675 99.750Q-7.873 100.109-8.211 100.319Q-8.550 100.529-8.960 100.529Q-9.414 100.529-9.753 100.208L-9.753 101.558L-9.380 101.558Q-9.199 101.578-9.165 101.770L-9.165 101.845Q-9.199 102.030-9.380 102.050L-10.682 102.050Q-10.860 102.030-10.901 101.845M-8.997 100.040Q-8.727 100.040-8.509 99.892Q-8.290 99.743-8.163 99.497Q-8.037 99.251-8.037 98.984Q-8.037 98.731-8.146 98.487Q-8.256 98.243-8.459 98.087Q-8.662 97.932-8.926 97.932Q-9.206 97.932-9.435 98.094Q-9.664 98.256-9.753 98.519L-9.753 99.265Q-9.674 99.586-9.481 99.813Q-9.288 100.040-8.997 100.040M-6.892 99.521Q-6.892 99.131-6.530 98.906Q-6.167 98.680-5.694 98.593Q-5.220 98.506-4.776 98.499Q-4.776 98.311-4.894 98.178Q-5.012 98.044-5.193 97.978Q-5.374 97.911-5.559 97.911Q-5.860 97.911-6 97.932L-6 97.983Q-6 98.130-6.104 98.231Q-6.208 98.331-6.352 98.331Q-6.506 98.331-6.606 98.224Q-6.707 98.116-6.707 97.969Q-6.707 97.614-6.374 97.518Q-6.041 97.422-5.552 97.422Q-5.316 97.422-5.082 97.491Q-4.848 97.559-4.651 97.691Q-4.455 97.822-4.335 98.015Q-4.216 98.208-4.216 98.451L-4.216 99.955Q-4.216 100.006-3.754 100.006Q-3.583 100.023-3.539 100.208L-3.539 100.287Q-3.583 100.474-3.754 100.495L-3.881 100.495Q-4.181 100.495-4.381 100.454Q-4.581 100.413-4.708 100.249Q-5.111 100.529-5.730 100.529Q-6.024 100.529-6.290 100.406Q-6.557 100.283-6.724 100.054Q-6.892 99.825-6.892 99.521M-6.331 99.528Q-6.331 99.767-6.119 99.904Q-5.907 100.040-5.658 100.040Q-5.467 100.040-5.263 99.989Q-5.060 99.938-4.918 99.817Q-4.776 99.695-4.776 99.500L-4.776 98.984Q-5.022 98.984-5.386 99.034Q-5.750 99.083-6.041 99.205Q-6.331 99.326-6.331 99.528M-3.019 100.321L-3.019 99.521Q-2.995 99.340-2.811 99.319L-2.664 99.319Q-2.520 99.340-2.469 99.480Q-2.291 100.040-1.656 100.040Q-1.474 100.040-1.274 100.010Q-1.074 99.979-0.928 99.878Q-0.781 99.777-0.781 99.599Q-0.781 99.415-0.975 99.316Q-1.170 99.217-1.409 99.179L-2.021 99.080Q-3.019 98.895-3.019 98.263Q-3.019 98.010-2.893 97.844Q-2.766 97.679-2.556 97.585Q-2.346 97.491-2.122 97.456Q-1.898 97.422-1.656 97.422Q-1.437 97.422-1.268 97.448Q-1.098 97.474-0.955 97.542Q-0.886 97.439-0.774 97.422L-0.705 97.422Q-0.620 97.433-0.565 97.487Q-0.511 97.542-0.500 97.624L-0.500 98.243Q-0.511 98.325-0.565 98.383Q-0.620 98.441-0.705 98.451L-0.852 98.451Q-0.934 98.441-0.992 98.383Q-1.051 98.325-1.061 98.243Q-1.061 97.911-1.669 97.911Q-1.973 97.911-2.252 97.983Q-2.531 98.055-2.531 98.270Q-2.531 98.502-1.943 98.598L-1.327 98.704Q-0.904 98.776-0.598 98.993Q-0.292 99.210-0.292 99.599Q-0.292 99.941-0.499 100.153Q-0.705 100.365-1.011 100.447Q-1.317 100.529-1.656 100.529Q-2.161 100.529-2.510 100.307Q-2.572 100.416-2.614 100.466Q-2.657 100.516-2.749 100.529L-2.811 100.529Q-2.999 100.509-3.019 100.321M1.233 99.528L1.233 97.969L0.576 97.969Q0.402 97.949 0.358 97.757L0.358 97.682Q0.402 97.497 0.576 97.477L1.233 97.477L1.233 96.821Q1.277 96.640 1.451 96.616L1.578 96.616Q1.749 96.640 1.793 96.821L1.793 97.477L2.983 97.477Q3.150 97.494 3.201 97.682L3.201 97.757Q3.154 97.949 2.983 97.969L1.793 97.969L1.793 99.500Q1.793 100.040 2.296 100.040Q2.514 100.040 2.658 99.878Q2.801 99.716 2.801 99.500Q2.801 99.418 2.865 99.357Q2.928 99.295 3.017 99.285L3.143 99.285Q3.318 99.306 3.362 99.487L3.362 99.528Q3.362 99.811 3.201 100.042Q3.041 100.273 2.784 100.401Q2.528 100.529 2.248 100.529Q1.800 100.529 1.516 100.257Q1.233 99.986 1.233 99.528M4.808 101.076L4.733 101.076Q4.640 101.066 4.581 101.003Q4.521 100.939 4.521 100.857Q4.521 100.734 4.613 100.676Q4.907 100.488 5.143 100.235Q5.379 99.982 5.539 99.678Q5.700 99.374 5.779 99.042Q5.857 98.711 5.857 98.352Q5.857 97.880 5.714 97.450Q5.570 97.019 5.291 96.657Q5.013 96.294 4.627 96.041Q4.521 95.970 4.521 95.853Q4.521 95.768 4.581 95.708Q4.640 95.648 4.733 95.638L4.808 95.638Q4.856 95.638 4.886 95.659Q5.225 95.853 5.522 96.158Q5.820 96.462 6.013 96.807Q6.206 97.152 6.312 97.542Q6.418 97.932 6.418 98.352Q6.418 98.776 6.312 99.171Q6.206 99.565 6.009 99.912Q5.813 100.259 5.529 100.551Q5.245 100.844 4.893 101.056Q4.832 101.076 4.808 101.076\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(171.062 -81.626)\">\u003Cpath d=\"M-32.623 100.287L-32.623 96.708L-32.992 96.708Q-33.173 96.687-33.210 96.499L-33.210 96.421Q-33.173 96.240-32.992 96.219L-32.277 96.219Q-32.106 96.240-32.062 96.421L-32.062 97.744Q-31.877 97.597-31.647 97.520Q-31.416 97.443-31.180 97.443Q-30.883 97.443-30.623 97.569Q-30.363 97.696-30.175 97.916Q-29.987 98.137-29.887 98.410Q-29.786 98.683-29.786 98.984Q-29.786 99.391-29.984 99.750Q-30.182 100.109-30.521 100.319Q-30.859 100.529-31.269 100.529Q-31.724 100.529-32.062 100.208L-32.062 100.287Q-32.106 100.478-32.277 100.495L-32.404 100.495Q-32.571 100.474-32.623 100.287M-31.307 100.040Q-31.037 100.040-30.818 99.892Q-30.599 99.743-30.473 99.497Q-30.346 99.251-30.346 98.984Q-30.346 98.731-30.456 98.487Q-30.565 98.243-30.768 98.087Q-30.972 97.932-31.235 97.932Q-31.515 97.932-31.744 98.094Q-31.973 98.256-32.062 98.519L-32.062 99.265Q-31.983 99.586-31.790 99.813Q-31.597 100.040-31.307 100.040M-29.164 100.287L-29.164 100.208Q-29.119 100.027-28.948 100.006L-27.981 100.006L-27.981 96.708L-28.948 96.708Q-29.119 96.687-29.164 96.499L-29.164 96.421Q-29.119 96.240-28.948 96.219L-27.639 96.219Q-27.472 96.240-27.420 96.421L-27.420 100.006L-26.457 100.006Q-26.282 100.027-26.238 100.208L-26.238 100.287Q-26.282 100.474-26.457 100.495L-28.948 100.495Q-29.119 100.474-29.164 100.287M-23.985 100.529Q-24.399 100.529-24.736 100.316Q-25.072 100.102-25.267 99.743Q-25.462 99.384-25.462 98.984Q-25.462 98.683-25.353 98.401Q-25.243 98.120-25.042 97.897Q-24.840 97.675-24.572 97.549Q-24.303 97.422-23.985 97.422Q-23.668 97.422-23.394 97.550Q-23.121 97.679-22.926 97.894Q-22.731 98.109-22.620 98.390Q-22.509 98.670-22.509 98.984Q-22.509 99.384-22.705 99.745Q-22.902 100.105-23.239 100.317Q-23.575 100.529-23.985 100.529M-23.985 100.040Q-23.579 100.040-23.324 99.695Q-23.069 99.350-23.069 98.926Q-23.069 98.670-23.187 98.436Q-23.305 98.202-23.515 98.056Q-23.726 97.911-23.985 97.911Q-24.252 97.911-24.460 98.056Q-24.669 98.202-24.787 98.436Q-24.905 98.670-24.905 98.926Q-24.905 99.347-24.648 99.693Q-24.392 100.040-23.985 100.040M-21.637 98.984Q-21.637 98.564-21.424 98.202Q-21.210 97.839-20.846 97.631Q-20.482 97.422-20.062 97.422Q-19.576 97.422-19.245 97.518Q-18.913 97.614-18.913 97.969Q-18.913 98.116-19.012 98.224Q-19.111 98.331-19.262 98.331Q-19.412 98.331-19.516 98.231Q-19.621 98.130-19.621 97.983L-19.621 97.932Q-19.761 97.911-20.055 97.911Q-20.342 97.911-20.576 98.060Q-20.810 98.208-20.943 98.456Q-21.077 98.704-21.077 98.984Q-21.077 99.265-20.926 99.511Q-20.776 99.757-20.526 99.899Q-20.277 100.040-19.990 100.040Q-19.716 100.040-19.605 99.950Q-19.494 99.859-19.392 99.693Q-19.289 99.528-19.187 99.514L-19.040 99.514Q-18.947 99.524-18.891 99.584Q-18.834 99.644-18.834 99.733Q-18.834 99.774-18.852 99.808Q-18.947 100.064-19.125 100.222Q-19.303 100.379-19.544 100.454Q-19.785 100.529-20.062 100.529Q-20.485 100.529-20.849 100.321Q-21.213 100.112-21.425 99.760Q-21.637 99.408-21.637 98.984M-18.284 100.287L-18.284 100.208Q-18.240 100.027-18.069 100.006L-17.662 100.006L-17.662 96.708L-18.069 96.708Q-18.240 96.687-18.284 96.499L-18.284 96.421Q-18.240 96.240-18.069 96.219L-17.416 96.219Q-17.245 96.236-17.201 96.421L-17.201 98.892L-16.199 97.969L-16.459 97.969Q-16.640 97.949-16.674 97.757L-16.674 97.682Q-16.640 97.497-16.459 97.477L-15.191 97.477Q-15.013 97.497-14.972 97.682L-14.972 97.757Q-15.010 97.949-15.191 97.969L-15.512 97.969L-16.339 98.724L-15.331 100.006L-15.037 100.006Q-14.856 100.027-14.818 100.208L-14.818 100.287Q-14.856 100.474-15.037 100.495L-16.059 100.495Q-16.230 100.474-16.274 100.287L-16.274 100.208Q-16.230 100.027-16.059 100.006L-15.919 100.006L-16.674 99.039L-17.201 99.521L-17.201 100.006L-16.794 100.006Q-16.626 100.027-16.575 100.208L-16.575 100.287Q-16.626 100.474-16.794 100.495L-18.069 100.495Q-18.240 100.474-18.284 100.287M-11.623 99.193L-13.759 99.193Q-13.711 99.435-13.538 99.630Q-13.366 99.825-13.123 99.933Q-12.880 100.040-12.631 100.040Q-12.217 100.040-12.022 99.787Q-12.016 99.777-11.966 99.685Q-11.917 99.593-11.874 99.555Q-11.831 99.517-11.749 99.507L-11.623 99.507Q-11.455 99.524-11.404 99.712L-11.404 99.760Q-11.462 100.023-11.664 100.196Q-11.865 100.369-12.139 100.449Q-12.412 100.529-12.679 100.529Q-13.103 100.529-13.487 100.329Q-13.872 100.129-14.106 99.779Q-14.340 99.429-14.340 98.998L-14.340 98.947Q-14.340 98.537-14.125 98.184Q-13.909 97.832-13.552 97.627Q-13.195 97.422-12.785 97.422Q-12.344 97.422-12.034 97.617Q-11.725 97.812-11.564 98.152Q-11.404 98.492-11.404 98.933L-11.404 98.984Q-11.455 99.172-11.623 99.193M-13.752 98.711L-11.978 98.711Q-12.019 98.352-12.228 98.131Q-12.436 97.911-12.785 97.911Q-13.130 97.911-13.398 98.140Q-13.667 98.369-13.752 98.711M-9.350 100.529Q-9.756 100.529-10.076 100.310Q-10.396 100.092-10.575 99.738Q-10.754 99.384-10.754 98.984Q-10.754 98.683-10.645 98.403Q-10.536 98.123-10.332 97.904Q-10.129 97.685-9.862 97.564Q-9.596 97.443-9.285 97.443Q-8.837 97.443-8.481 97.723L-8.481 96.708L-8.851 96.708Q-9.035 96.687-9.069 96.499L-9.069 96.421Q-9.035 96.240-8.851 96.219L-8.140 96.219Q-7.965 96.240-7.921 96.421L-7.921 100.006L-7.548 100.006Q-7.367 100.027-7.333 100.208L-7.333 100.287Q-7.367 100.474-7.548 100.495L-8.263 100.495Q-8.437 100.474-8.481 100.287L-8.481 100.174Q-8.652 100.341-8.881 100.435Q-9.110 100.529-9.350 100.529M-9.315 100.040Q-9.001 100.040-8.781 99.805Q-8.560 99.569-8.481 99.241L-8.481 98.513Q-8.533 98.349-8.644 98.217Q-8.755 98.085-8.910 98.008Q-9.066 97.932-9.237 97.932Q-9.507 97.932-9.726 98.080Q-9.944 98.229-10.071 98.478Q-10.197 98.728-10.197 98.991Q-10.197 99.384-9.948 99.712Q-9.698 100.040-9.315 100.040\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(171.062 -81.626)\">\u003Cpath d=\"M-0.798 101.056Q-1.263 100.786-1.613 100.358Q-1.963 99.931-2.148 99.412Q-2.333 98.892-2.333 98.352Q-2.333 97.812-2.150 97.297Q-1.967 96.783-1.620 96.363Q-1.273 95.942-0.805 95.659Q-0.743 95.638-0.716 95.638L-0.637 95.638Q-0.552 95.648-0.494 95.706Q-0.436 95.765-0.436 95.853Q-0.436 95.980-0.524 96.035Q-0.918 96.287-1.203 96.651Q-1.488 97.016-1.630 97.446Q-1.772 97.877-1.772 98.352Q-1.772 98.707-1.688 99.046Q-1.605 99.384-1.449 99.678Q-1.293 99.972-1.066 100.220Q-0.839 100.468-0.535 100.669Q-0.436 100.738-0.436 100.857Q-0.436 100.943-0.494 101.004Q-0.552 101.066-0.637 101.076L-0.716 101.076Q-0.767 101.076-0.798 101.056M0.474 100.287L0.474 100.208Q0.518 100.027 0.689 100.006L1.461 100.006L1.461 97.969L0.713 97.969Q0.539 97.949 0.494 97.757L0.494 97.682Q0.539 97.497 0.713 97.477L1.461 97.477L1.461 97.080Q1.461 96.674 1.817 96.428Q2.172 96.182 2.593 96.182Q2.866 96.182 3.080 96.287Q3.293 96.393 3.293 96.640Q3.293 96.783 3.198 96.886Q3.102 96.988 2.958 96.988Q2.829 96.988 2.723 96.896Q2.617 96.804 2.617 96.674L2.545 96.674Q2.412 96.674 2.292 96.727Q2.172 96.780 2.097 96.880Q2.022 96.981 2.022 97.108L2.022 97.477L2.924 97.477Q3.095 97.494 3.140 97.682L3.140 97.757Q3.095 97.949 2.924 97.969L2.022 97.969L2.022 100.006L2.791 100.006Q2.962 100.027 3.006 100.208L3.006 100.287Q2.962 100.474 2.791 100.495L0.689 100.495Q0.518 100.474 0.474 100.287M4.558 99.746L4.558 97.969L4.189 97.969Q4.008 97.949 3.970 97.757L3.970 97.682Q4.011 97.497 4.189 97.477L4.903 97.477Q5.074 97.497 5.119 97.682L5.119 99.719Q5.119 99.924 5.267 99.982Q5.416 100.040 5.665 100.040Q5.847 100.040 6.018 99.974Q6.188 99.907 6.298 99.776Q6.407 99.644 6.407 99.459L6.407 97.969L6.038 97.969Q5.853 97.949 5.819 97.757L5.819 97.682Q5.853 97.497 6.038 97.477L6.749 97.477Q6.923 97.497 6.968 97.682L6.968 100.006L7.340 100.006Q7.521 100.027 7.556 100.208L7.556 100.287Q7.521 100.474 7.340 100.495L6.626 100.495Q6.452 100.474 6.407 100.300Q6.055 100.529 5.611 100.529Q5.406 100.529 5.218 100.493Q5.030 100.457 4.884 100.369Q4.739 100.280 4.649 100.124Q4.558 99.969 4.558 99.746M8.673 99.528L8.673 97.969L8.017 97.969Q7.843 97.949 7.798 97.757L7.798 97.682Q7.843 97.497 8.017 97.477L8.673 97.477L8.673 96.821Q8.718 96.640 8.892 96.616L9.019 96.616Q9.189 96.640 9.234 96.821L9.234 97.477L10.423 97.477Q10.591 97.494 10.642 97.682L10.642 97.757Q10.594 97.949 10.423 97.969L9.234 97.969L9.234 99.500Q9.234 100.040 9.736 100.040Q9.955 100.040 10.099 99.878Q10.242 99.716 10.242 99.500Q10.242 99.418 10.305 99.357Q10.369 99.295 10.457 99.285L10.584 99.285Q10.758 99.306 10.803 99.487L10.803 99.528Q10.803 99.811 10.642 100.042Q10.481 100.273 10.225 100.401Q9.969 100.529 9.688 100.529Q9.241 100.529 8.957 100.257Q8.673 99.986 8.673 99.528M11.989 99.746L11.989 97.969L11.620 97.969Q11.438 97.949 11.401 97.757L11.401 97.682Q11.442 97.497 11.620 97.477L12.334 97.477Q12.505 97.497 12.549 97.682L12.549 99.719Q12.549 99.924 12.698 99.982Q12.847 100.040 13.096 100.040Q13.277 100.040 13.448 99.974Q13.619 99.907 13.728 99.776Q13.838 99.644 13.838 99.459L13.838 97.969L13.469 97.969Q13.284 97.949 13.250 97.757L13.250 97.682Q13.284 97.497 13.469 97.477L14.180 97.477Q14.354 97.497 14.398 97.682L14.398 100.006L14.771 100.006Q14.952 100.027 14.986 100.208L14.986 100.287Q14.952 100.474 14.771 100.495L14.057 100.495Q13.882 100.474 13.838 100.300Q13.486 100.529 13.041 100.529Q12.836 100.529 12.648 100.493Q12.460 100.457 12.315 100.369Q12.170 100.280 12.079 100.124Q11.989 99.969 11.989 99.746M15.249 100.287L15.249 100.208Q15.301 100.027 15.468 100.006L16.090 100.006L16.090 97.969L15.468 97.969Q15.297 97.949 15.249 97.757L15.249 97.682Q15.301 97.497 15.468 97.477L16.432 97.477Q16.606 97.494 16.651 97.682L16.651 97.969Q16.880 97.720 17.191 97.581Q17.502 97.443 17.840 97.443Q18.097 97.443 18.302 97.561Q18.507 97.679 18.507 97.911Q18.507 98.058 18.411 98.161Q18.315 98.263 18.168 98.263Q18.035 98.263 17.934 98.166Q17.833 98.068 17.833 97.932Q17.505 97.932 17.230 98.108Q16.955 98.284 16.803 98.576Q16.651 98.868 16.651 99.200L16.651 100.006L17.478 100.006Q17.659 100.027 17.693 100.208L17.693 100.287Q17.659 100.474 17.478 100.495L15.468 100.495Q15.301 100.474 15.249 100.287M21.843 99.193L19.707 99.193Q19.754 99.435 19.927 99.630Q20.100 99.825 20.342 99.933Q20.585 100.040 20.834 100.040Q21.248 100.040 21.443 99.787Q21.450 99.777 21.499 99.685Q21.549 99.593 21.592 99.555Q21.634 99.517 21.716 99.507L21.843 99.507Q22.010 99.524 22.061 99.712L22.061 99.760Q22.003 100.023 21.802 100.196Q21.600 100.369 21.327 100.449Q21.053 100.529 20.787 100.529Q20.363 100.529 19.978 100.329Q19.594 100.129 19.360 99.779Q19.125 99.429 19.125 98.998L19.125 98.947Q19.125 98.537 19.341 98.184Q19.556 97.832 19.913 97.627Q20.270 97.422 20.681 97.422Q21.122 97.422 21.431 97.617Q21.740 97.812 21.901 98.152Q22.061 98.492 22.061 98.933L22.061 98.984Q22.010 99.172 21.843 99.193M19.713 98.711L21.487 98.711Q21.446 98.352 21.238 98.131Q21.029 97.911 20.681 97.911Q20.335 97.911 20.067 98.140Q19.799 98.369 19.713 98.711M23.395 101.076L23.319 101.076Q23.227 101.066 23.167 101.003Q23.107 100.939 23.107 100.857Q23.107 100.734 23.200 100.676Q23.494 100.488 23.729 100.235Q23.965 99.982 24.126 99.678Q24.287 99.374 24.365 99.042Q24.444 98.711 24.444 98.352Q24.444 97.880 24.300 97.450Q24.157 97.019 23.878 96.657Q23.600 96.294 23.213 96.041Q23.107 95.970 23.107 95.853Q23.107 95.768 23.167 95.708Q23.227 95.648 23.319 95.638L23.395 95.638Q23.442 95.638 23.473 95.659Q23.811 95.853 24.109 96.158Q24.406 96.462 24.599 96.807Q24.792 97.152 24.898 97.542Q25.004 97.932 25.004 98.352Q25.004 98.776 24.898 99.171Q24.792 99.565 24.596 99.912Q24.399 100.259 24.116 100.551Q23.832 100.844 23.480 101.056Q23.418 101.076 23.395 101.076\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">The causal mask. Query row \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> attends only to key columns \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.854em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>: the lower triangle (blue) is kept, the upper triangle (shaded, \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>) is blocked before the softmax.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:518.827px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 389.120 129.555\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg transform=\"translate(-11.156 22.056)\">\u003Cpath d=\"M-15.507-13.129L-15.507-14.688L-16.163-14.688Q-16.337-14.708-16.382-14.900L-16.382-14.975Q-16.337-15.160-16.163-15.180L-15.507-15.180L-15.507-15.836Q-15.462-16.017-15.288-16.041L-15.161-16.041Q-14.991-16.017-14.946-15.836L-14.946-15.180L-13.757-15.180Q-13.589-15.163-13.538-14.975L-13.538-14.900Q-13.586-14.708-13.757-14.688L-14.946-14.688L-14.946-13.157Q-14.946-12.617-14.444-12.617Q-14.225-12.617-14.081-12.779Q-13.938-12.941-13.938-13.157Q-13.938-13.239-13.875-13.300Q-13.811-13.362-13.723-13.372L-13.596-13.372Q-13.422-13.351-13.377-13.170L-13.377-13.129Q-13.377-12.846-13.538-12.615Q-13.699-12.384-13.955-12.256Q-14.211-12.128-14.492-12.128Q-14.939-12.128-15.223-12.400Q-15.507-12.671-15.507-13.129M-10.985-12.128Q-11.398-12.128-11.735-12.341Q-12.072-12.555-12.266-12.914Q-12.461-13.273-12.461-13.673Q-12.461-13.974-12.352-14.256Q-12.243-14.537-12.041-14.760Q-11.839-14.982-11.571-15.108Q-11.303-15.235-10.985-15.235Q-10.667-15.235-10.393-15.107Q-10.120-14.978-9.925-14.763Q-9.730-14.548-9.619-14.267Q-9.508-13.987-9.508-13.673Q-9.508-13.273-9.705-12.912Q-9.901-12.552-10.238-12.340Q-10.575-12.128-10.985-12.128M-10.985-12.617Q-10.578-12.617-10.323-12.962Q-10.069-13.307-10.069-13.731Q-10.069-13.987-10.187-14.221Q-10.305-14.455-10.515-14.601Q-10.725-14.746-10.985-14.746Q-11.251-14.746-11.460-14.601Q-11.668-14.455-11.786-14.221Q-11.904-13.987-11.904-13.731Q-11.904-13.310-11.648-12.964Q-11.391-12.617-10.985-12.617M-8.999-12.370L-8.999-12.449Q-8.954-12.630-8.784-12.651L-8.377-12.651L-8.377-15.949L-8.784-15.949Q-8.954-15.970-8.999-16.158L-8.999-16.236Q-8.954-16.417-8.784-16.438L-8.131-16.438Q-7.960-16.421-7.915-16.236L-7.915-13.765L-6.914-14.688L-7.174-14.688Q-7.355-14.708-7.389-14.900L-7.389-14.975Q-7.355-15.160-7.174-15.180L-5.906-15.180Q-5.728-15.160-5.687-14.975L-5.687-14.900Q-5.724-14.708-5.906-14.688L-6.227-14.688L-7.054-13.933L-6.046-12.651L-5.752-12.651Q-5.571-12.630-5.533-12.449L-5.533-12.370Q-5.571-12.183-5.752-12.162L-6.774-12.162Q-6.945-12.183-6.989-12.370L-6.989-12.449Q-6.945-12.630-6.774-12.651L-6.634-12.651L-7.389-13.618L-7.915-13.136L-7.915-12.651L-7.509-12.651Q-7.341-12.630-7.290-12.449L-7.290-12.370Q-7.341-12.183-7.509-12.162L-8.784-12.162Q-8.954-12.183-8.999-12.370M-2.337-13.464L-4.473-13.464Q-4.426-13.222-4.253-13.027Q-4.080-12.832-3.838-12.724Q-3.595-12.617-3.346-12.617Q-2.932-12.617-2.737-12.870Q-2.730-12.880-2.681-12.972Q-2.631-13.064-2.588-13.102Q-2.546-13.140-2.464-13.150L-2.337-13.150Q-2.170-13.133-2.119-12.945L-2.119-12.897Q-2.177-12.634-2.378-12.461Q-2.580-12.288-2.853-12.208Q-3.127-12.128-3.393-12.128Q-3.817-12.128-4.202-12.328Q-4.586-12.528-4.820-12.878Q-5.055-13.228-5.055-13.659L-5.055-13.710Q-5.055-14.120-4.839-14.473Q-4.624-14.825-4.267-15.030Q-3.910-15.235-3.499-15.235Q-3.058-15.235-2.749-15.040Q-2.440-14.845-2.279-14.505Q-2.119-14.165-2.119-13.724L-2.119-13.673Q-2.170-13.485-2.337-13.464M-4.467-13.946L-2.693-13.946Q-2.734-14.305-2.942-14.526Q-3.151-14.746-3.499-14.746Q-3.845-14.746-4.113-14.517Q-4.381-14.288-4.467-13.946M-1.633-12.370L-1.633-12.449Q-1.596-12.630-1.414-12.651L-1.045-12.651L-1.045-14.688L-1.414-14.688Q-1.596-14.708-1.633-14.900L-1.633-14.975Q-1.592-15.160-1.414-15.180L-0.700-15.180Q-0.529-15.160-0.485-14.975L-0.485-14.900L-0.492-14.879Q-0.293-15.037-0.054-15.125Q0.185-15.214 0.442-15.214Q0.746-15.214 0.954-15.091Q1.163-14.968 1.264-14.743Q1.364-14.517 1.364-14.206L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L0.517-12.162Q0.346-12.183 0.301-12.370L0.301-12.449Q0.346-12.634 0.517-12.651L0.804-12.651L0.804-14.179Q0.804-14.449 0.725-14.587Q0.647-14.725 0.390-14.725Q0.154-14.725-0.046-14.611Q-0.245-14.496-0.365-14.297Q-0.485-14.097-0.485-13.864L-0.485-12.651L-0.112-12.651Q0.069-12.630 0.103-12.449L0.103-12.370Q0.069-12.183-0.112-12.162L-1.414-12.162Q-1.596-12.183-1.633-12.370M2.533-12.336L2.533-13.136Q2.557-13.317 2.742-13.338L2.889-13.338Q3.032-13.317 3.084-13.177Q3.261-12.617 3.897-12.617Q4.078-12.617 4.278-12.647Q4.478-12.678 4.625-12.779Q4.772-12.880 4.772-13.058Q4.772-13.242 4.577-13.341Q4.382-13.440 4.143-13.478L3.531-13.577Q2.533-13.762 2.533-14.394Q2.533-14.647 2.660-14.813Q2.786-14.978 2.996-15.072Q3.207-15.166 3.431-15.201Q3.654-15.235 3.897-15.235Q4.116-15.235 4.285-15.209Q4.454-15.183 4.598-15.115Q4.666-15.218 4.779-15.235L4.847-15.235Q4.933-15.225 4.987-15.170Q5.042-15.115 5.052-15.033L5.052-14.414Q5.042-14.332 4.987-14.274Q4.933-14.216 4.847-14.206L4.700-14.206Q4.618-14.216 4.560-14.274Q4.502-14.332 4.492-14.414Q4.492-14.746 3.883-14.746Q3.579-14.746 3.301-14.674Q3.022-14.602 3.022-14.387Q3.022-14.155 3.610-14.059L4.225-13.953Q4.649-13.881 4.955-13.664Q5.261-13.447 5.261-13.058Q5.261-12.716 5.054-12.504Q4.847-12.292 4.541-12.210Q4.236-12.128 3.897-12.128Q3.391-12.128 3.043-12.350Q2.981-12.241 2.938-12.191Q2.896-12.141 2.803-12.128L2.742-12.128Q2.554-12.148 2.533-12.336\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M-45.01-9.316h56.906v-17.072h-56.905Z\"\u002F>\u003Cg transform=\"translate(-13.016 -3.552)\">\u003Cpath d=\"M-13.483-13.464L-15.619-13.464Q-15.572-13.222-15.399-13.027Q-15.226-12.832-14.984-12.724Q-14.741-12.617-14.492-12.617Q-14.078-12.617-13.883-12.870Q-13.876-12.880-13.827-12.972Q-13.777-13.064-13.734-13.102Q-13.692-13.140-13.610-13.150L-13.483-13.150Q-13.316-13.133-13.264-12.945L-13.264-12.897Q-13.323-12.634-13.524-12.461Q-13.726-12.288-13.999-12.208Q-14.273-12.128-14.539-12.128Q-14.963-12.128-15.348-12.328Q-15.732-12.528-15.966-12.878Q-16.201-13.228-16.201-13.659L-16.201-13.710Q-16.201-14.120-15.985-14.473Q-15.770-14.825-15.413-15.030Q-15.056-15.235-14.645-15.235Q-14.204-15.235-13.895-15.040Q-13.586-14.845-13.425-14.505Q-13.264-14.165-13.264-13.724L-13.264-13.673Q-13.316-13.485-13.483-13.464M-15.613-13.946L-13.839-13.946Q-13.880-14.305-14.088-14.526Q-14.297-14.746-14.645-14.746Q-14.991-14.746-15.259-14.517Q-15.527-14.288-15.613-13.946M-12.779-12.370L-12.779-12.449Q-12.742-12.630-12.560-12.651L-12.191-12.651L-12.191-14.688L-12.560-14.688Q-12.742-14.708-12.779-14.900L-12.779-14.975Q-12.738-15.160-12.560-15.180L-11.846-15.180Q-11.675-15.160-11.631-14.975L-11.631-14.900L-11.638-14.879Q-11.439-15.037-11.200-15.125Q-10.961-15.214-10.704-15.214Q-10.400-15.214-10.192-15.091Q-9.983-14.968-9.882-14.743Q-9.782-14.517-9.782-14.206L-9.782-12.651L-9.409-12.651Q-9.228-12.630-9.194-12.449L-9.194-12.370Q-9.228-12.183-9.409-12.162L-10.629-12.162Q-10.800-12.183-10.845-12.370L-10.845-12.449Q-10.800-12.634-10.629-12.651L-10.342-12.651L-10.342-14.179Q-10.342-14.449-10.421-14.587Q-10.499-14.725-10.756-14.725Q-10.992-14.725-11.191-14.611Q-11.391-14.496-11.511-14.297Q-11.631-14.097-11.631-13.864L-11.631-12.651L-11.258-12.651Q-11.077-12.630-11.043-12.449L-11.043-12.370Q-11.077-12.183-11.258-12.162L-12.560-12.162Q-12.742-12.183-12.779-12.370M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M-45.01-34.924h56.906v-17.072h-56.905Z\"\u002F>\u003Cg transform=\"translate(-13.016 -29.16)\">\u003Cpath d=\"M-13.483-13.464L-15.619-13.464Q-15.572-13.222-15.399-13.027Q-15.226-12.832-14.984-12.724Q-14.741-12.617-14.492-12.617Q-14.078-12.617-13.883-12.870Q-13.876-12.880-13.827-12.972Q-13.777-13.064-13.734-13.102Q-13.692-13.140-13.610-13.150L-13.483-13.150Q-13.316-13.133-13.264-12.945L-13.264-12.897Q-13.323-12.634-13.524-12.461Q-13.726-12.288-13.999-12.208Q-14.273-12.128-14.539-12.128Q-14.963-12.128-15.348-12.328Q-15.732-12.528-15.966-12.878Q-16.201-13.228-16.201-13.659L-16.201-13.710Q-16.201-14.120-15.985-14.473Q-15.770-14.825-15.413-15.030Q-15.056-15.235-14.645-15.235Q-14.204-15.235-13.895-15.040Q-13.586-14.845-13.425-14.505Q-13.264-14.165-13.264-13.724L-13.264-13.673Q-13.316-13.485-13.483-13.464M-15.613-13.946L-13.839-13.946Q-13.880-14.305-14.088-14.526Q-14.297-14.746-14.645-14.746Q-14.991-14.746-15.259-14.517Q-15.527-14.288-15.613-13.946M-12.779-12.370L-12.779-12.449Q-12.742-12.630-12.560-12.651L-12.191-12.651L-12.191-14.688L-12.560-14.688Q-12.742-14.708-12.779-14.900L-12.779-14.975Q-12.738-15.160-12.560-15.180L-11.846-15.180Q-11.675-15.160-11.631-14.975L-11.631-14.900L-11.638-14.879Q-11.439-15.037-11.200-15.125Q-10.961-15.214-10.704-15.214Q-10.400-15.214-10.192-15.091Q-9.983-14.968-9.882-14.743Q-9.782-14.517-9.782-14.206L-9.782-12.651L-9.409-12.651Q-9.228-12.630-9.194-12.449L-9.194-12.370Q-9.228-12.183-9.409-12.162L-10.629-12.162Q-10.800-12.183-10.845-12.370L-10.845-12.449Q-10.800-12.634-10.629-12.651L-10.342-12.651L-10.342-14.179Q-10.342-14.449-10.421-14.587Q-10.499-14.725-10.756-14.725Q-10.992-14.725-11.191-14.611Q-11.391-14.496-11.511-14.297Q-11.631-14.097-11.631-13.864L-11.631-12.651L-11.258-12.651Q-11.077-12.630-11.043-12.449L-11.043-12.370Q-11.077-12.183-11.258-12.162L-12.560-12.162Q-12.742-12.183-12.779-12.370M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(-14.875 -51.921)\">\u003Cpath d=\"M-16.276-12.370L-16.276-12.449Q-16.231-12.630-16.060-12.651L-15.288-12.651L-15.288-14.688L-16.036-14.688Q-16.211-14.708-16.255-14.900L-16.255-14.975Q-16.211-15.160-16.036-15.180L-15.288-15.180L-15.288-15.577Q-15.288-15.983-14.932-16.229Q-14.577-16.475-14.157-16.475Q-13.883-16.475-13.670-16.370Q-13.456-16.264-13.456-16.017Q-13.456-15.874-13.552-15.771Q-13.647-15.669-13.791-15.669Q-13.921-15.669-14.027-15.761Q-14.133-15.853-14.133-15.983L-14.204-15.983Q-14.338-15.983-14.457-15.930Q-14.577-15.877-14.652-15.777Q-14.727-15.676-14.727-15.549L-14.727-15.180L-13.825-15.180Q-13.654-15.163-13.610-14.975L-13.610-14.900Q-13.654-14.708-13.825-14.688L-14.727-14.688L-14.727-12.651L-13.958-12.651Q-13.787-12.630-13.743-12.449L-13.743-12.370Q-13.787-12.183-13.958-12.162L-16.060-12.162Q-16.231-12.183-16.276-12.370M-9.768-13.464L-11.904-13.464Q-11.856-13.222-11.684-13.027Q-11.511-12.832-11.268-12.724Q-11.026-12.617-10.776-12.617Q-10.363-12.617-10.168-12.870Q-10.161-12.880-10.111-12.972Q-10.062-13.064-10.019-13.102Q-9.976-13.140-9.894-13.150L-9.768-13.150Q-9.600-13.133-9.549-12.945L-9.549-12.897Q-9.607-12.634-9.809-12.461Q-10.011-12.288-10.284-12.208Q-10.557-12.128-10.824-12.128Q-11.248-12.128-11.632-12.328Q-12.017-12.528-12.251-12.878Q-12.485-13.228-12.485-13.659L-12.485-13.710Q-12.485-14.120-12.270-14.473Q-12.055-14.825-11.697-15.030Q-11.340-15.235-10.930-15.235Q-10.489-15.235-10.180-15.040Q-9.870-14.845-9.710-14.505Q-9.549-14.165-9.549-13.724L-9.549-13.673Q-9.600-13.485-9.768-13.464M-11.897-13.946L-10.123-13.946Q-10.164-14.305-10.373-14.526Q-10.581-14.746-10.930-14.746Q-11.275-14.746-11.544-14.517Q-11.812-14.288-11.897-13.946M-8.770-13.136Q-8.770-13.526-8.408-13.751Q-8.045-13.977-7.572-14.064Q-7.098-14.151-6.654-14.158Q-6.654-14.346-6.772-14.479Q-6.890-14.613-7.071-14.679Q-7.252-14.746-7.437-14.746Q-7.738-14.746-7.878-14.725L-7.878-14.674Q-7.878-14.527-7.982-14.426Q-8.086-14.326-8.230-14.326Q-8.384-14.326-8.484-14.433Q-8.585-14.541-8.585-14.688Q-8.585-15.043-8.252-15.139Q-7.919-15.235-7.430-15.235Q-7.194-15.235-6.960-15.166Q-6.726-15.098-6.529-14.966Q-6.333-14.835-6.213-14.642Q-6.094-14.449-6.094-14.206L-6.094-12.702Q-6.094-12.651-5.632-12.651Q-5.461-12.634-5.417-12.449L-5.417-12.370Q-5.461-12.183-5.632-12.162L-5.759-12.162Q-6.059-12.162-6.259-12.203Q-6.459-12.244-6.586-12.408Q-6.989-12.128-7.608-12.128Q-7.902-12.128-8.168-12.251Q-8.435-12.374-8.602-12.603Q-8.770-12.832-8.770-13.136M-8.209-13.129Q-8.209-12.890-7.997-12.753Q-7.785-12.617-7.536-12.617Q-7.345-12.617-7.141-12.668Q-6.938-12.719-6.796-12.840Q-6.654-12.962-6.654-13.157L-6.654-13.673Q-6.900-13.673-7.264-13.623Q-7.628-13.574-7.919-13.452Q-8.209-13.331-8.209-13.129M-4.361-13.129L-4.361-14.688L-5.017-14.688Q-5.191-14.708-5.236-14.900L-5.236-14.975Q-5.191-15.160-5.017-15.180L-4.361-15.180L-4.361-15.836Q-4.316-16.017-4.142-16.041L-4.015-16.041Q-3.845-16.017-3.800-15.836L-3.800-15.180L-2.611-15.180Q-2.443-15.163-2.392-14.975L-2.392-14.900Q-2.440-14.708-2.611-14.688L-3.800-14.688L-3.800-13.157Q-3.800-12.617-3.298-12.617Q-3.079-12.617-2.935-12.779Q-2.792-12.941-2.792-13.157Q-2.792-13.239-2.729-13.300Q-2.665-13.362-2.577-13.372L-2.450-13.372Q-2.276-13.351-2.231-13.170L-2.231-13.129Q-2.231-12.846-2.392-12.615Q-2.553-12.384-2.809-12.256Q-3.065-12.128-3.346-12.128Q-3.793-12.128-4.077-12.400Q-4.361-12.671-4.361-13.129M-1.045-12.911L-1.045-14.688L-1.414-14.688Q-1.596-14.708-1.633-14.900L-1.633-14.975Q-1.592-15.160-1.414-15.180L-0.700-15.180Q-0.529-15.160-0.485-14.975L-0.485-12.938Q-0.485-12.733-0.336-12.675Q-0.187-12.617 0.062-12.617Q0.243-12.617 0.414-12.683Q0.585-12.750 0.694-12.881Q0.804-13.013 0.804-13.198L0.804-14.688L0.435-14.688Q0.250-14.708 0.216-14.900L0.216-14.975Q0.250-15.160 0.435-15.180L1.146-15.180Q1.320-15.160 1.364-14.975L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.357Q0.452-12.128 0.007-12.128Q-0.198-12.128-0.386-12.164Q-0.574-12.200-0.719-12.288Q-0.864-12.377-0.955-12.533Q-1.045-12.688-1.045-12.911M2.215-12.370L2.215-12.449Q2.267-12.630 2.434-12.651L3.056-12.651L3.056-14.688L2.434-14.688Q2.263-14.708 2.215-14.900L2.215-14.975Q2.267-15.160 2.434-15.180L3.398-15.180Q3.572-15.163 3.617-14.975L3.617-14.688Q3.846-14.937 4.157-15.076Q4.468-15.214 4.806-15.214Q5.063-15.214 5.268-15.096Q5.473-14.978 5.473-14.746Q5.473-14.599 5.377-14.496Q5.281-14.394 5.134-14.394Q5.001-14.394 4.900-14.491Q4.799-14.589 4.799-14.725Q4.471-14.725 4.196-14.549Q3.921-14.373 3.769-14.081Q3.617-13.789 3.617-13.457L3.617-12.651L4.444-12.651Q4.625-12.630 4.659-12.449L4.659-12.370Q4.625-12.183 4.444-12.162L2.434-12.162Q2.267-12.183 2.215-12.370M8.809-13.464L6.673-13.464Q6.720-13.222 6.893-13.027Q7.066-12.832 7.308-12.724Q7.551-12.617 7.800-12.617Q8.214-12.617 8.409-12.870Q8.416-12.880 8.465-12.972Q8.515-13.064 8.558-13.102Q8.600-13.140 8.682-13.150L8.809-13.150Q8.976-13.133 9.027-12.945L9.027-12.897Q8.969-12.634 8.768-12.461Q8.566-12.288 8.293-12.208Q8.019-12.128 7.753-12.128Q7.329-12.128 6.944-12.328Q6.560-12.528 6.326-12.878Q6.091-13.228 6.091-13.659L6.091-13.710Q6.091-14.120 6.307-14.473Q6.522-14.825 6.879-15.030Q7.236-15.235 7.647-15.235Q8.088-15.235 8.397-15.040Q8.706-14.845 8.867-14.505Q9.027-14.165 9.027-13.724L9.027-13.673Q8.976-13.485 8.809-13.464M6.679-13.946L8.453-13.946Q8.412-14.305 8.204-14.526Q7.995-14.746 7.647-14.746Q7.301-14.746 7.033-14.517Q6.765-14.288 6.679-13.946M9.964-12.336L9.964-13.136Q9.988-13.317 10.173-13.338L10.319-13.338Q10.463-13.317 10.514-13.177Q10.692-12.617 11.328-12.617Q11.509-12.617 11.709-12.647Q11.909-12.678 12.056-12.779Q12.203-12.880 12.203-13.058Q12.203-13.242 12.008-13.341Q11.813-13.440 11.574-13.478L10.962-13.577Q9.964-13.762 9.964-14.394Q9.964-14.647 10.090-14.813Q10.217-14.978 10.427-15.072Q10.637-15.166 10.861-15.201Q11.085-15.235 11.328-15.235Q11.547-15.235 11.716-15.209Q11.885-15.183 12.028-15.115Q12.097-15.218 12.210-15.235L12.278-15.235Q12.363-15.225 12.418-15.170Q12.473-15.115 12.483-15.033L12.483-14.414Q12.473-14.332 12.418-14.274Q12.363-14.216 12.278-14.206L12.131-14.206Q12.049-14.216 11.991-14.274Q11.933-14.332 11.923-14.414Q11.923-14.746 11.314-14.746Q11.010-14.746 10.731-14.674Q10.453-14.602 10.453-14.387Q10.453-14.155 11.041-14.059L11.656-13.953Q12.080-13.881 12.386-13.664Q12.692-13.447 12.692-13.058Q12.692-12.716 12.485-12.504Q12.278-12.292 11.972-12.210Q11.666-12.128 11.328-12.128Q10.822-12.128 10.473-12.350Q10.412-12.241 10.369-12.191Q10.326-12.141 10.234-12.128L10.173-12.128Q9.985-12.148 9.964-12.336\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-16.556 2.083v-8.6\"\u002F>\u003Cpath stroke=\"none\" d=\"m-16.556-9.116-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-16.556-26.588v-5.536\"\u002F>\u003Cpath stroke=\"none\" d=\"m-16.556-34.724-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-16.556-52.196v-5.754\"\u002F>\u003Cpath stroke=\"none\" d=\"m-16.556-60.55-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-25.5 44.235)\">\u003Cpath d=\"M-13.044-13.650L-15.486-13.650Q-15.431-13.373-15.234-13.150Q-15.036-12.928-14.759-12.805Q-14.482-12.682-14.197-12.682Q-13.724-12.682-13.501-12.971Q-13.494-12.982-13.437-13.088Q-13.380-13.193-13.331-13.236Q-13.283-13.279-13.189-13.291L-13.044-13.291Q-12.853-13.271-12.794-13.057L-12.794-13.002Q-12.861-12.701-13.091-12.504Q-13.322-12.307-13.634-12.215Q-13.947-12.123-14.251-12.123Q-14.736-12.123-15.175-12.351Q-15.615-12.580-15.882-12.980Q-16.150-13.381-16.150-13.873L-16.150-13.932Q-16.150-14.400-15.904-14.803Q-15.658-15.205-15.249-15.439Q-14.841-15.674-14.372-15.674Q-13.869-15.674-13.515-15.451Q-13.161-15.228-12.978-14.840Q-12.794-14.451-12.794-13.947L-12.794-13.889Q-12.853-13.674-13.044-13.650M-15.478-14.201L-13.451-14.201Q-13.497-14.611-13.736-14.863Q-13.974-15.115-14.372-15.115Q-14.767-15.115-15.074-14.853Q-15.380-14.592-15.478-14.201M-12.240-12.400L-12.240-12.490Q-12.197-12.697-11.990-12.721L-11.568-12.721L-11.568-15.049L-11.990-15.049Q-12.197-15.072-12.240-15.291L-12.240-15.377Q-12.193-15.588-11.990-15.611L-11.173-15.611Q-10.978-15.588-10.927-15.377L-10.927-15.291L-10.935-15.267Q-10.708-15.447-10.435-15.549Q-10.161-15.650-9.869-15.650Q-9.521-15.650-9.283-15.510Q-9.044-15.369-8.929-15.111Q-8.814-14.853-8.814-14.498L-8.814-12.721L-8.388-12.721Q-8.181-12.697-8.142-12.490L-8.142-12.400Q-8.181-12.185-8.388-12.162L-9.783-12.162Q-9.978-12.185-10.029-12.400L-10.029-12.490Q-9.978-12.701-9.783-12.721L-9.454-12.721L-9.454-14.467Q-9.454-14.775-9.544-14.933Q-9.634-15.092-9.927-15.092Q-10.197-15.092-10.425-14.961Q-10.654-14.830-10.790-14.601Q-10.927-14.373-10.927-14.107L-10.927-12.721L-10.501-12.721Q-10.294-12.697-10.255-12.490L-10.255-12.400Q-10.294-12.185-10.501-12.162L-11.990-12.162Q-12.197-12.185-12.240-12.400M-7.505-13.889Q-7.505-14.369-7.261-14.783Q-7.017-15.197-6.601-15.435Q-6.185-15.674-5.704-15.674Q-5.150-15.674-4.771-15.564Q-4.392-15.455-4.392-15.049Q-4.392-14.881-4.505-14.758Q-4.619-14.635-4.790-14.635Q-4.962-14.635-5.081-14.750Q-5.201-14.865-5.201-15.033L-5.201-15.092Q-5.361-15.115-5.697-15.115Q-6.025-15.115-6.292-14.945Q-6.560-14.775-6.712-14.492Q-6.865-14.209-6.865-13.889Q-6.865-13.568-6.693-13.287Q-6.521-13.006-6.236-12.844Q-5.951-12.682-5.622-12.682Q-5.310-12.682-5.183-12.785Q-5.056-12.889-4.939-13.078Q-4.822-13.267-4.704-13.283L-4.536-13.283Q-4.431-13.271-4.367-13.203Q-4.302-13.135-4.302-13.033Q-4.302-12.986-4.322-12.947Q-4.431-12.654-4.634-12.475Q-4.837-12.295-5.113-12.209Q-5.388-12.123-5.704-12.123Q-6.189-12.123-6.605-12.361Q-7.021-12.600-7.263-13.002Q-7.505-13.404-7.505-13.889M-1.697-12.123Q-2.169-12.123-2.554-12.367Q-2.939-12.611-3.161-13.021Q-3.384-13.432-3.384-13.889Q-3.384-14.232-3.259-14.555Q-3.134-14.877-2.904-15.131Q-2.673-15.385-2.367-15.529Q-2.060-15.674-1.697-15.674Q-1.333-15.674-1.021-15.527Q-0.708-15.381-0.486-15.135Q-0.263-14.889-0.136-14.568Q-0.009-14.248-0.009-13.889Q-0.009-13.432-0.234-13.019Q-0.458-12.607-0.843-12.365Q-1.228-12.123-1.697-12.123M-1.697-12.682Q-1.232-12.682-0.941-13.076Q-0.650-13.471-0.650-13.955Q-0.650-14.248-0.785-14.516Q-0.919-14.783-1.160-14.949Q-1.400-15.115-1.697-15.115Q-2.001-15.115-2.240-14.949Q-2.478-14.783-2.613-14.516Q-2.747-14.248-2.747-13.955Q-2.747-13.475-2.454-13.078Q-2.161-12.682-1.697-12.682M2.292-12.123Q1.827-12.123 1.462-12.373Q1.096-12.623 0.891-13.027Q0.686-13.432 0.686-13.889Q0.686-14.232 0.811-14.553Q0.936-14.873 1.169-15.123Q1.401-15.373 1.706-15.512Q2.010-15.650 2.366-15.650Q2.878-15.650 3.284-15.330L3.284-16.490L2.862-16.490Q2.651-16.514 2.612-16.728L2.612-16.818Q2.651-17.025 2.862-17.049L3.674-17.049Q3.874-17.025 3.924-16.818L3.924-12.721L4.350-12.721Q4.557-12.697 4.596-12.490L4.596-12.400Q4.557-12.185 4.350-12.162L3.534-12.162Q3.335-12.185 3.284-12.400L3.284-12.529Q3.089-12.338 2.827-12.230Q2.565-12.123 2.292-12.123M2.331-12.682Q2.690-12.682 2.942-12.951Q3.194-13.221 3.284-13.596L3.284-14.428Q3.225-14.615 3.098-14.766Q2.971-14.916 2.794-15.004Q2.616-15.092 2.421-15.092Q2.112-15.092 1.862-14.922Q1.612-14.752 1.467-14.467Q1.323-14.182 1.323-13.881Q1.323-13.432 1.608-13.057Q1.893-12.682 2.331-12.682M8.186-13.650L5.745-13.650Q5.799-13.373 5.997-13.150Q6.194-12.928 6.471-12.805Q6.749-12.682 7.034-12.682Q7.506-12.682 7.729-12.971Q7.737-12.982 7.794-13.088Q7.850-13.193 7.899-13.236Q7.948-13.279 8.042-13.291L8.186-13.291Q8.378-13.271 8.436-13.057L8.436-13.002Q8.370-12.701 8.139-12.504Q7.909-12.307 7.596-12.215Q7.284-12.123 6.979-12.123Q6.495-12.123 6.055-12.351Q5.616-12.580 5.348-12.980Q5.081-13.381 5.081-13.873L5.081-13.932Q5.081-14.400 5.327-14.803Q5.573-15.205 5.981-15.439Q6.389-15.674 6.858-15.674Q7.362-15.674 7.715-15.451Q8.069-15.228 8.253-14.840Q8.436-14.451 8.436-13.947L8.436-13.889Q8.378-13.674 8.186-13.650M5.753-14.201L7.780-14.201Q7.733-14.611 7.495-14.863Q7.256-15.115 6.858-15.115Q6.464-15.115 6.157-14.853Q5.850-14.592 5.753-14.201M9.143-12.400L9.143-12.490Q9.202-12.697 9.393-12.721L10.104-12.721L10.104-15.049L9.393-15.049Q9.198-15.072 9.143-15.291L9.143-15.377Q9.202-15.588 9.393-15.611L10.495-15.611Q10.694-15.592 10.745-15.377L10.745-15.049Q11.006-15.334 11.362-15.492Q11.717-15.650 12.104-15.650Q12.397-15.650 12.631-15.516Q12.866-15.381 12.866-15.115Q12.866-14.947 12.756-14.830Q12.647-14.713 12.479-14.713Q12.327-14.713 12.212-14.824Q12.096-14.935 12.096-15.092Q11.721-15.092 11.407-14.891Q11.092-14.689 10.919-14.355Q10.745-14.021 10.745-13.642L10.745-12.721L11.690-12.721Q11.897-12.697 11.936-12.490L11.936-12.400Q11.897-12.185 11.690-12.162L9.393-12.162Q9.202-12.185 9.143-12.400M16.663-14.299L13.921-14.299Q13.796-14.310 13.710-14.396Q13.624-14.482 13.624-14.611Q13.624-14.740 13.710-14.822Q13.796-14.904 13.921-14.916L16.663-14.916Q16.788-14.904 16.870-14.822Q16.952-14.740 16.952-14.611Q16.952-14.482 16.870-14.396Q16.788-14.310 16.663-14.299M19.534-12.123Q19.061-12.123 18.676-12.367Q18.292-12.611 18.069-13.021Q17.846-13.432 17.846-13.889Q17.846-14.232 17.971-14.555Q18.096-14.877 18.327-15.131Q18.557-15.385 18.864-15.529Q19.171-15.674 19.534-15.674Q19.897-15.674 20.210-15.527Q20.522-15.381 20.745-15.135Q20.967-14.889 21.094-14.568Q21.221-14.248 21.221-13.889Q21.221-13.432 20.997-13.019Q20.772-12.607 20.387-12.365Q20.003-12.123 19.534-12.123M19.534-12.682Q19.999-12.682 20.290-13.076Q20.581-13.471 20.581-13.955Q20.581-14.248 20.446-14.516Q20.311-14.783 20.071-14.949Q19.831-15.115 19.534-15.115Q19.229-15.115 18.991-14.949Q18.753-14.783 18.618-14.516Q18.483-14.248 18.483-13.955Q18.483-13.475 18.776-13.078Q19.069-12.682 19.534-12.682M21.729-12.400L21.729-12.490Q21.772-12.697 21.979-12.721L22.401-12.721L22.401-15.049L21.979-15.049Q21.772-15.072 21.729-15.291L21.729-15.377Q21.776-15.588 21.979-15.611L22.796-15.611Q22.991-15.588 23.042-15.377L23.042-15.291L23.034-15.267Q23.260-15.447 23.534-15.549Q23.807-15.650 24.100-15.650Q24.448-15.650 24.686-15.510Q24.924-15.369 25.040-15.111Q25.155-14.853 25.155-14.498L25.155-12.721L25.581-12.721Q25.788-12.697 25.827-12.490L25.827-12.400Q25.788-12.185 25.581-12.162L24.186-12.162Q23.991-12.185 23.940-12.400L23.940-12.490Q23.991-12.701 24.186-12.721L24.514-12.721L24.514-14.467Q24.514-14.775 24.424-14.933Q24.335-15.092 24.042-15.092Q23.772-15.092 23.544-14.961Q23.315-14.830 23.178-14.601Q23.042-14.373 23.042-14.107L23.042-12.721L23.467-12.721Q23.674-12.697 23.714-12.490L23.714-12.400Q23.674-12.185 23.467-12.162L21.979-12.162Q21.772-12.185 21.729-12.400M26.354-12.400L26.354-12.490Q26.405-12.697 26.600-12.721L27.706-12.721L27.706-16.490L26.600-16.490Q26.405-16.514 26.354-16.728L26.354-16.818Q26.405-17.025 26.600-17.049L28.096-17.049Q28.288-17.025 28.346-16.818L28.346-12.721L29.448-12.721Q29.647-12.697 29.698-12.490L29.698-12.400Q29.647-12.185 29.448-12.162L26.600-12.162Q26.405-12.185 26.354-12.400M30.495-11.041Q30.495-11.150 30.546-11.242Q30.596-11.334 30.688-11.385Q30.780-11.435 30.885-11.435Q30.995-11.435 31.087-11.385Q31.178-11.334 31.229-11.242Q31.280-11.150 31.280-11.041L31.135-11.041Q31.135-10.904 31.159-10.904Q31.417-10.904 31.604-11.096Q31.792-11.287 31.878-11.553L32.089-12.162L30.952-15.049L30.624-15.049Q30.428-15.072 30.374-15.291L30.374-15.377Q30.432-15.588 30.624-15.611L31.784-15.611Q31.979-15.588 32.030-15.377L32.030-15.291Q31.979-15.072 31.784-15.049L31.518-15.049Q31.854-14.201 32.098-13.547Q32.342-12.892 32.342-12.803L32.350-12.803Q32.350-12.861 32.442-13.154Q32.534-13.447 32.727-14.031Q32.921-14.615 33.061-15.049L32.784-15.049Q32.573-15.072 32.534-15.291L32.534-15.377Q32.585-15.592 32.784-15.611L33.936-15.611Q34.143-15.588 34.182-15.377L34.182-15.291Q34.143-15.072 33.936-15.049L33.616-15.049L32.440-11.553Q32.272-11.053 31.946-10.699Q31.620-10.346 31.159-10.346Q30.885-10.346 30.690-10.557Q30.495-10.767 30.495-11.041\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(-39.047 58.85)\">\u003Cpath d=\"M-13.832-11.601Q-14.297-11.871-14.647-12.299Q-14.997-12.726-15.182-13.245Q-15.367-13.765-15.367-14.305Q-15.367-14.845-15.184-15.360Q-15.001-15.874-14.654-16.294Q-14.307-16.715-13.839-16.998Q-13.777-17.019-13.750-17.019L-13.671-17.019Q-13.586-17.009-13.528-16.951Q-13.470-16.892-13.470-16.804Q-13.470-16.677-13.558-16.622Q-13.952-16.370-14.237-16.006Q-14.522-15.641-14.664-15.211Q-14.806-14.780-14.806-14.305Q-14.806-13.950-14.722-13.611Q-14.639-13.273-14.483-12.979Q-14.327-12.685-14.100-12.437Q-13.873-12.189-13.569-11.988Q-13.470-11.919-13.470-11.800Q-13.470-11.714-13.528-11.653Q-13.586-11.591-13.671-11.581L-13.750-11.581Q-13.801-11.581-13.832-11.601M-12.694-12.370L-12.694-12.449Q-12.660-12.630-12.478-12.651L-12.225-12.651L-12.225-15.949L-12.478-15.949Q-12.660-15.970-12.694-16.158L-12.694-16.236Q-12.660-16.417-12.478-16.438L-10.763-16.438Q-10.527-16.438-10.316-16.354Q-10.106-16.270-9.939-16.122Q-9.771-15.973-9.676-15.773Q-9.580-15.573-9.580-15.341Q-9.580-15.019-9.790-14.766Q-10-14.514-10.322-14.401Q-10.076-14.346-9.872-14.194Q-9.669-14.042-9.551-13.818Q-9.433-13.594-9.433-13.345Q-9.433-13.030-9.592-12.758Q-9.751-12.487-10.026-12.324Q-10.301-12.162-10.616-12.162L-12.478-12.162Q-12.660-12.183-12.694-12.370M-11.665-14.144L-11.665-12.651L-10.763-12.651Q-10.564-12.651-10.387-12.741Q-10.209-12.832-10.099-12.989Q-9.990-13.146-9.990-13.345Q-9.990-13.546-10.079-13.729Q-10.168-13.912-10.327-14.028Q-10.486-14.144-10.684-14.144L-11.665-14.144M-11.665-15.949L-11.665-14.633L-10.910-14.633Q-10.609-14.633-10.373-14.838Q-10.137-15.043-10.137-15.341Q-10.137-15.505-10.223-15.645Q-10.308-15.785-10.453-15.867Q-10.598-15.949-10.763-15.949L-11.665-15.949M-8.965-12.370L-8.965-12.449Q-8.931-12.630-8.746-12.651L-8.476-12.651L-8.476-15.949L-8.746-15.949Q-8.931-15.970-8.965-16.158L-8.965-16.236Q-8.931-16.417-8.746-16.438L-5.940-16.438Q-5.769-16.417-5.724-16.236L-5.724-15.501Q-5.769-15.313-5.940-15.289L-6.066-15.289Q-6.237-15.313-6.285-15.501L-6.285-15.949L-7.915-15.949L-7.915-14.620L-7.061-14.620L-7.061-14.808Q-7.016-14.989-6.842-15.013L-6.716-15.013Q-6.545-14.989-6.500-14.808L-6.500-13.946Q-6.545-13.758-6.716-13.738L-6.842-13.738Q-7.016-13.758-7.061-13.946L-7.061-14.127L-7.915-14.127L-7.915-12.651L-6.128-12.651L-6.128-13.211Q-6.083-13.392-5.912-13.416L-5.786-13.416Q-5.615-13.392-5.571-13.211L-5.571-12.370Q-5.615-12.179-5.786-12.162L-8.746-12.162Q-8.931-12.183-8.965-12.370M-4.033-12.162L-5.068-12.162Q-5.239-12.183-5.284-12.370L-5.284-12.449Q-5.239-12.630-5.068-12.651L-4.829-12.651L-4.829-15.949L-5.068-15.949Q-5.239-15.970-5.284-16.158L-5.284-16.236Q-5.239-16.417-5.068-16.438L-3.694-16.438Q-3.356-16.438-3.045-16.289Q-2.734-16.141-2.539-15.869Q-2.344-15.597-2.344-15.248Q-2.344-15.050-2.416-14.867Q-2.488-14.684-2.612-14.537Q-2.737-14.391-2.905-14.285Q-2.734-14.151-2.633-13.962Q-2.532-13.772-2.532-13.563L-2.532-13.058Q-2.532-12.582-2.358-12.582Q-2.317-12.582-2.295-12.695Q-2.272-12.808-2.272-12.897Q-2.228-13.078-2.057-13.099L-1.931-13.099Q-1.760-13.081-1.715-12.897L-1.715-12.849Q-1.715-12.558-1.895-12.326Q-2.074-12.094-2.351-12.094Q-2.713-12.094-2.903-12.362Q-3.093-12.630-3.093-13.010L-3.093-13.512Q-3.093-13.765-3.275-13.912Q-3.458-14.059-3.708-14.059L-4.268-14.059L-4.268-12.651L-4.033-12.651Q-3.858-12.630-3.814-12.449L-3.814-12.370Q-3.858-12.183-4.033-12.162M-4.268-15.949L-4.268-14.548L-3.766-14.548Q-3.561-14.548-3.363-14.631Q-3.164-14.715-3.035-14.876Q-2.905-15.037-2.905-15.248Q-2.905-15.460-3.035-15.621Q-3.164-15.782-3.361-15.865Q-3.557-15.949-3.766-15.949L-4.268-15.949M-0.765-12.370L-0.765-12.449Q-0.714-12.630-0.546-12.651L-0.119-12.651L-0.119-15.949L-0.946-15.949L-0.946-15.501Q-0.987-15.313-1.161-15.289L-1.288-15.289Q-1.462-15.313-1.507-15.501L-1.507-16.236Q-1.462-16.417-1.288-16.438L1.611-16.438Q1.781-16.421 1.826-16.236L1.826-15.501Q1.785-15.313 1.611-15.289L1.484-15.289Q1.310-15.313 1.265-15.501L1.265-15.949L0.442-15.949L0.442-12.651L0.869-12.651Q1.040-12.630 1.084-12.449L1.084-12.370Q1.040-12.183 0.869-12.162L-0.546-12.162Q-0.714-12.183-0.765-12.370M3.525-11.188Q3.425-11.188 3.347-11.266Q3.268-11.345 3.268-11.441Q3.268-11.595 3.436-11.660Q3.627-11.704 3.777-11.842Q3.928-11.981 3.986-12.176Q3.965-12.176 3.938-12.162L3.883-12.162Q3.682-12.162 3.537-12.304Q3.391-12.446 3.391-12.651Q3.391-12.856 3.535-12.996Q3.678-13.136 3.883-13.136Q4.068-13.136 4.212-13.030Q4.355-12.924 4.434-12.755Q4.512-12.586 4.512-12.401Q4.512-11.984 4.251-11.644Q3.989-11.304 3.583-11.195Q3.562-11.188 3.525-11.188\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-39.047 58.85)\">\u003Cpath d=\"M10.124-12.370L10.124-15.949L9.755-15.949Q9.574-15.970 9.537-16.158L9.537-16.236Q9.574-16.417 9.755-16.438L10.470-16.438Q10.641-16.417 10.685-16.236L10.685-14.913Q10.870-15.060 11.100-15.137Q11.331-15.214 11.567-15.214Q11.864-15.214 12.124-15.088Q12.384-14.961 12.572-14.741Q12.760-14.520 12.860-14.247Q12.961-13.974 12.961-13.673Q12.961-13.266 12.763-12.907Q12.565-12.548 12.226-12.338Q11.888-12.128 11.478-12.128Q11.023-12.128 10.685-12.449L10.685-12.370Q10.641-12.179 10.470-12.162L10.343-12.162Q10.176-12.183 10.124-12.370M11.440-12.617Q11.710-12.617 11.929-12.765Q12.148-12.914 12.274-13.160Q12.401-13.406 12.401-13.673Q12.401-13.926 12.291-14.170Q12.182-14.414 11.979-14.570Q11.775-14.725 11.512-14.725Q11.232-14.725 11.003-14.563Q10.774-14.401 10.685-14.138L10.685-13.392Q10.764-13.071 10.957-12.844Q11.150-12.617 11.440-12.617M13.730-12.370L13.730-12.449Q13.775-12.630 13.946-12.651L14.855-12.651L14.855-14.688L14.004-14.688Q13.829-14.708 13.785-14.900L13.785-14.975Q13.829-15.160 14.004-15.180L15.200-15.180Q15.371-15.163 15.415-14.975L15.415-12.651L16.215-12.651Q16.386-12.630 16.431-12.449L16.431-12.370Q16.386-12.183 16.215-12.162L13.946-12.162Q13.775-12.183 13.730-12.370M14.633-16.035L14.633-16.082Q14.633-16.233 14.752-16.339Q14.872-16.445 15.026-16.445Q15.176-16.445 15.296-16.339Q15.415-16.233 15.415-16.082L15.415-16.035Q15.415-15.881 15.296-15.775Q15.176-15.669 15.026-15.669Q14.872-15.669 14.752-15.775Q14.633-15.881 14.633-16.035M18.536-12.128Q18.129-12.128 17.810-12.347Q17.490-12.565 17.311-12.919Q17.131-13.273 17.131-13.673Q17.131-13.974 17.241-14.254Q17.350-14.534 17.553-14.753Q17.757-14.972 18.023-15.093Q18.290-15.214 18.601-15.214Q19.049-15.214 19.404-14.934L19.404-15.949L19.035-15.949Q18.850-15.970 18.816-16.158L18.816-16.236Q18.850-16.417 19.035-16.438L19.746-16.438Q19.920-16.417 19.965-16.236L19.965-12.651L20.337-12.651Q20.518-12.630 20.553-12.449L20.553-12.370Q20.518-12.183 20.337-12.162L19.623-12.162Q19.449-12.183 19.404-12.370L19.404-12.483Q19.233-12.316 19.004-12.222Q18.775-12.128 18.536-12.128M18.570-12.617Q18.885-12.617 19.105-12.852Q19.326-13.088 19.404-13.416L19.404-14.144Q19.353-14.308 19.242-14.440Q19.131-14.572 18.975-14.649Q18.820-14.725 18.649-14.725Q18.379-14.725 18.160-14.577Q17.941-14.428 17.815-14.179Q17.688-13.929 17.688-13.666Q17.688-13.273 17.938-12.945Q18.187-12.617 18.570-12.617M21.161-12.370L21.161-12.449Q21.205-12.630 21.376-12.651L22.286-12.651L22.286-14.688L21.434-14.688Q21.260-14.708 21.216-14.900L21.216-14.975Q21.260-15.160 21.434-15.180L22.631-15.180Q22.802-15.163 22.846-14.975L22.846-12.651L23.646-12.651Q23.817-12.630 23.861-12.449L23.861-12.370Q23.817-12.183 23.646-12.162L21.376-12.162Q21.205-12.183 21.161-12.370M22.063-16.035L22.063-16.082Q22.063-16.233 22.183-16.339Q22.303-16.445 22.456-16.445Q22.607-16.445 22.726-16.339Q22.846-16.233 22.846-16.082L22.846-16.035Q22.846-15.881 22.726-15.775Q22.607-15.669 22.456-15.669Q22.303-15.669 22.183-15.775Q22.063-15.881 22.063-16.035M24.531-12.370L24.531-12.449Q24.582-12.630 24.750-12.651L25.372-12.651L25.372-14.688L24.750-14.688Q24.579-14.708 24.531-14.900L24.531-14.975Q24.582-15.160 24.750-15.180L25.714-15.180Q25.888-15.163 25.933-14.975L25.933-14.688Q26.162-14.937 26.473-15.076Q26.784-15.214 27.122-15.214Q27.378-15.214 27.583-15.096Q27.788-14.978 27.788-14.746Q27.788-14.599 27.693-14.496Q27.597-14.394 27.450-14.394Q27.317-14.394 27.216-14.491Q27.115-14.589 27.115-14.725Q26.787-14.725 26.512-14.549Q26.237-14.373 26.085-14.081Q25.933-13.789 25.933-13.457L25.933-12.651L26.760-12.651Q26.941-12.630 26.975-12.449L26.975-12.370Q26.941-12.183 26.760-12.162L24.750-12.162Q24.582-12.183 24.531-12.370M31.124-13.464L28.988-13.464Q29.036-13.222 29.209-13.027Q29.381-12.832 29.624-12.724Q29.867-12.617 30.116-12.617Q30.530-12.617 30.725-12.870Q30.731-12.880 30.781-12.972Q30.830-13.064 30.873-13.102Q30.916-13.140 30.998-13.150L31.124-13.150Q31.292-13.133 31.343-12.945L31.343-12.897Q31.285-12.634 31.083-12.461Q30.882-12.288 30.608-12.208Q30.335-12.128 30.068-12.128Q29.644-12.128 29.260-12.328Q28.875-12.528 28.641-12.878Q28.407-13.228 28.407-13.659L28.407-13.710Q28.407-14.120 28.622-14.473Q28.838-14.825 29.195-15.030Q29.552-15.235 29.962-15.235Q30.403-15.235 30.713-15.040Q31.022-14.845 31.183-14.505Q31.343-14.165 31.343-13.724L31.343-13.673Q31.292-13.485 31.124-13.464M28.995-13.946L30.769-13.946Q30.728-14.305 30.519-14.526Q30.311-14.746 29.962-14.746Q29.617-14.746 29.349-14.517Q29.080-14.288 28.995-13.946M32.256-13.673Q32.256-14.093 32.469-14.455Q32.683-14.818 33.047-15.026Q33.411-15.235 33.831-15.235Q34.317-15.235 34.648-15.139Q34.980-15.043 34.980-14.688Q34.980-14.541 34.881-14.433Q34.782-14.326 34.631-14.326Q34.481-14.326 34.377-14.426Q34.272-14.527 34.272-14.674L34.272-14.725Q34.132-14.746 33.838-14.746Q33.551-14.746 33.317-14.597Q33.083-14.449 32.950-14.201Q32.816-13.953 32.816-13.673Q32.816-13.392 32.967-13.146Q33.117-12.900 33.367-12.758Q33.616-12.617 33.903-12.617Q34.177-12.617 34.288-12.707Q34.399-12.798 34.501-12.964Q34.604-13.129 34.706-13.143L34.853-13.143Q34.946-13.133 35.002-13.073Q35.058-13.013 35.058-12.924Q35.058-12.883 35.041-12.849Q34.946-12.593 34.768-12.435Q34.590-12.278 34.349-12.203Q34.108-12.128 33.831-12.128Q33.408-12.128 33.044-12.336Q32.680-12.545 32.468-12.897Q32.256-13.249 32.256-13.673M36.532-13.129L36.532-14.688L35.875-14.688Q35.701-14.708 35.657-14.900L35.657-14.975Q35.701-15.160 35.875-15.180L36.532-15.180L36.532-15.836Q36.576-16.017 36.750-16.041L36.877-16.041Q37.048-16.017 37.092-15.836L37.092-15.180L38.282-15.180Q38.449-15.163 38.500-14.975L38.500-14.900Q38.453-14.708 38.282-14.688L37.092-14.688L37.092-13.157Q37.092-12.617 37.595-12.617Q37.813-12.617 37.957-12.779Q38.100-12.941 38.100-13.157Q38.100-13.239 38.164-13.300Q38.227-13.362 38.316-13.372L38.442-13.372Q38.617-13.351 38.661-13.170L38.661-13.129Q38.661-12.846 38.500-12.615Q38.340-12.384 38.083-12.256Q37.827-12.128 37.547-12.128Q37.099-12.128 36.815-12.400Q36.532-12.671 36.532-13.129M39.738-12.370L39.738-12.449Q39.782-12.630 39.953-12.651L40.862-12.651L40.862-14.688L40.011-14.688Q39.837-14.708 39.792-14.900L39.792-14.975Q39.837-15.160 40.011-15.180L41.207-15.180Q41.378-15.163 41.423-14.975L41.423-12.651L42.223-12.651Q42.393-12.630 42.438-12.449L42.438-12.370Q42.393-12.183 42.223-12.162L39.953-12.162Q39.782-12.183 39.738-12.370M40.640-16.035L40.640-16.082Q40.640-16.233 40.760-16.339Q40.879-16.445 41.033-16.445Q41.183-16.445 41.303-16.339Q41.423-16.233 41.423-16.082L41.423-16.035Q41.423-15.881 41.303-15.775Q41.183-15.669 41.033-15.669Q40.879-15.669 40.760-15.775Q40.640-15.881 40.640-16.035M44.769-12.128Q44.355-12.128 44.019-12.341Q43.682-12.555 43.487-12.914Q43.292-13.273 43.292-13.673Q43.292-13.974 43.402-14.256Q43.511-14.537 43.713-14.760Q43.914-14.982 44.183-15.108Q44.451-15.235 44.769-15.235Q45.087-15.235 45.360-15.107Q45.634-14.978 45.829-14.763Q46.023-14.548 46.134-14.267Q46.246-13.987 46.246-13.673Q46.246-13.273 46.049-12.912Q45.852-12.552 45.516-12.340Q45.179-12.128 44.769-12.128M44.769-12.617Q45.176-12.617 45.430-12.962Q45.685-13.307 45.685-13.731Q45.685-13.987 45.567-14.221Q45.449-14.455 45.239-14.601Q45.029-14.746 44.769-14.746Q44.502-14.746 44.294-14.601Q44.085-14.455 43.967-14.221Q43.850-13.987 43.850-13.731Q43.850-13.310 44.106-12.964Q44.362-12.617 44.769-12.617M46.690-12.370L46.690-12.449Q46.727-12.630 46.909-12.651L47.278-12.651L47.278-14.688L46.909-14.688Q46.727-14.708 46.690-14.900L46.690-14.975Q46.731-15.160 46.909-15.180L47.623-15.180Q47.794-15.160 47.838-14.975L47.838-14.900L47.831-14.879Q48.030-15.037 48.269-15.125Q48.508-15.214 48.765-15.214Q49.069-15.214 49.277-15.091Q49.486-14.968 49.587-14.743Q49.687-14.517 49.687-14.206L49.687-12.651L50.060-12.651Q50.241-12.630 50.275-12.449L50.275-12.370Q50.241-12.183 50.060-12.162L48.840-12.162Q48.669-12.183 48.624-12.370L48.624-12.449Q48.669-12.634 48.840-12.651L49.127-12.651L49.127-14.179Q49.127-14.449 49.048-14.587Q48.970-14.725 48.713-14.725Q48.477-14.725 48.277-14.611Q48.078-14.496 47.958-14.297Q47.838-14.097 47.838-13.864L47.838-12.651L48.211-12.651Q48.392-12.630 48.426-12.449L48.426-12.370Q48.392-12.183 48.211-12.162L46.909-12.162Q46.727-12.183 46.690-12.370M50.699-13.136Q50.699-13.526 51.061-13.751Q51.424-13.977 51.897-14.064Q52.371-14.151 52.815-14.158Q52.815-14.346 52.697-14.479Q52.579-14.613 52.398-14.679Q52.217-14.746 52.032-14.746Q51.731-14.746 51.591-14.725L51.591-14.674Q51.591-14.527 51.487-14.426Q51.383-14.326 51.239-14.326Q51.085-14.326 50.985-14.433Q50.884-14.541 50.884-14.688Q50.884-15.043 51.217-15.139Q51.550-15.235 52.039-15.235Q52.275-15.235 52.509-15.166Q52.743-15.098 52.940-14.966Q53.136-14.835 53.256-14.642Q53.375-14.449 53.375-14.206L53.375-12.702Q53.375-12.651 53.837-12.651Q54.008-12.634 54.052-12.449L54.052-12.370Q54.008-12.183 53.837-12.162L53.710-12.162Q53.410-12.162 53.210-12.203Q53.010-12.244 52.883-12.408Q52.480-12.128 51.861-12.128Q51.567-12.128 51.301-12.251Q51.034-12.374 50.867-12.603Q50.699-12.832 50.699-13.136M51.260-13.129Q51.260-12.890 51.472-12.753Q51.683-12.617 51.933-12.617Q52.124-12.617 52.328-12.668Q52.531-12.719 52.673-12.840Q52.815-12.962 52.815-13.157L52.815-13.673Q52.569-13.673 52.205-13.623Q51.841-13.574 51.550-13.452Q51.260-13.331 51.260-13.129M54.452-12.370L54.452-12.449Q54.496-12.630 54.667-12.651L55.635-12.651L55.635-15.949L54.667-15.949Q54.496-15.970 54.452-16.158L54.452-16.236Q54.496-16.417 54.667-16.438L55.976-16.438Q56.144-16.417 56.195-16.236L56.195-12.651L57.159-12.651Q57.333-12.630 57.378-12.449L57.378-12.370Q57.333-12.183 57.159-12.162L54.667-12.162Q54.496-12.183 54.452-12.370M58.683-11.581L58.608-11.581Q58.516-11.591 58.456-11.654Q58.396-11.718 58.396-11.800Q58.396-11.923 58.489-11.981Q58.783-12.169 59.018-12.422Q59.254-12.675 59.415-12.979Q59.576-13.283 59.654-13.615Q59.733-13.946 59.733-14.305Q59.733-14.777 59.589-15.207Q59.446-15.638 59.167-16Q58.889-16.363 58.502-16.616Q58.396-16.687 58.396-16.804Q58.396-16.889 58.456-16.949Q58.516-17.009 58.608-17.019L58.683-17.019Q58.731-17.019 58.762-16.998Q59.100-16.804 59.398-16.499Q59.695-16.195 59.888-15.850Q60.081-15.505 60.187-15.115Q60.293-14.725 60.293-14.305Q60.293-13.881 60.187-13.486Q60.081-13.092 59.885-12.745Q59.688-12.398 59.405-12.106Q59.121-11.813 58.769-11.601Q58.707-11.581 58.683-11.581\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(91.274 22.056)\">\u003Cpath d=\"M-15.507-13.129L-15.507-14.688L-16.163-14.688Q-16.337-14.708-16.382-14.900L-16.382-14.975Q-16.337-15.160-16.163-15.180L-15.507-15.180L-15.507-15.836Q-15.462-16.017-15.288-16.041L-15.161-16.041Q-14.991-16.017-14.946-15.836L-14.946-15.180L-13.757-15.180Q-13.589-15.163-13.538-14.975L-13.538-14.900Q-13.586-14.708-13.757-14.688L-14.946-14.688L-14.946-13.157Q-14.946-12.617-14.444-12.617Q-14.225-12.617-14.081-12.779Q-13.938-12.941-13.938-13.157Q-13.938-13.239-13.875-13.300Q-13.811-13.362-13.723-13.372L-13.596-13.372Q-13.422-13.351-13.377-13.170L-13.377-13.129Q-13.377-12.846-13.538-12.615Q-13.699-12.384-13.955-12.256Q-14.211-12.128-14.492-12.128Q-14.939-12.128-15.223-12.400Q-15.507-12.671-15.507-13.129M-10.985-12.128Q-11.398-12.128-11.735-12.341Q-12.072-12.555-12.266-12.914Q-12.461-13.273-12.461-13.673Q-12.461-13.974-12.352-14.256Q-12.243-14.537-12.041-14.760Q-11.839-14.982-11.571-15.108Q-11.303-15.235-10.985-15.235Q-10.667-15.235-10.393-15.107Q-10.120-14.978-9.925-14.763Q-9.730-14.548-9.619-14.267Q-9.508-13.987-9.508-13.673Q-9.508-13.273-9.705-12.912Q-9.901-12.552-10.238-12.340Q-10.575-12.128-10.985-12.128M-10.985-12.617Q-10.578-12.617-10.323-12.962Q-10.069-13.307-10.069-13.731Q-10.069-13.987-10.187-14.221Q-10.305-14.455-10.515-14.601Q-10.725-14.746-10.985-14.746Q-11.251-14.746-11.460-14.601Q-11.668-14.455-11.786-14.221Q-11.904-13.987-11.904-13.731Q-11.904-13.310-11.648-12.964Q-11.391-12.617-10.985-12.617M-8.999-12.370L-8.999-12.449Q-8.954-12.630-8.784-12.651L-8.377-12.651L-8.377-15.949L-8.784-15.949Q-8.954-15.970-8.999-16.158L-8.999-16.236Q-8.954-16.417-8.784-16.438L-8.131-16.438Q-7.960-16.421-7.915-16.236L-7.915-13.765L-6.914-14.688L-7.174-14.688Q-7.355-14.708-7.389-14.900L-7.389-14.975Q-7.355-15.160-7.174-15.180L-5.906-15.180Q-5.728-15.160-5.687-14.975L-5.687-14.900Q-5.724-14.708-5.906-14.688L-6.227-14.688L-7.054-13.933L-6.046-12.651L-5.752-12.651Q-5.571-12.630-5.533-12.449L-5.533-12.370Q-5.571-12.183-5.752-12.162L-6.774-12.162Q-6.945-12.183-6.989-12.370L-6.989-12.449Q-6.945-12.630-6.774-12.651L-6.634-12.651L-7.389-13.618L-7.915-13.136L-7.915-12.651L-7.509-12.651Q-7.341-12.630-7.290-12.449L-7.290-12.370Q-7.341-12.183-7.509-12.162L-8.784-12.162Q-8.954-12.183-8.999-12.370M-2.337-13.464L-4.473-13.464Q-4.426-13.222-4.253-13.027Q-4.080-12.832-3.838-12.724Q-3.595-12.617-3.346-12.617Q-2.932-12.617-2.737-12.870Q-2.730-12.880-2.681-12.972Q-2.631-13.064-2.588-13.102Q-2.546-13.140-2.464-13.150L-2.337-13.150Q-2.170-13.133-2.119-12.945L-2.119-12.897Q-2.177-12.634-2.378-12.461Q-2.580-12.288-2.853-12.208Q-3.127-12.128-3.393-12.128Q-3.817-12.128-4.202-12.328Q-4.586-12.528-4.820-12.878Q-5.055-13.228-5.055-13.659L-5.055-13.710Q-5.055-14.120-4.839-14.473Q-4.624-14.825-4.267-15.030Q-3.910-15.235-3.499-15.235Q-3.058-15.235-2.749-15.040Q-2.440-14.845-2.279-14.505Q-2.119-14.165-2.119-13.724L-2.119-13.673Q-2.170-13.485-2.337-13.464M-4.467-13.946L-2.693-13.946Q-2.734-14.305-2.942-14.526Q-3.151-14.746-3.499-14.746Q-3.845-14.746-4.113-14.517Q-4.381-14.288-4.467-13.946M-1.633-12.370L-1.633-12.449Q-1.596-12.630-1.414-12.651L-1.045-12.651L-1.045-14.688L-1.414-14.688Q-1.596-14.708-1.633-14.900L-1.633-14.975Q-1.592-15.160-1.414-15.180L-0.700-15.180Q-0.529-15.160-0.485-14.975L-0.485-14.900L-0.492-14.879Q-0.293-15.037-0.054-15.125Q0.185-15.214 0.442-15.214Q0.746-15.214 0.954-15.091Q1.163-14.968 1.264-14.743Q1.364-14.517 1.364-14.206L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L0.517-12.162Q0.346-12.183 0.301-12.370L0.301-12.449Q0.346-12.634 0.517-12.651L0.804-12.651L0.804-14.179Q0.804-14.449 0.725-14.587Q0.647-14.725 0.390-14.725Q0.154-14.725-0.046-14.611Q-0.245-14.496-0.365-14.297Q-0.485-14.097-0.485-13.864L-0.485-12.651L-0.112-12.651Q0.069-12.630 0.103-12.449L0.103-12.370Q0.069-12.183-0.112-12.162L-1.414-12.162Q-1.596-12.183-1.633-12.370M2.533-12.336L2.533-13.136Q2.557-13.317 2.742-13.338L2.889-13.338Q3.032-13.317 3.084-13.177Q3.261-12.617 3.897-12.617Q4.078-12.617 4.278-12.647Q4.478-12.678 4.625-12.779Q4.772-12.880 4.772-13.058Q4.772-13.242 4.577-13.341Q4.382-13.440 4.143-13.478L3.531-13.577Q2.533-13.762 2.533-14.394Q2.533-14.647 2.660-14.813Q2.786-14.978 2.996-15.072Q3.207-15.166 3.431-15.201Q3.654-15.235 3.897-15.235Q4.116-15.235 4.285-15.209Q4.454-15.183 4.598-15.115Q4.666-15.218 4.779-15.235L4.847-15.235Q4.933-15.225 4.987-15.170Q5.042-15.115 5.052-15.033L5.052-14.414Q5.042-14.332 4.987-14.274Q4.933-14.216 4.847-14.206L4.700-14.206Q4.618-14.216 4.560-14.274Q4.502-14.332 4.492-14.414Q4.492-14.746 3.883-14.746Q3.579-14.746 3.301-14.674Q3.022-14.602 3.022-14.387Q3.022-14.155 3.610-14.059L4.225-13.953Q4.649-13.881 4.955-13.664Q5.261-13.447 5.261-13.058Q5.261-12.716 5.054-12.504Q4.847-12.292 4.541-12.210Q4.236-12.128 3.897-12.128Q3.391-12.128 3.043-12.350Q2.981-12.241 2.938-12.191Q2.896-12.141 2.803-12.128L2.742-12.128Q2.554-12.148 2.533-12.336\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-warn)\">\u003Cpath fill=\"none\" d=\"M57.421-9.316h56.905v-17.072H57.421Z\"\u002F>\u003Cg transform=\"translate(89.414 -3.552)\">\u003Cpath d=\"M-14.926-12.128Q-15.332-12.128-15.652-12.347Q-15.972-12.565-16.151-12.919Q-16.330-13.273-16.330-13.673Q-16.330-13.974-16.221-14.254Q-16.112-14.534-15.908-14.753Q-15.705-14.972-15.438-15.093Q-15.172-15.214-14.861-15.214Q-14.413-15.214-14.057-14.934L-14.057-15.949L-14.427-15.949Q-14.611-15.970-14.645-16.158L-14.645-16.236Q-14.611-16.417-14.427-16.438L-13.716-16.438Q-13.541-16.417-13.497-16.236L-13.497-12.651L-13.124-12.651Q-12.943-12.630-12.909-12.449L-12.909-12.370Q-12.943-12.183-13.124-12.162L-13.839-12.162Q-14.013-12.183-14.057-12.370L-14.057-12.483Q-14.228-12.316-14.457-12.222Q-14.686-12.128-14.926-12.128M-14.891-12.617Q-14.577-12.617-14.357-12.852Q-14.136-13.088-14.057-13.416L-14.057-14.144Q-14.109-14.308-14.220-14.440Q-14.331-14.572-14.486-14.649Q-14.642-14.725-14.813-14.725Q-15.083-14.725-15.302-14.577Q-15.520-14.428-15.647-14.179Q-15.773-13.929-15.773-13.666Q-15.773-13.273-15.524-12.945Q-15.274-12.617-14.891-12.617M-9.768-13.464L-11.904-13.464Q-11.856-13.222-11.684-13.027Q-11.511-12.832-11.268-12.724Q-11.026-12.617-10.776-12.617Q-10.363-12.617-10.168-12.870Q-10.161-12.880-10.111-12.972Q-10.062-13.064-10.019-13.102Q-9.976-13.140-9.894-13.150L-9.768-13.150Q-9.600-13.133-9.549-12.945L-9.549-12.897Q-9.607-12.634-9.809-12.461Q-10.011-12.288-10.284-12.208Q-10.557-12.128-10.824-12.128Q-11.248-12.128-11.632-12.328Q-12.017-12.528-12.251-12.878Q-12.485-13.228-12.485-13.659L-12.485-13.710Q-12.485-14.120-12.270-14.473Q-12.055-14.825-11.697-15.030Q-11.340-15.235-10.930-15.235Q-10.489-15.235-10.180-15.040Q-9.870-14.845-9.710-14.505Q-9.549-14.165-9.549-13.724L-9.549-13.673Q-9.600-13.485-9.768-13.464M-11.897-13.946L-10.123-13.946Q-10.164-14.305-10.373-14.526Q-10.581-14.746-10.930-14.746Q-11.275-14.746-11.544-14.517Q-11.812-14.288-11.897-13.946M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-warn)\" stroke=\"var(--tk-warn)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-warn)\">\u003Cpath fill=\"none\" d=\"M57.421-34.924h56.905v-17.072H57.421Z\"\u002F>\u003Cg transform=\"translate(89.414 -29.16)\">\u003Cpath d=\"M-14.926-12.128Q-15.332-12.128-15.652-12.347Q-15.972-12.565-16.151-12.919Q-16.330-13.273-16.330-13.673Q-16.330-13.974-16.221-14.254Q-16.112-14.534-15.908-14.753Q-15.705-14.972-15.438-15.093Q-15.172-15.214-14.861-15.214Q-14.413-15.214-14.057-14.934L-14.057-15.949L-14.427-15.949Q-14.611-15.970-14.645-16.158L-14.645-16.236Q-14.611-16.417-14.427-16.438L-13.716-16.438Q-13.541-16.417-13.497-16.236L-13.497-12.651L-13.124-12.651Q-12.943-12.630-12.909-12.449L-12.909-12.370Q-12.943-12.183-13.124-12.162L-13.839-12.162Q-14.013-12.183-14.057-12.370L-14.057-12.483Q-14.228-12.316-14.457-12.222Q-14.686-12.128-14.926-12.128M-14.891-12.617Q-14.577-12.617-14.357-12.852Q-14.136-13.088-14.057-13.416L-14.057-14.144Q-14.109-14.308-14.220-14.440Q-14.331-14.572-14.486-14.649Q-14.642-14.725-14.813-14.725Q-15.083-14.725-15.302-14.577Q-15.520-14.428-15.647-14.179Q-15.773-13.929-15.773-13.666Q-15.773-13.273-15.524-12.945Q-15.274-12.617-14.891-12.617M-9.768-13.464L-11.904-13.464Q-11.856-13.222-11.684-13.027Q-11.511-12.832-11.268-12.724Q-11.026-12.617-10.776-12.617Q-10.363-12.617-10.168-12.870Q-10.161-12.880-10.111-12.972Q-10.062-13.064-10.019-13.102Q-9.976-13.140-9.894-13.150L-9.768-13.150Q-9.600-13.133-9.549-12.945L-9.549-12.897Q-9.607-12.634-9.809-12.461Q-10.011-12.288-10.284-12.208Q-10.557-12.128-10.824-12.128Q-11.248-12.128-11.632-12.328Q-12.017-12.528-12.251-12.878Q-12.485-13.228-12.485-13.659L-12.485-13.710Q-12.485-14.120-12.270-14.473Q-12.055-14.825-11.697-15.030Q-11.340-15.235-10.930-15.235Q-10.489-15.235-10.180-15.040Q-9.870-14.845-9.710-14.505Q-9.549-14.165-9.549-13.724L-9.549-13.673Q-9.600-13.485-9.768-13.464M-11.897-13.946L-10.123-13.946Q-10.164-14.305-10.373-14.526Q-10.581-14.746-10.930-14.746Q-11.275-14.746-11.544-14.517Q-11.812-14.288-11.897-13.946M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-warn)\" stroke=\"var(--tk-warn)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(83.836 -51.921)\">\u003Cpath d=\"M-16.494-12.370L-16.494-12.449Q-16.457-12.630-16.276-12.651L-15.907-12.651L-15.907-14.688L-16.276-14.688Q-16.457-14.708-16.494-14.900L-16.494-14.975Q-16.453-15.160-16.276-15.180L-15.561-15.180Q-15.390-15.160-15.346-14.975L-15.346-14.900L-15.353-14.879Q-15.155-15.037-14.915-15.125Q-14.676-15.214-14.420-15.214Q-14.116-15.214-13.907-15.091Q-13.699-14.968-13.598-14.743Q-13.497-14.517-13.497-14.206L-13.497-12.651L-13.124-12.651Q-12.943-12.630-12.909-12.449L-12.909-12.370Q-12.943-12.183-13.124-12.162L-14.345-12.162Q-14.515-12.183-14.560-12.370L-14.560-12.449Q-14.515-12.634-14.345-12.651L-14.057-12.651L-14.057-14.179Q-14.057-14.449-14.136-14.587Q-14.215-14.725-14.471-14.725Q-14.707-14.725-14.907-14.611Q-15.107-14.496-15.226-14.297Q-15.346-14.097-15.346-13.864L-15.346-12.651L-14.973-12.651Q-14.792-12.630-14.758-12.449L-14.758-12.370Q-14.792-12.183-14.973-12.162L-16.276-12.162Q-16.457-12.183-16.494-12.370M-9.768-13.464L-11.904-13.464Q-11.856-13.222-11.684-13.027Q-11.511-12.832-11.268-12.724Q-11.026-12.617-10.776-12.617Q-10.363-12.617-10.168-12.870Q-10.161-12.880-10.111-12.972Q-10.062-13.064-10.019-13.102Q-9.976-13.140-9.894-13.150L-9.768-13.150Q-9.600-13.133-9.549-12.945L-9.549-12.897Q-9.607-12.634-9.809-12.461Q-10.011-12.288-10.284-12.208Q-10.557-12.128-10.824-12.128Q-11.248-12.128-11.632-12.328Q-12.017-12.528-12.251-12.878Q-12.485-13.228-12.485-13.659L-12.485-13.710Q-12.485-14.120-12.270-14.473Q-12.055-14.825-11.697-15.030Q-11.340-15.235-10.930-15.235Q-10.489-15.235-10.180-15.040Q-9.870-14.845-9.710-14.505Q-9.549-14.165-9.549-13.724L-9.549-13.673Q-9.600-13.485-9.768-13.464M-11.897-13.946L-10.123-13.946Q-10.164-14.305-10.373-14.526Q-10.581-14.746-10.930-14.746Q-11.275-14.746-11.544-14.517Q-11.812-14.288-11.897-13.946M-8.900-12.370L-8.900-12.449Q-8.866-12.630-8.684-12.651L-8.329-12.651L-7.515-13.717L-8.278-14.688L-8.643-14.688Q-8.814-14.705-8.859-14.900L-8.859-14.975Q-8.814-15.160-8.643-15.180L-7.628-15.180Q-7.454-15.160-7.410-14.975L-7.410-14.900Q-7.454-14.708-7.628-14.688L-7.724-14.688L-7.290-14.114L-6.873-14.688L-6.975-14.688Q-7.150-14.708-7.194-14.900L-7.194-14.975Q-7.150-15.160-6.975-15.180L-5.960-15.180Q-5.789-15.163-5.745-14.975L-5.745-14.900Q-5.789-14.708-5.960-14.688L-6.319-14.688L-7.061-13.717L-6.220-12.651L-5.865-12.651Q-5.690-12.630-5.646-12.449L-5.646-12.370Q-5.680-12.183-5.865-12.162L-6.873-12.162Q-7.054-12.183-7.088-12.370L-7.088-12.449Q-7.054-12.630-6.873-12.651L-6.760-12.651L-7.290-13.399L-7.803-12.651L-7.676-12.651Q-7.495-12.630-7.461-12.449L-7.461-12.370Q-7.495-12.183-7.676-12.162L-8.684-12.162Q-8.855-12.179-8.900-12.370M-4.361-13.129L-4.361-14.688L-5.017-14.688Q-5.191-14.708-5.236-14.900L-5.236-14.975Q-5.191-15.160-5.017-15.180L-4.361-15.180L-4.361-15.836Q-4.316-16.017-4.142-16.041L-4.015-16.041Q-3.845-16.017-3.800-15.836L-3.800-15.180L-2.611-15.180Q-2.443-15.163-2.392-14.975L-2.392-14.900Q-2.440-14.708-2.611-14.688L-3.800-14.688L-3.800-13.157Q-3.800-12.617-3.298-12.617Q-3.079-12.617-2.935-12.779Q-2.792-12.941-2.792-13.157Q-2.792-13.239-2.729-13.300Q-2.665-13.362-2.577-13.372L-2.450-13.372Q-2.276-13.351-2.231-13.170L-2.231-13.129Q-2.231-12.846-2.392-12.615Q-2.553-12.384-2.809-12.256Q-3.065-12.128-3.346-12.128Q-3.793-12.128-4.077-12.400Q-4.361-12.671-4.361-13.129\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(83.836 -51.921)\">\u003Cpath d=\"M3.087-13.129L3.087-14.688L2.431-14.688Q2.257-14.708 2.212-14.900L2.212-14.975Q2.257-15.160 2.431-15.180L3.087-15.180L3.087-15.836Q3.132-16.017 3.306-16.041L3.433-16.041Q3.603-16.017 3.648-15.836L3.648-15.180L4.837-15.180Q5.005-15.163 5.056-14.975L5.056-14.900Q5.008-14.708 4.837-14.688L3.648-14.688L3.648-13.157Q3.648-12.617 4.150-12.617Q4.369-12.617 4.513-12.779Q4.656-12.941 4.656-13.157Q4.656-13.239 4.719-13.300Q4.783-13.362 4.871-13.372L4.998-13.372Q5.172-13.351 5.217-13.170L5.217-13.129Q5.217-12.846 5.056-12.615Q4.895-12.384 4.639-12.256Q4.383-12.128 4.102-12.128Q3.655-12.128 3.371-12.400Q3.087-12.671 3.087-13.129M7.609-12.128Q7.196-12.128 6.859-12.341Q6.522-12.555 6.328-12.914Q6.133-13.273 6.133-13.673Q6.133-13.974 6.242-14.256Q6.351-14.537 6.553-14.760Q6.755-14.982 7.023-15.108Q7.291-15.235 7.609-15.235Q7.927-15.235 8.201-15.107Q8.474-14.978 8.669-14.763Q8.864-14.548 8.975-14.267Q9.086-13.987 9.086-13.673Q9.086-13.273 8.889-12.912Q8.693-12.552 8.356-12.340Q8.019-12.128 7.609-12.128M7.609-12.617Q8.016-12.617 8.271-12.962Q8.525-13.307 8.525-13.731Q8.525-13.987 8.407-14.221Q8.289-14.455 8.079-14.601Q7.869-14.746 7.609-14.746Q7.343-14.746 7.134-14.601Q6.926-14.455 6.808-14.221Q6.690-13.987 6.690-13.731Q6.690-13.310 6.946-12.964Q7.203-12.617 7.609-12.617M9.595-12.370L9.595-12.449Q9.640-12.630 9.810-12.651L10.217-12.651L10.217-15.949L9.810-15.949Q9.640-15.970 9.595-16.158L9.595-16.236Q9.640-16.417 9.810-16.438L10.463-16.438Q10.634-16.421 10.679-16.236L10.679-13.765L11.680-14.688L11.420-14.688Q11.239-14.708 11.205-14.900L11.205-14.975Q11.239-15.160 11.420-15.180L12.688-15.180Q12.866-15.160 12.907-14.975L12.907-14.900Q12.870-14.708 12.688-14.688L12.367-14.688L11.540-13.933L12.548-12.651L12.842-12.651Q13.023-12.630 13.061-12.449L13.061-12.370Q13.023-12.183 12.842-12.162L11.820-12.162Q11.649-12.183 11.605-12.370L11.605-12.449Q11.649-12.630 11.820-12.651L11.960-12.651L11.205-13.618L10.679-13.136L10.679-12.651L11.085-12.651Q11.253-12.630 11.304-12.449L11.304-12.370Q11.253-12.183 11.085-12.162L9.810-12.162Q9.640-12.183 9.595-12.370M16.257-13.464L14.121-13.464Q14.168-13.222 14.341-13.027Q14.514-12.832 14.756-12.724Q14.999-12.617 15.248-12.617Q15.662-12.617 15.857-12.870Q15.864-12.880 15.913-12.972Q15.963-13.064 16.006-13.102Q16.048-13.140 16.130-13.150L16.257-13.150Q16.424-13.133 16.476-12.945L16.476-12.897Q16.417-12.634 16.216-12.461Q16.014-12.288 15.741-12.208Q15.467-12.128 15.201-12.128Q14.777-12.128 14.392-12.328Q14.008-12.528 13.774-12.878Q13.539-13.228 13.539-13.659L13.539-13.710Q13.539-14.120 13.755-14.473Q13.970-14.825 14.327-15.030Q14.684-15.235 15.095-15.235Q15.536-15.235 15.845-15.040Q16.154-14.845 16.315-14.505Q16.476-14.165 16.476-13.724L16.476-13.673Q16.424-13.485 16.257-13.464M14.127-13.946L15.901-13.946Q15.860-14.305 15.652-14.526Q15.443-14.746 15.095-14.746Q14.749-14.746 14.481-14.517Q14.213-14.288 14.127-13.946M16.961-12.370L16.961-12.449Q16.998-12.630 17.180-12.651L17.549-12.651L17.549-14.688L17.180-14.688Q16.998-14.708 16.961-14.900L16.961-14.975Q17.002-15.160 17.180-15.180L17.894-15.180Q18.065-15.160 18.109-14.975L18.109-14.900L18.102-14.879Q18.301-15.037 18.540-15.125Q18.779-15.214 19.036-15.214Q19.340-15.214 19.548-15.091Q19.757-14.968 19.858-14.743Q19.958-14.517 19.958-14.206L19.958-12.651L20.331-12.651Q20.512-12.630 20.546-12.449L20.546-12.370Q20.512-12.183 20.331-12.162L19.111-12.162Q18.940-12.183 18.895-12.370L18.895-12.449Q18.940-12.634 19.111-12.651L19.398-12.651L19.398-14.179Q19.398-14.449 19.319-14.587Q19.241-14.725 18.984-14.725Q18.748-14.725 18.548-14.611Q18.349-14.496 18.229-14.297Q18.109-14.097 18.109-13.864L18.109-12.651L18.482-12.651Q18.663-12.630 18.697-12.449L18.697-12.370Q18.663-12.183 18.482-12.162L17.180-12.162Q16.998-12.183 16.961-12.370\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M85.874 2.083v-8.6\"\u002F>\u003Cpath stroke=\"none\" d=\"m85.874-9.116-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M85.874-26.588v-5.536\"\u002F>\u003Cpath stroke=\"none\" d=\"m85.874-34.724-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M85.874-52.196v-5.754\"\u002F>\u003Cpath stroke=\"none\" d=\"m85.874-60.55-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(76.93 44.235)\">\u003Cpath d=\"M-14.693-12.123Q-15.158-12.123-15.523-12.373Q-15.888-12.623-16.093-13.027Q-16.298-13.432-16.298-13.889Q-16.298-14.232-16.173-14.553Q-16.048-14.873-15.816-15.123Q-15.583-15.373-15.279-15.512Q-14.974-15.650-14.619-15.650Q-14.107-15.650-13.701-15.330L-13.701-16.490L-14.122-16.490Q-14.333-16.514-14.372-16.728L-14.372-16.818Q-14.333-17.025-14.122-17.049L-13.310-17.049Q-13.111-17.025-13.060-16.818L-13.060-12.721L-12.634-12.721Q-12.427-12.697-12.388-12.490L-12.388-12.400Q-12.427-12.185-12.634-12.162L-13.451-12.162Q-13.650-12.185-13.701-12.400L-13.701-12.529Q-13.896-12.338-14.158-12.230Q-14.419-12.123-14.693-12.123M-14.654-12.682Q-14.294-12.682-14.042-12.951Q-13.790-13.221-13.701-13.596L-13.701-14.428Q-13.759-14.615-13.886-14.766Q-14.013-14.916-14.191-15.004Q-14.369-15.092-14.564-15.092Q-14.872-15.092-15.122-14.922Q-15.372-14.752-15.517-14.467Q-15.661-14.182-15.661-13.881Q-15.661-13.432-15.376-13.057Q-15.091-12.682-14.654-12.682M-8.798-13.650L-11.240-13.650Q-11.185-13.373-10.988-13.150Q-10.790-12.928-10.513-12.805Q-10.236-12.682-9.951-12.682Q-9.478-12.682-9.255-12.971Q-9.247-12.982-9.191-13.088Q-9.134-13.193-9.085-13.236Q-9.036-13.279-8.943-13.291L-8.798-13.291Q-8.607-13.271-8.548-13.057L-8.548-13.002Q-8.615-12.701-8.845-12.504Q-9.076-12.307-9.388-12.215Q-9.701-12.123-10.005-12.123Q-10.490-12.123-10.929-12.351Q-11.369-12.580-11.636-12.980Q-11.904-13.381-11.904-13.873L-11.904-13.932Q-11.904-14.400-11.658-14.803Q-11.411-15.205-11.003-15.439Q-10.595-15.674-10.126-15.674Q-9.622-15.674-9.269-15.451Q-8.915-15.228-8.732-14.840Q-8.548-14.451-8.548-13.947L-8.548-13.889Q-8.607-13.674-8.798-13.650M-11.232-14.201L-9.204-14.201Q-9.251-14.611-9.490-14.863Q-9.728-15.115-10.126-15.115Q-10.521-15.115-10.827-14.853Q-11.134-14.592-11.232-14.201M-7.505-13.889Q-7.505-14.369-7.261-14.783Q-7.017-15.197-6.601-15.435Q-6.185-15.674-5.704-15.674Q-5.150-15.674-4.771-15.564Q-4.392-15.455-4.392-15.049Q-4.392-14.881-4.505-14.758Q-4.619-14.635-4.790-14.635Q-4.962-14.635-5.081-14.750Q-5.201-14.865-5.201-15.033L-5.201-15.092Q-5.361-15.115-5.697-15.115Q-6.025-15.115-6.292-14.945Q-6.560-14.775-6.712-14.492Q-6.865-14.209-6.865-13.889Q-6.865-13.568-6.693-13.287Q-6.521-13.006-6.236-12.844Q-5.951-12.682-5.622-12.682Q-5.310-12.682-5.183-12.785Q-5.056-12.889-4.939-13.078Q-4.822-13.267-4.704-13.283L-4.536-13.283Q-4.431-13.271-4.367-13.203Q-4.302-13.135-4.302-13.033Q-4.302-12.986-4.322-12.947Q-4.431-12.654-4.634-12.475Q-4.837-12.295-5.113-12.209Q-5.388-12.123-5.704-12.123Q-6.189-12.123-6.605-12.361Q-7.021-12.600-7.263-13.002Q-7.505-13.404-7.505-13.889M-1.697-12.123Q-2.169-12.123-2.554-12.367Q-2.939-12.611-3.161-13.021Q-3.384-13.432-3.384-13.889Q-3.384-14.232-3.259-14.555Q-3.134-14.877-2.904-15.131Q-2.673-15.385-2.367-15.529Q-2.060-15.674-1.697-15.674Q-1.333-15.674-1.021-15.527Q-0.708-15.381-0.486-15.135Q-0.263-14.889-0.136-14.568Q-0.009-14.248-0.009-13.889Q-0.009-13.432-0.234-13.019Q-0.458-12.607-0.843-12.365Q-1.228-12.123-1.697-12.123M-1.697-12.682Q-1.232-12.682-0.941-13.076Q-0.650-13.471-0.650-13.955Q-0.650-14.248-0.785-14.516Q-0.919-14.783-1.160-14.949Q-1.400-15.115-1.697-15.115Q-2.001-15.115-2.240-14.949Q-2.478-14.783-2.613-14.516Q-2.747-14.248-2.747-13.955Q-2.747-13.475-2.454-13.078Q-2.161-12.682-1.697-12.682M2.292-12.123Q1.827-12.123 1.462-12.373Q1.096-12.623 0.891-13.027Q0.686-13.432 0.686-13.889Q0.686-14.232 0.811-14.553Q0.936-14.873 1.169-15.123Q1.401-15.373 1.706-15.512Q2.010-15.650 2.366-15.650Q2.878-15.650 3.284-15.330L3.284-16.490L2.862-16.490Q2.651-16.514 2.612-16.728L2.612-16.818Q2.651-17.025 2.862-17.049L3.674-17.049Q3.874-17.025 3.924-16.818L3.924-12.721L4.350-12.721Q4.557-12.697 4.596-12.490L4.596-12.400Q4.557-12.185 4.350-12.162L3.534-12.162Q3.335-12.185 3.284-12.400L3.284-12.529Q3.089-12.338 2.827-12.230Q2.565-12.123 2.292-12.123M2.331-12.682Q2.690-12.682 2.942-12.951Q3.194-13.221 3.284-13.596L3.284-14.428Q3.225-14.615 3.098-14.766Q2.971-14.916 2.794-15.004Q2.616-15.092 2.421-15.092Q2.112-15.092 1.862-14.922Q1.612-14.752 1.467-14.467Q1.323-14.182 1.323-13.881Q1.323-13.432 1.608-13.057Q1.893-12.682 2.331-12.682M8.186-13.650L5.745-13.650Q5.799-13.373 5.997-13.150Q6.194-12.928 6.471-12.805Q6.749-12.682 7.034-12.682Q7.506-12.682 7.729-12.971Q7.737-12.982 7.794-13.088Q7.850-13.193 7.899-13.236Q7.948-13.279 8.042-13.291L8.186-13.291Q8.378-13.271 8.436-13.057L8.436-13.002Q8.370-12.701 8.139-12.504Q7.909-12.307 7.596-12.215Q7.284-12.123 6.979-12.123Q6.495-12.123 6.055-12.351Q5.616-12.580 5.348-12.980Q5.081-13.381 5.081-13.873L5.081-13.932Q5.081-14.400 5.327-14.803Q5.573-15.205 5.981-15.439Q6.389-15.674 6.858-15.674Q7.362-15.674 7.715-15.451Q8.069-15.228 8.253-14.840Q8.436-14.451 8.436-13.947L8.436-13.889Q8.378-13.674 8.186-13.650M5.753-14.201L7.780-14.201Q7.733-14.611 7.495-14.863Q7.256-15.115 6.858-15.115Q6.464-15.115 6.157-14.853Q5.850-14.592 5.753-14.201M9.143-12.400L9.143-12.490Q9.202-12.697 9.393-12.721L10.104-12.721L10.104-15.049L9.393-15.049Q9.198-15.072 9.143-15.291L9.143-15.377Q9.202-15.588 9.393-15.611L10.495-15.611Q10.694-15.592 10.745-15.377L10.745-15.049Q11.006-15.334 11.362-15.492Q11.717-15.650 12.104-15.650Q12.397-15.650 12.631-15.516Q12.866-15.381 12.866-15.115Q12.866-14.947 12.756-14.830Q12.647-14.713 12.479-14.713Q12.327-14.713 12.212-14.824Q12.096-14.935 12.096-15.092Q11.721-15.092 11.407-14.891Q11.092-14.689 10.919-14.355Q10.745-14.021 10.745-13.642L10.745-12.721L11.690-12.721Q11.897-12.697 11.936-12.490L11.936-12.400Q11.897-12.185 11.690-12.162L9.393-12.162Q9.202-12.185 9.143-12.400M16.663-14.299L13.921-14.299Q13.796-14.310 13.710-14.396Q13.624-14.482 13.624-14.611Q13.624-14.740 13.710-14.822Q13.796-14.904 13.921-14.916L16.663-14.916Q16.788-14.904 16.870-14.822Q16.952-14.740 16.952-14.611Q16.952-14.482 16.870-14.396Q16.788-14.310 16.663-14.299M19.534-12.123Q19.061-12.123 18.676-12.367Q18.292-12.611 18.069-13.021Q17.846-13.432 17.846-13.889Q17.846-14.232 17.971-14.555Q18.096-14.877 18.327-15.131Q18.557-15.385 18.864-15.529Q19.171-15.674 19.534-15.674Q19.897-15.674 20.210-15.527Q20.522-15.381 20.745-15.135Q20.967-14.889 21.094-14.568Q21.221-14.248 21.221-13.889Q21.221-13.432 20.997-13.019Q20.772-12.607 20.387-12.365Q20.003-12.123 19.534-12.123M19.534-12.682Q19.999-12.682 20.290-13.076Q20.581-13.471 20.581-13.955Q20.581-14.248 20.446-14.516Q20.311-14.783 20.071-14.949Q19.831-15.115 19.534-15.115Q19.229-15.115 18.991-14.949Q18.753-14.783 18.618-14.516Q18.483-14.248 18.483-13.955Q18.483-13.475 18.776-13.078Q19.069-12.682 19.534-12.682M21.729-12.400L21.729-12.490Q21.772-12.697 21.979-12.721L22.401-12.721L22.401-15.049L21.979-15.049Q21.772-15.072 21.729-15.291L21.729-15.377Q21.776-15.588 21.979-15.611L22.796-15.611Q22.991-15.588 23.042-15.377L23.042-15.291L23.034-15.267Q23.260-15.447 23.534-15.549Q23.807-15.650 24.100-15.650Q24.448-15.650 24.686-15.510Q24.924-15.369 25.040-15.111Q25.155-14.853 25.155-14.498L25.155-12.721L25.581-12.721Q25.788-12.697 25.827-12.490L25.827-12.400Q25.788-12.185 25.581-12.162L24.186-12.162Q23.991-12.185 23.940-12.400L23.940-12.490Q23.991-12.701 24.186-12.721L24.514-12.721L24.514-14.467Q24.514-14.775 24.424-14.933Q24.335-15.092 24.042-15.092Q23.772-15.092 23.544-14.961Q23.315-14.830 23.178-14.601Q23.042-14.373 23.042-14.107L23.042-12.721L23.467-12.721Q23.674-12.697 23.714-12.490L23.714-12.400Q23.674-12.185 23.467-12.162L21.979-12.162Q21.772-12.185 21.729-12.400M26.354-12.400L26.354-12.490Q26.405-12.697 26.600-12.721L27.706-12.721L27.706-16.490L26.600-16.490Q26.405-16.514 26.354-16.728L26.354-16.818Q26.405-17.025 26.600-17.049L28.096-17.049Q28.288-17.025 28.346-16.818L28.346-12.721L29.448-12.721Q29.647-12.697 29.698-12.490L29.698-12.400Q29.647-12.185 29.448-12.162L26.600-12.162Q26.405-12.185 26.354-12.400M30.495-11.041Q30.495-11.150 30.546-11.242Q30.596-11.334 30.688-11.385Q30.780-11.435 30.885-11.435Q30.995-11.435 31.087-11.385Q31.178-11.334 31.229-11.242Q31.280-11.150 31.280-11.041L31.135-11.041Q31.135-10.904 31.159-10.904Q31.417-10.904 31.604-11.096Q31.792-11.287 31.878-11.553L32.089-12.162L30.952-15.049L30.624-15.049Q30.428-15.072 30.374-15.291L30.374-15.377Q30.432-15.588 30.624-15.611L31.784-15.611Q31.979-15.588 32.030-15.377L32.030-15.291Q31.979-15.072 31.784-15.049L31.518-15.049Q31.854-14.201 32.098-13.547Q32.342-12.892 32.342-12.803L32.350-12.803Q32.350-12.861 32.442-13.154Q32.534-13.447 32.727-14.031Q32.921-14.615 33.061-15.049L32.784-15.049Q32.573-15.072 32.534-15.291L32.534-15.377Q32.585-15.592 32.784-15.611L33.936-15.611Q34.143-15.588 34.182-15.377L34.182-15.291Q34.143-15.072 33.936-15.049L33.616-15.049L32.440-11.553Q32.272-11.053 31.946-10.699Q31.620-10.346 31.159-10.346Q30.885-10.346 30.690-10.557Q30.495-10.767 30.495-11.041\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(78.258 58.85)\">\u003Cpath d=\"M-13.832-11.601Q-14.297-11.871-14.647-12.299Q-14.997-12.726-15.182-13.245Q-15.367-13.765-15.367-14.305Q-15.367-14.845-15.184-15.360Q-15.001-15.874-14.654-16.294Q-14.307-16.715-13.839-16.998Q-13.777-17.019-13.750-17.019L-13.671-17.019Q-13.586-17.009-13.528-16.951Q-13.470-16.892-13.470-16.804Q-13.470-16.677-13.558-16.622Q-13.952-16.370-14.237-16.006Q-14.522-15.641-14.664-15.211Q-14.806-14.780-14.806-14.305Q-14.806-13.950-14.722-13.611Q-14.639-13.273-14.483-12.979Q-14.327-12.685-14.100-12.437Q-13.873-12.189-13.569-11.988Q-13.470-11.919-13.470-11.800Q-13.470-11.714-13.528-11.653Q-13.586-11.591-13.671-11.581L-13.750-11.581Q-13.801-11.581-13.832-11.601M-10.998-12.094Q-11.504-12.094-11.863-12.439Q-12.222-12.784-12.398-13.298Q-12.574-13.813-12.574-14.305Q-12.574-14.787-12.398-15.303Q-12.222-15.819-11.863-16.164Q-11.504-16.510-10.998-16.510Q-10.561-16.510-10.209-16.223Q-10.168-16.298-10.130-16.361Q-10.093-16.424-10.046-16.462Q-10-16.499-9.935-16.510L-9.867-16.510Q-9.782-16.499-9.727-16.445Q-9.672-16.390-9.662-16.305L-9.662-15.142Q-9.672-15.060-9.727-15.002Q-9.782-14.944-9.867-14.934L-10.014-14.934Q-10.185-14.958-10.216-15.115Q-10.264-15.481-10.448-15.749Q-10.633-16.017-10.957-16.017Q-11.303-16.017-11.544-15.734Q-11.785-15.450-11.899-15.047Q-12.014-14.643-12.014-14.305Q-12.014-13.953-11.901-13.551Q-11.788-13.150-11.552-12.866Q-11.316-12.582-10.971-12.582Q-10.636-12.582-10.457-12.892Q-10.277-13.201-10.236-13.591L-10.602-13.591Q-10.786-13.611-10.817-13.799L-10.817-13.878Q-10.783-14.059-10.602-14.079L-9.549-14.079Q-9.368-14.059-9.334-13.878L-9.334-13.799Q-9.365-13.611-9.549-13.591L-9.662-13.591L-9.662-12.357Q-9.706-12.179-9.881-12.148L-10.007-12.148Q-10.178-12.176-10.223-12.357L-10.223-12.401Q-10.547-12.094-10.998-12.094M-8.965-12.370L-8.965-12.449Q-8.931-12.630-8.746-12.651L-8.476-12.651L-8.476-15.949L-8.746-15.949Q-8.931-15.970-8.965-16.158L-8.965-16.236Q-8.931-16.417-8.746-16.438L-7.040-16.438Q-6.692-16.438-6.389-16.262Q-6.087-16.086-5.906-15.783Q-5.724-15.481-5.724-15.129Q-5.724-14.773-5.904-14.473Q-6.083-14.172-6.386-13.992Q-6.688-13.813-7.040-13.813L-7.915-13.813L-7.915-12.651L-7.642-12.651Q-7.457-12.630-7.423-12.449L-7.423-12.370Q-7.457-12.183-7.642-12.162L-8.746-12.162Q-8.931-12.183-8.965-12.370M-7.915-15.949L-7.915-14.305L-7.181-14.305Q-6.952-14.305-6.745-14.413Q-6.538-14.520-6.411-14.708Q-6.285-14.896-6.285-15.129Q-6.285-15.365-6.411-15.549Q-6.538-15.734-6.745-15.841Q-6.952-15.949-7.181-15.949L-7.915-15.949M-4.480-12.370L-4.480-12.449Q-4.429-12.630-4.262-12.651L-3.834-12.651L-3.834-15.949L-4.661-15.949L-4.661-15.501Q-4.702-15.313-4.877-15.289L-5.003-15.289Q-5.178-15.313-5.222-15.501L-5.222-16.236Q-5.178-16.417-5.003-16.438L-2.105-16.438Q-1.934-16.421-1.889-16.236L-1.889-15.501Q-1.931-15.313-2.105-15.289L-2.231-15.289Q-2.406-15.313-2.450-15.501L-2.450-15.949L-3.274-15.949L-3.274-12.651L-2.847-12.651Q-2.676-12.630-2.631-12.449L-2.631-12.370Q-2.676-12.183-2.847-12.162L-4.262-12.162Q-4.429-12.183-4.480-12.370M-0.191-11.188Q-0.290-11.188-0.369-11.266Q-0.447-11.345-0.447-11.441Q-0.447-11.595-0.280-11.660Q-0.088-11.704 0.062-11.842Q0.213-11.981 0.271-12.176Q0.250-12.176 0.223-12.162L0.168-12.162Q-0.034-12.162-0.179-12.304Q-0.324-12.446-0.324-12.651Q-0.324-12.856-0.181-12.996Q-0.037-13.136 0.168-13.136Q0.353-13.136 0.496-13.030Q0.640-12.924 0.718-12.755Q0.797-12.586 0.797-12.401Q0.797-11.984 0.536-11.644Q0.274-11.304-0.133-11.195Q-0.153-11.188-0.191-11.188\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(78.258 58.85)\">\u003Cpath d=\"M6.245-13.673Q6.245-14.093 6.458-14.455Q6.672-14.818 7.036-15.026Q7.400-15.235 7.820-15.235Q8.306-15.235 8.637-15.139Q8.969-15.043 8.969-14.688Q8.969-14.541 8.870-14.433Q8.771-14.326 8.620-14.326Q8.470-14.326 8.366-14.426Q8.261-14.527 8.261-14.674L8.261-14.725Q8.121-14.746 7.827-14.746Q7.540-14.746 7.306-14.597Q7.072-14.449 6.939-14.201Q6.805-13.953 6.805-13.673Q6.805-13.392 6.956-13.146Q7.106-12.900 7.356-12.758Q7.605-12.617 7.892-12.617Q8.166-12.617 8.277-12.707Q8.388-12.798 8.490-12.964Q8.593-13.129 8.695-13.143L8.842-13.143Q8.935-13.133 8.991-13.073Q9.048-13.013 9.048-12.924Q9.048-12.883 9.030-12.849Q8.935-12.593 8.757-12.435Q8.579-12.278 8.338-12.203Q8.097-12.128 7.820-12.128Q7.397-12.128 7.033-12.336Q6.669-12.545 6.457-12.897Q6.245-13.249 6.245-13.673M9.827-13.136Q9.827-13.526 10.189-13.751Q10.551-13.977 11.025-14.064Q11.498-14.151 11.943-14.158Q11.943-14.346 11.825-14.479Q11.707-14.613 11.526-14.679Q11.344-14.746 11.160-14.746Q10.859-14.746 10.719-14.725L10.719-14.674Q10.719-14.527 10.615-14.426Q10.510-14.326 10.367-14.326Q10.213-14.326 10.112-14.433Q10.011-14.541 10.011-14.688Q10.011-15.043 10.345-15.139Q10.678-15.235 11.167-15.235Q11.402-15.235 11.637-15.166Q11.871-15.098 12.067-14.966Q12.264-14.835 12.383-14.642Q12.503-14.449 12.503-14.206L12.503-12.702Q12.503-12.651 12.964-12.651Q13.135-12.634 13.180-12.449L13.180-12.370Q13.135-12.183 12.964-12.162L12.838-12.162Q12.537-12.162 12.337-12.203Q12.137-12.244 12.011-12.408Q11.608-12.128 10.989-12.128Q10.695-12.128 10.428-12.251Q10.162-12.374 9.994-12.603Q9.827-12.832 9.827-13.136M10.387-13.129Q10.387-12.890 10.599-12.753Q10.811-12.617 11.061-12.617Q11.252-12.617 11.455-12.668Q11.659-12.719 11.801-12.840Q11.943-12.962 11.943-13.157L11.943-13.673Q11.696-13.673 11.332-13.623Q10.968-13.574 10.678-13.452Q10.387-13.331 10.387-13.129M13.836-12.911L13.836-14.688L13.467-14.688Q13.286-14.708 13.248-14.900L13.248-14.975Q13.289-15.160 13.467-15.180L14.181-15.180Q14.352-15.160 14.397-14.975L14.397-12.938Q14.397-12.733 14.545-12.675Q14.694-12.617 14.944-12.617Q15.125-12.617 15.296-12.683Q15.466-12.750 15.576-12.881Q15.685-13.013 15.685-13.198L15.685-14.688L15.316-14.688Q15.131-14.708 15.097-14.900L15.097-14.975Q15.131-15.160 15.316-15.180L16.027-15.180Q16.201-15.160 16.246-14.975L16.246-12.651L16.618-12.651Q16.799-12.630 16.834-12.449L16.834-12.370Q16.799-12.183 16.618-12.162L15.904-12.162Q15.730-12.183 15.685-12.357Q15.333-12.128 14.889-12.128Q14.684-12.128 14.496-12.164Q14.308-12.200 14.162-12.288Q14.017-12.377 13.927-12.533Q13.836-12.688 13.836-12.911M17.415-12.336L17.415-13.136Q17.439-13.317 17.623-13.338L17.770-13.338Q17.914-13.317 17.965-13.177Q18.143-12.617 18.778-12.617Q18.960-12.617 19.160-12.647Q19.360-12.678 19.506-12.779Q19.653-12.880 19.653-13.058Q19.653-13.242 19.459-13.341Q19.264-13.440 19.025-13.478L18.413-13.577Q17.415-13.762 17.415-14.394Q17.415-14.647 17.541-14.813Q17.668-14.978 17.878-15.072Q18.088-15.166 18.312-15.201Q18.536-15.235 18.778-15.235Q18.997-15.235 19.166-15.209Q19.336-15.183 19.479-15.115Q19.548-15.218 19.660-15.235L19.729-15.235Q19.814-15.225 19.869-15.170Q19.923-15.115 19.934-15.033L19.934-14.414Q19.923-14.332 19.869-14.274Q19.814-14.216 19.729-14.206L19.582-14.206Q19.500-14.216 19.442-14.274Q19.383-14.332 19.373-14.414Q19.373-14.746 18.765-14.746Q18.461-14.746 18.182-14.674Q17.903-14.602 17.903-14.387Q17.903-14.155 18.491-14.059L19.107-13.953Q19.530-13.881 19.836-13.664Q20.142-13.447 20.142-13.058Q20.142-12.716 19.935-12.504Q19.729-12.292 19.423-12.210Q19.117-12.128 18.778-12.128Q18.273-12.128 17.924-12.350Q17.862-12.241 17.820-12.191Q17.777-12.141 17.685-12.128L17.623-12.128Q17.435-12.148 17.415-12.336M20.973-13.136Q20.973-13.526 21.335-13.751Q21.697-13.977 22.171-14.064Q22.644-14.151 23.089-14.158Q23.089-14.346 22.971-14.479Q22.853-14.613 22.672-14.679Q22.490-14.746 22.306-14.746Q22.005-14.746 21.865-14.725L21.865-14.674Q21.865-14.527 21.761-14.426Q21.656-14.326 21.513-14.326Q21.359-14.326 21.258-14.433Q21.157-14.541 21.157-14.688Q21.157-15.043 21.491-15.139Q21.824-15.235 22.313-15.235Q22.548-15.235 22.783-15.166Q23.017-15.098 23.213-14.966Q23.410-14.835 23.529-14.642Q23.649-14.449 23.649-14.206L23.649-12.702Q23.649-12.651 24.110-12.651Q24.281-12.634 24.326-12.449L24.326-12.370Q24.281-12.183 24.110-12.162L23.984-12.162Q23.683-12.162 23.483-12.203Q23.283-12.244 23.157-12.408Q22.754-12.128 22.135-12.128Q21.841-12.128 21.574-12.251Q21.308-12.374 21.140-12.603Q20.973-12.832 20.973-13.136M21.533-13.129Q21.533-12.890 21.745-12.753Q21.957-12.617 22.207-12.617Q22.398-12.617 22.601-12.668Q22.805-12.719 22.947-12.840Q23.089-12.962 23.089-13.157L23.089-13.673Q22.842-13.673 22.478-13.623Q22.114-13.574 21.824-13.452Q21.533-13.331 21.533-13.129M24.726-12.370L24.726-12.449Q24.770-12.630 24.941-12.651L25.908-12.651L25.908-15.949L24.941-15.949Q24.770-15.970 24.726-16.158L24.726-16.236Q24.770-16.417 24.941-16.438L26.250-16.438Q26.418-16.417 26.469-16.236L26.469-12.651L27.433-12.651Q27.607-12.630 27.652-12.449L27.652-12.370Q27.607-12.183 27.433-12.162L24.941-12.162Q24.770-12.183 24.726-12.370M28.957-11.581L28.882-11.581Q28.790-11.591 28.730-11.654Q28.670-11.718 28.670-11.800Q28.670-11.923 28.762-11.981Q29.056-12.169 29.292-12.422Q29.528-12.675 29.689-12.979Q29.849-13.283 29.928-13.615Q30.006-13.946 30.006-14.305Q30.006-14.777 29.863-15.207Q29.719-15.638 29.441-16Q29.162-16.363 28.776-16.616Q28.670-16.687 28.670-16.804Q28.670-16.889 28.730-16.949Q28.790-17.009 28.882-17.019L28.957-17.019Q29.005-17.019 29.036-16.998Q29.374-16.804 29.672-16.499Q29.969-16.195 30.162-15.850Q30.355-15.505 30.461-15.115Q30.567-14.725 30.567-14.305Q30.567-13.881 30.461-13.486Q30.355-13.092 30.159-12.745Q29.962-12.398 29.678-12.106Q29.395-11.813 29.043-11.601Q28.981-11.581 28.957-11.581\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(190.858 21.424)\">\u003Cpath d=\"M-16.043-12.336L-16.043-13.136Q-16.019-13.317-15.835-13.338L-15.688-13.338Q-15.544-13.317-15.493-13.177Q-15.315-12.617-14.680-12.617Q-14.498-12.617-14.298-12.647Q-14.098-12.678-13.952-12.779Q-13.805-12.880-13.805-13.058Q-13.805-13.242-13.999-13.341Q-14.194-13.440-14.433-13.478L-15.045-13.577Q-16.043-13.762-16.043-14.394Q-16.043-14.647-15.917-14.813Q-15.790-14.978-15.580-15.072Q-15.370-15.166-15.146-15.201Q-14.922-15.235-14.680-15.235Q-14.461-15.235-14.292-15.209Q-14.122-15.183-13.979-15.115Q-13.910-15.218-13.798-15.235L-13.729-15.235Q-13.644-15.225-13.589-15.170Q-13.535-15.115-13.524-15.033L-13.524-14.414Q-13.535-14.332-13.589-14.274Q-13.644-14.216-13.729-14.206L-13.876-14.206Q-13.958-14.216-14.016-14.274Q-14.075-14.332-14.085-14.414Q-14.085-14.746-14.693-14.746Q-14.997-14.746-15.276-14.674Q-15.555-14.602-15.555-14.387Q-15.555-14.155-14.967-14.059L-14.351-13.953Q-13.928-13.881-13.622-13.664Q-13.316-13.447-13.316-13.058Q-13.316-12.716-13.523-12.504Q-13.729-12.292-14.035-12.210Q-14.341-12.128-14.680-12.128Q-15.185-12.128-15.534-12.350Q-15.596-12.241-15.638-12.191Q-15.681-12.141-15.773-12.128L-15.835-12.128Q-16.023-12.148-16.043-12.336M-10.985-12.128Q-11.398-12.128-11.735-12.341Q-12.072-12.555-12.266-12.914Q-12.461-13.273-12.461-13.673Q-12.461-13.974-12.352-14.256Q-12.243-14.537-12.041-14.760Q-11.839-14.982-11.571-15.108Q-11.303-15.235-10.985-15.235Q-10.667-15.235-10.393-15.107Q-10.120-14.978-9.925-14.763Q-9.730-14.548-9.619-14.267Q-9.508-13.987-9.508-13.673Q-9.508-13.273-9.705-12.912Q-9.901-12.552-10.238-12.340Q-10.575-12.128-10.985-12.128M-10.985-12.617Q-10.578-12.617-10.323-12.962Q-10.069-13.307-10.069-13.731Q-10.069-13.987-10.187-14.221Q-10.305-14.455-10.515-14.601Q-10.725-14.746-10.985-14.746Q-11.251-14.746-11.460-14.601Q-11.668-14.455-11.786-14.221Q-11.904-13.987-11.904-13.731Q-11.904-13.310-11.648-12.964Q-11.391-12.617-10.985-12.617M-8.476-12.911L-8.476-14.688L-8.845-14.688Q-9.026-14.708-9.064-14.900L-9.064-14.975Q-9.023-15.160-8.845-15.180L-8.131-15.180Q-7.960-15.160-7.915-14.975L-7.915-12.938Q-7.915-12.733-7.767-12.675Q-7.618-12.617-7.369-12.617Q-7.187-12.617-7.016-12.683Q-6.846-12.750-6.736-12.881Q-6.627-13.013-6.627-13.198L-6.627-14.688L-6.996-14.688Q-7.181-14.708-7.215-14.900L-7.215-14.975Q-7.181-15.160-6.996-15.180L-6.285-15.180Q-6.111-15.160-6.066-14.975L-6.066-12.651L-5.694-12.651Q-5.513-12.630-5.478-12.449L-5.478-12.370Q-5.513-12.183-5.694-12.162L-6.408-12.162Q-6.582-12.183-6.627-12.357Q-6.979-12.128-7.423-12.128Q-7.628-12.128-7.816-12.164Q-8.004-12.200-8.150-12.288Q-8.295-12.377-8.385-12.533Q-8.476-12.688-8.476-12.911M-5.215-12.370L-5.215-12.449Q-5.164-12.630-4.996-12.651L-4.374-12.651L-4.374-14.688L-4.996-14.688Q-5.167-14.708-5.215-14.900L-5.215-14.975Q-5.164-15.160-4.996-15.180L-4.033-15.180Q-3.858-15.163-3.814-14.975L-3.814-14.688Q-3.585-14.937-3.274-15.076Q-2.963-15.214-2.624-15.214Q-2.368-15.214-2.163-15.096Q-1.958-14.978-1.958-14.746Q-1.958-14.599-2.054-14.496Q-2.149-14.394-2.296-14.394Q-2.430-14.394-2.530-14.491Q-2.631-14.589-2.631-14.725Q-2.959-14.725-3.234-14.549Q-3.510-14.373-3.662-14.081Q-3.814-13.789-3.814-13.457L-3.814-12.651L-2.987-12.651Q-2.806-12.630-2.771-12.449L-2.771-12.370Q-2.806-12.183-2.987-12.162L-4.996-12.162Q-5.164-12.183-5.215-12.370M-1.206-13.673Q-1.206-14.093-0.992-14.455Q-0.779-14.818-0.415-15.026Q-0.051-15.235 0.370-15.235Q0.855-15.235 1.187-15.139Q1.518-15.043 1.518-14.688Q1.518-14.541 1.419-14.433Q1.320-14.326 1.170-14.326Q1.019-14.326 0.915-14.426Q0.811-14.527 0.811-14.674L0.811-14.725Q0.671-14.746 0.377-14.746Q0.090-14.746-0.145-14.597Q-0.379-14.449-0.512-14.201Q-0.645-13.953-0.645-13.673Q-0.645-13.392-0.495-13.146Q-0.345-12.900-0.095-12.758Q0.154-12.617 0.442-12.617Q0.715-12.617 0.826-12.707Q0.937-12.798 1.040-12.964Q1.142-13.129 1.245-13.143L1.392-13.143Q1.484-13.133 1.540-13.073Q1.597-13.013 1.597-12.924Q1.597-12.883 1.580-12.849Q1.484-12.593 1.306-12.435Q1.129-12.278 0.888-12.203Q0.647-12.128 0.370-12.128Q-0.054-12.128-0.418-12.336Q-0.782-12.545-0.994-12.897Q-1.206-13.249-1.206-13.673M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M157.005-9.316h56.906v-17.072h-56.906Z\"\u002F>\u003Cg transform=\"translate(188.999 -3.552)\">\u003Cpath d=\"M-13.483-13.464L-15.619-13.464Q-15.572-13.222-15.399-13.027Q-15.226-12.832-14.984-12.724Q-14.741-12.617-14.492-12.617Q-14.078-12.617-13.883-12.870Q-13.876-12.880-13.827-12.972Q-13.777-13.064-13.734-13.102Q-13.692-13.140-13.610-13.150L-13.483-13.150Q-13.316-13.133-13.264-12.945L-13.264-12.897Q-13.323-12.634-13.524-12.461Q-13.726-12.288-13.999-12.208Q-14.273-12.128-14.539-12.128Q-14.963-12.128-15.348-12.328Q-15.732-12.528-15.966-12.878Q-16.201-13.228-16.201-13.659L-16.201-13.710Q-16.201-14.120-15.985-14.473Q-15.770-14.825-15.413-15.030Q-15.056-15.235-14.645-15.235Q-14.204-15.235-13.895-15.040Q-13.586-14.845-13.425-14.505Q-13.264-14.165-13.264-13.724L-13.264-13.673Q-13.316-13.485-13.483-13.464M-15.613-13.946L-13.839-13.946Q-13.880-14.305-14.088-14.526Q-14.297-14.746-14.645-14.746Q-14.991-14.746-15.259-14.517Q-15.527-14.288-15.613-13.946M-12.779-12.370L-12.779-12.449Q-12.742-12.630-12.560-12.651L-12.191-12.651L-12.191-14.688L-12.560-14.688Q-12.742-14.708-12.779-14.900L-12.779-14.975Q-12.738-15.160-12.560-15.180L-11.846-15.180Q-11.675-15.160-11.631-14.975L-11.631-14.900L-11.638-14.879Q-11.439-15.037-11.200-15.125Q-10.961-15.214-10.704-15.214Q-10.400-15.214-10.192-15.091Q-9.983-14.968-9.882-14.743Q-9.782-14.517-9.782-14.206L-9.782-12.651L-9.409-12.651Q-9.228-12.630-9.194-12.449L-9.194-12.370Q-9.228-12.183-9.409-12.162L-10.629-12.162Q-10.800-12.183-10.845-12.370L-10.845-12.449Q-10.800-12.634-10.629-12.651L-10.342-12.651L-10.342-14.179Q-10.342-14.449-10.421-14.587Q-10.499-14.725-10.756-14.725Q-10.992-14.725-11.191-14.611Q-11.391-14.496-11.511-14.297Q-11.631-14.097-11.631-13.864L-11.631-12.651L-11.258-12.651Q-11.077-12.630-11.043-12.449L-11.043-12.370Q-11.077-12.183-11.258-12.162L-12.560-12.162Q-12.742-12.183-12.779-12.370M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M157.005-34.924h56.906v-17.072h-56.906Z\"\u002F>\u003Cg transform=\"translate(188.999 -29.16)\">\u003Cpath d=\"M-13.483-13.464L-15.619-13.464Q-15.572-13.222-15.399-13.027Q-15.226-12.832-14.984-12.724Q-14.741-12.617-14.492-12.617Q-14.078-12.617-13.883-12.870Q-13.876-12.880-13.827-12.972Q-13.777-13.064-13.734-13.102Q-13.692-13.140-13.610-13.150L-13.483-13.150Q-13.316-13.133-13.264-12.945L-13.264-12.897Q-13.323-12.634-13.524-12.461Q-13.726-12.288-13.999-12.208Q-14.273-12.128-14.539-12.128Q-14.963-12.128-15.348-12.328Q-15.732-12.528-15.966-12.878Q-16.201-13.228-16.201-13.659L-16.201-13.710Q-16.201-14.120-15.985-14.473Q-15.770-14.825-15.413-15.030Q-15.056-15.235-14.645-15.235Q-14.204-15.235-13.895-15.040Q-13.586-14.845-13.425-14.505Q-13.264-14.165-13.264-13.724L-13.264-13.673Q-13.316-13.485-13.483-13.464M-15.613-13.946L-13.839-13.946Q-13.880-14.305-14.088-14.526Q-14.297-14.746-14.645-14.746Q-14.991-14.746-15.259-14.517Q-15.527-14.288-15.613-13.946M-12.779-12.370L-12.779-12.449Q-12.742-12.630-12.560-12.651L-12.191-12.651L-12.191-14.688L-12.560-14.688Q-12.742-14.708-12.779-14.900L-12.779-14.975Q-12.738-15.160-12.560-15.180L-11.846-15.180Q-11.675-15.160-11.631-14.975L-11.631-14.900L-11.638-14.879Q-11.439-15.037-11.200-15.125Q-10.961-15.214-10.704-15.214Q-10.400-15.214-10.192-15.091Q-9.983-14.968-9.882-14.743Q-9.782-14.517-9.782-14.206L-9.782-12.651L-9.409-12.651Q-9.228-12.630-9.194-12.449L-9.194-12.370Q-9.228-12.183-9.409-12.162L-10.629-12.162Q-10.800-12.183-10.845-12.370L-10.845-12.449Q-10.800-12.634-10.629-12.651L-10.342-12.651L-10.342-14.179Q-10.342-14.449-10.421-14.587Q-10.499-14.725-10.756-14.725Q-10.992-14.725-11.191-14.611Q-11.391-14.496-11.511-14.297Q-11.631-14.097-11.631-13.864L-11.631-12.651L-11.258-12.651Q-11.077-12.630-11.043-12.449L-11.043-12.370Q-11.077-12.183-11.258-12.162L-12.560-12.162Q-12.742-12.183-12.779-12.370M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(287.598 21.077)\">\u003Cpath d=\"M-15.507-13.129L-15.507-14.688L-16.163-14.688Q-16.337-14.708-16.382-14.900L-16.382-14.975Q-16.337-15.160-16.163-15.180L-15.507-15.180L-15.507-15.836Q-15.462-16.017-15.288-16.041L-15.161-16.041Q-14.991-16.017-14.946-15.836L-14.946-15.180L-13.757-15.180Q-13.589-15.163-13.538-14.975L-13.538-14.900Q-13.586-14.708-13.757-14.688L-14.946-14.688L-14.946-13.157Q-14.946-12.617-14.444-12.617Q-14.225-12.617-14.081-12.779Q-13.938-12.941-13.938-13.157Q-13.938-13.239-13.875-13.300Q-13.811-13.362-13.723-13.372L-13.596-13.372Q-13.422-13.351-13.377-13.170L-13.377-13.129Q-13.377-12.846-13.538-12.615Q-13.699-12.384-13.955-12.256Q-14.211-12.128-14.492-12.128Q-14.939-12.128-15.223-12.400Q-15.507-12.671-15.507-13.129M-12.485-13.136Q-12.485-13.526-12.123-13.751Q-11.761-13.977-11.287-14.064Q-10.814-14.151-10.369-14.158Q-10.369-14.346-10.487-14.479Q-10.605-14.613-10.786-14.679Q-10.968-14.746-11.152-14.746Q-11.453-14.746-11.593-14.725L-11.593-14.674Q-11.593-14.527-11.697-14.426Q-11.802-14.326-11.945-14.326Q-12.099-14.326-12.200-14.433Q-12.301-14.541-12.301-14.688Q-12.301-15.043-11.967-15.139Q-11.634-15.235-11.145-15.235Q-10.910-15.235-10.675-15.166Q-10.441-15.098-10.245-14.966Q-10.048-14.835-9.929-14.642Q-9.809-14.449-9.809-14.206L-9.809-12.702Q-9.809-12.651-9.348-12.651Q-9.177-12.634-9.132-12.449L-9.132-12.370Q-9.177-12.183-9.348-12.162L-9.474-12.162Q-9.775-12.162-9.975-12.203Q-10.175-12.244-10.301-12.408Q-10.704-12.128-11.323-12.128Q-11.617-12.128-11.884-12.251Q-12.150-12.374-12.318-12.603Q-12.485-12.832-12.485-13.136M-11.925-13.129Q-11.925-12.890-11.713-12.753Q-11.501-12.617-11.251-12.617Q-11.060-12.617-10.857-12.668Q-10.653-12.719-10.511-12.840Q-10.369-12.962-10.369-13.157L-10.369-13.673Q-10.616-13.673-10.980-13.623Q-11.344-13.574-11.634-13.452Q-11.925-13.331-11.925-13.129M-8.931-12.370L-8.931-12.449Q-8.879-12.630-8.712-12.651L-8.090-12.651L-8.090-14.688L-8.712-14.688Q-8.883-14.708-8.931-14.900L-8.931-14.975Q-8.879-15.160-8.712-15.180L-7.748-15.180Q-7.574-15.163-7.529-14.975L-7.529-14.688Q-7.300-14.937-6.989-15.076Q-6.678-15.214-6.340-15.214Q-6.083-15.214-5.878-15.096Q-5.673-14.978-5.673-14.746Q-5.673-14.599-5.769-14.496Q-5.865-14.394-6.012-14.394Q-6.145-14.394-6.246-14.491Q-6.347-14.589-6.347-14.725Q-6.675-14.725-6.950-14.549Q-7.225-14.373-7.377-14.081Q-7.529-13.789-7.529-13.457L-7.529-12.651L-6.702-12.651Q-6.521-12.630-6.487-12.449L-6.487-12.370Q-6.521-12.183-6.702-12.162L-8.712-12.162Q-8.879-12.183-8.931-12.370M-5.202-11.595Q-5.202-11.858-5.072-12.087Q-4.942-12.316-4.723-12.456Q-4.884-12.678-4.884-12.958Q-4.884-13.208-4.750-13.437Q-4.969-13.721-4.969-14.086Q-4.969-14.401-4.802-14.661Q-4.634-14.920-4.356-15.067Q-4.077-15.214-3.759-15.214Q-3.578-15.214-3.400-15.161Q-3.223-15.108-3.079-15.019Q-2.744-15.248-2.330-15.248Q-2.122-15.248-1.963-15.134Q-1.804-15.019-1.804-14.821Q-1.804-14.691-1.893-14.599Q-1.982-14.507-2.119-14.507Q-2.235-14.507-2.318-14.575Q-2.402-14.643-2.430-14.753Q-2.556-14.746-2.730-14.667Q-2.553-14.394-2.553-14.086Q-2.553-13.840-2.650-13.637Q-2.747-13.433-2.918-13.278Q-3.089-13.122-3.310-13.037Q-3.530-12.952-3.759-12.952Q-4.098-12.952-4.388-13.116Q-4.398-13.116-4.407-13.052Q-4.415-12.989-4.415-12.958Q-4.415-12.852-4.357-12.758Q-4.299-12.664-4.193-12.630Q-4.180-12.634-4.168-12.635Q-4.156-12.637-4.135-12.637Q-4.121-12.637-4.094-12.630Q-4.067-12.623-4.060-12.623L-3.540-12.623Q-2.857-12.623-2.383-12.412Q-1.910-12.200-1.910-11.595Q-1.910-11.331-2.067-11.133Q-2.224-10.935-2.484-10.808Q-2.744-10.682-3.024-10.624Q-3.305-10.566-3.554-10.566Q-3.896-10.566-4.282-10.673Q-4.668-10.781-4.935-11.015Q-5.202-11.249-5.202-11.595M-4.730-11.601Q-4.730-11.410-4.520-11.287Q-4.309-11.164-4.026-11.106Q-3.742-11.048-3.554-11.048Q-3.366-11.048-3.082-11.106Q-2.799-11.164-2.588-11.287Q-2.378-11.410-2.378-11.601Q-2.378-11.854-2.575-11.976Q-2.771-12.097-3.017-12.126Q-3.264-12.155-3.568-12.155L-4.108-12.155Q-4.268-12.155-4.410-12.085Q-4.552-12.015-4.641-11.887Q-4.730-11.759-4.730-11.601M-3.759-13.437Q-3.496-13.437-3.305-13.628Q-3.113-13.820-3.113-14.086Q-3.113-14.223-3.161-14.338Q-3.209-14.452-3.301-14.544Q-3.393-14.637-3.508-14.684Q-3.622-14.732-3.759-14.732Q-4.026-14.732-4.217-14.541Q-4.409-14.350-4.409-14.086Q-4.409-13.827-4.214-13.632Q-4.019-13.437-3.759-13.437M1.378-13.464L-0.758-13.464Q-0.710-13.222-0.538-13.027Q-0.365-12.832-0.122-12.724Q0.120-12.617 0.370-12.617Q0.783-12.617 0.978-12.870Q0.985-12.880 1.035-12.972Q1.084-13.064 1.127-13.102Q1.170-13.140 1.252-13.150L1.378-13.150Q1.546-13.133 1.597-12.945L1.597-12.897Q1.539-12.634 1.337-12.461Q1.135-12.288 0.862-12.208Q0.589-12.128 0.322-12.128Q-0.102-12.128-0.486-12.328Q-0.871-12.528-1.105-12.878Q-1.339-13.228-1.339-13.659L-1.339-13.710Q-1.339-14.120-1.124-14.473Q-0.909-14.825-0.551-15.030Q-0.194-15.235 0.216-15.235Q0.657-15.235 0.966-15.040Q1.276-14.845 1.436-14.505Q1.597-14.165 1.597-13.724L1.597-13.673Q1.546-13.485 1.378-13.464M-0.751-13.946L1.023-13.946Q0.982-14.305 0.773-14.526Q0.565-14.746 0.216-14.746Q-0.129-14.746-0.398-14.517Q-0.666-14.288-0.751-13.946M3.070-13.129L3.070-14.688L2.414-14.688Q2.239-14.708 2.195-14.900L2.195-14.975Q2.239-15.160 2.414-15.180L3.070-15.180L3.070-15.836Q3.114-16.017 3.289-16.041L3.415-16.041Q3.586-16.017 3.631-15.836L3.631-15.180L4.820-15.180Q4.987-15.163 5.039-14.975L5.039-14.900Q4.991-14.708 4.820-14.688L3.631-14.688L3.631-13.157Q3.631-12.617 4.133-12.617Q4.352-12.617 4.495-12.779Q4.639-12.941 4.639-13.157Q4.639-13.239 4.702-13.300Q4.765-13.362 4.854-13.372L4.981-13.372Q5.155-13.351 5.199-13.170L5.199-13.129Q5.199-12.846 5.039-12.615Q4.878-12.384 4.622-12.256Q4.365-12.128 4.085-12.128Q3.637-12.128 3.354-12.400Q3.070-12.671 3.070-13.129\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-warn)\">\u003Cpath fill=\"none\" d=\"M253.745-9.316h56.905v-17.072h-56.905Z\"\u002F>\u003Cg transform=\"translate(285.738 -3.552)\">\u003Cpath d=\"M-14.926-12.128Q-15.332-12.128-15.652-12.347Q-15.972-12.565-16.151-12.919Q-16.330-13.273-16.330-13.673Q-16.330-13.974-16.221-14.254Q-16.112-14.534-15.908-14.753Q-15.705-14.972-15.438-15.093Q-15.172-15.214-14.861-15.214Q-14.413-15.214-14.057-14.934L-14.057-15.949L-14.427-15.949Q-14.611-15.970-14.645-16.158L-14.645-16.236Q-14.611-16.417-14.427-16.438L-13.716-16.438Q-13.541-16.417-13.497-16.236L-13.497-12.651L-13.124-12.651Q-12.943-12.630-12.909-12.449L-12.909-12.370Q-12.943-12.183-13.124-12.162L-13.839-12.162Q-14.013-12.183-14.057-12.370L-14.057-12.483Q-14.228-12.316-14.457-12.222Q-14.686-12.128-14.926-12.128M-14.891-12.617Q-14.577-12.617-14.357-12.852Q-14.136-13.088-14.057-13.416L-14.057-14.144Q-14.109-14.308-14.220-14.440Q-14.331-14.572-14.486-14.649Q-14.642-14.725-14.813-14.725Q-15.083-14.725-15.302-14.577Q-15.520-14.428-15.647-14.179Q-15.773-13.929-15.773-13.666Q-15.773-13.273-15.524-12.945Q-15.274-12.617-14.891-12.617M-9.768-13.464L-11.904-13.464Q-11.856-13.222-11.684-13.027Q-11.511-12.832-11.268-12.724Q-11.026-12.617-10.776-12.617Q-10.363-12.617-10.168-12.870Q-10.161-12.880-10.111-12.972Q-10.062-13.064-10.019-13.102Q-9.976-13.140-9.894-13.150L-9.768-13.150Q-9.600-13.133-9.549-12.945L-9.549-12.897Q-9.607-12.634-9.809-12.461Q-10.011-12.288-10.284-12.208Q-10.557-12.128-10.824-12.128Q-11.248-12.128-11.632-12.328Q-12.017-12.528-12.251-12.878Q-12.485-13.228-12.485-13.659L-12.485-13.710Q-12.485-14.120-12.270-14.473Q-12.055-14.825-11.697-15.030Q-11.340-15.235-10.930-15.235Q-10.489-15.235-10.180-15.040Q-9.870-14.845-9.710-14.505Q-9.549-14.165-9.549-13.724L-9.549-13.673Q-9.600-13.485-9.768-13.464M-11.897-13.946L-10.123-13.946Q-10.164-14.305-10.373-14.526Q-10.581-14.746-10.930-14.746Q-11.275-14.746-11.544-14.517Q-11.812-14.288-11.897-13.946M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-warn)\" stroke=\"var(--tk-warn)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-warn)\">\u003Cpath fill=\"none\" d=\"M253.745-34.924h56.905v-17.072h-56.905Z\"\u002F>\u003Cg transform=\"translate(285.738 -29.16)\">\u003Cpath d=\"M-14.926-12.128Q-15.332-12.128-15.652-12.347Q-15.972-12.565-16.151-12.919Q-16.330-13.273-16.330-13.673Q-16.330-13.974-16.221-14.254Q-16.112-14.534-15.908-14.753Q-15.705-14.972-15.438-15.093Q-15.172-15.214-14.861-15.214Q-14.413-15.214-14.057-14.934L-14.057-15.949L-14.427-15.949Q-14.611-15.970-14.645-16.158L-14.645-16.236Q-14.611-16.417-14.427-16.438L-13.716-16.438Q-13.541-16.417-13.497-16.236L-13.497-12.651L-13.124-12.651Q-12.943-12.630-12.909-12.449L-12.909-12.370Q-12.943-12.183-13.124-12.162L-13.839-12.162Q-14.013-12.183-14.057-12.370L-14.057-12.483Q-14.228-12.316-14.457-12.222Q-14.686-12.128-14.926-12.128M-14.891-12.617Q-14.577-12.617-14.357-12.852Q-14.136-13.088-14.057-13.416L-14.057-14.144Q-14.109-14.308-14.220-14.440Q-14.331-14.572-14.486-14.649Q-14.642-14.725-14.813-14.725Q-15.083-14.725-15.302-14.577Q-15.520-14.428-15.647-14.179Q-15.773-13.929-15.773-13.666Q-15.773-13.273-15.524-12.945Q-15.274-12.617-14.891-12.617M-9.768-13.464L-11.904-13.464Q-11.856-13.222-11.684-13.027Q-11.511-12.832-11.268-12.724Q-11.026-12.617-10.776-12.617Q-10.363-12.617-10.168-12.870Q-10.161-12.880-10.111-12.972Q-10.062-13.064-10.019-13.102Q-9.976-13.140-9.894-13.150L-9.768-13.150Q-9.600-13.133-9.549-12.945L-9.549-12.897Q-9.607-12.634-9.809-12.461Q-10.011-12.288-10.284-12.208Q-10.557-12.128-10.824-12.128Q-11.248-12.128-11.632-12.328Q-12.017-12.528-12.251-12.878Q-12.485-13.228-12.485-13.659L-12.485-13.710Q-12.485-14.120-12.270-14.473Q-12.055-14.825-11.697-15.030Q-11.340-15.235-10.930-15.235Q-10.489-15.235-10.180-15.040Q-9.870-14.845-9.710-14.505Q-9.549-14.165-9.549-13.724L-9.549-13.673Q-9.600-13.485-9.768-13.464M-11.897-13.946L-10.123-13.946Q-10.164-14.305-10.373-14.526Q-10.581-14.746-10.930-14.746Q-11.275-14.746-11.544-14.517Q-11.812-14.288-11.897-13.946M-8.637-13.673Q-8.637-14.093-8.423-14.455Q-8.209-14.818-7.845-15.026Q-7.481-15.235-7.061-15.235Q-6.576-15.235-6.244-15.139Q-5.912-15.043-5.912-14.688Q-5.912-14.541-6.012-14.433Q-6.111-14.326-6.261-14.326Q-6.411-14.326-6.516-14.426Q-6.620-14.527-6.620-14.674L-6.620-14.725Q-6.760-14.746-7.054-14.746Q-7.341-14.746-7.575-14.597Q-7.809-14.449-7.943-14.201Q-8.076-13.953-8.076-13.673Q-8.076-13.392-7.926-13.146Q-7.775-12.900-7.526-12.758Q-7.276-12.617-6.989-12.617Q-6.716-12.617-6.605-12.707Q-6.494-12.798-6.391-12.964Q-6.288-13.129-6.186-13.143L-6.039-13.143Q-5.947-13.133-5.890-13.073Q-5.834-13.013-5.834-12.924Q-5.834-12.883-5.851-12.849Q-5.947-12.593-6.124-12.435Q-6.302-12.278-6.543-12.203Q-6.784-12.128-7.061-12.128Q-7.485-12.128-7.849-12.336Q-8.213-12.545-8.425-12.897Q-8.637-13.249-8.637-13.673M-3.554-12.128Q-3.968-12.128-4.304-12.341Q-4.641-12.555-4.836-12.914Q-5.031-13.273-5.031-13.673Q-5.031-13.974-4.921-14.256Q-4.812-14.537-4.610-14.760Q-4.409-14.982-4.140-15.108Q-3.872-15.235-3.554-15.235Q-3.236-15.235-2.963-15.107Q-2.689-14.978-2.494-14.763Q-2.300-14.548-2.189-14.267Q-2.077-13.987-2.077-13.673Q-2.077-13.273-2.274-12.912Q-2.471-12.552-2.807-12.340Q-3.144-12.128-3.554-12.128M-3.554-12.617Q-3.147-12.617-2.893-12.962Q-2.638-13.307-2.638-13.731Q-2.638-13.987-2.756-14.221Q-2.874-14.455-3.084-14.601Q-3.294-14.746-3.554-14.746Q-3.821-14.746-4.029-14.601Q-4.238-14.455-4.356-14.221Q-4.473-13.987-4.473-13.731Q-4.473-13.310-4.217-12.964Q-3.961-12.617-3.554-12.617M-0.064-12.128Q-0.471-12.128-0.791-12.347Q-1.110-12.565-1.290-12.919Q-1.469-13.273-1.469-13.673Q-1.469-13.974-1.360-14.254Q-1.250-14.534-1.047-14.753Q-0.844-14.972-0.577-15.093Q-0.310-15.214 0.001-15.214Q0.448-15.214 0.804-14.934L0.804-15.949L0.435-15.949Q0.250-15.970 0.216-16.158L0.216-16.236Q0.250-16.417 0.435-16.438L1.146-16.438Q1.320-16.417 1.364-16.236L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.370L0.804-12.483Q0.633-12.316 0.404-12.222Q0.175-12.128-0.064-12.128M-0.030-12.617Q0.284-12.617 0.505-12.852Q0.725-13.088 0.804-13.416L0.804-14.144Q0.753-14.308 0.642-14.440Q0.530-14.572 0.375-14.649Q0.219-14.725 0.048-14.725Q-0.222-14.725-0.440-14.577Q-0.659-14.428-0.785-14.179Q-0.912-13.929-0.912-13.666Q-0.912-13.273-0.662-12.945Q-0.413-12.617-0.030-12.617M5.093-13.464L2.957-13.464Q3.005-13.222 3.178-13.027Q3.350-12.832 3.593-12.724Q3.836-12.617 4.085-12.617Q4.499-12.617 4.694-12.870Q4.700-12.880 4.750-12.972Q4.799-13.064 4.842-13.102Q4.885-13.140 4.967-13.150L5.093-13.150Q5.261-13.133 5.312-12.945L5.312-12.897Q5.254-12.634 5.052-12.461Q4.851-12.288 4.577-12.208Q4.304-12.128 4.037-12.128Q3.613-12.128 3.229-12.328Q2.844-12.528 2.610-12.878Q2.376-13.228 2.376-13.659L2.376-13.710Q2.376-14.120 2.591-14.473Q2.807-14.825 3.164-15.030Q3.521-15.235 3.931-15.235Q4.372-15.235 4.682-15.040Q4.991-14.845 5.152-14.505Q5.312-14.165 5.312-13.724L5.312-13.673Q5.261-13.485 5.093-13.464M2.964-13.946L4.738-13.946Q4.697-14.305 4.488-14.526Q4.280-14.746 3.931-14.746Q3.586-14.746 3.318-14.517Q3.049-14.288 2.964-13.946M5.931-12.370L5.931-12.449Q5.982-12.630 6.150-12.651L6.772-12.651L6.772-14.688L6.150-14.688Q5.979-14.708 5.931-14.900L5.931-14.975Q5.982-15.160 6.150-15.180L7.113-15.180Q7.288-15.163 7.332-14.975L7.332-14.688Q7.561-14.937 7.872-15.076Q8.183-15.214 8.522-15.214Q8.778-15.214 8.983-15.096Q9.188-14.978 9.188-14.746Q9.188-14.599 9.092-14.496Q8.997-14.394 8.850-14.394Q8.716-14.394 8.616-14.491Q8.515-14.589 8.515-14.725Q8.187-14.725 7.912-14.549Q7.636-14.373 7.484-14.081Q7.332-13.789 7.332-13.457L7.332-12.651L8.159-12.651Q8.340-12.630 8.375-12.449L8.375-12.370Q8.340-12.183 8.159-12.162L6.150-12.162Q5.982-12.183 5.931-12.370\" fill=\"var(--tk-warn)\" stroke=\"var(--tk-warn)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg transform=\"translate(287.598 -52.9)\">\u003Cpath d=\"M-14.700-12.128Q-15.114-12.128-15.450-12.341Q-15.787-12.555-15.982-12.914Q-16.177-13.273-16.177-13.673Q-16.177-13.974-16.067-14.256Q-15.958-14.537-15.756-14.760Q-15.555-14.982-15.286-15.108Q-15.018-15.235-14.700-15.235Q-14.382-15.235-14.109-15.107Q-13.835-14.978-13.640-14.763Q-13.446-14.548-13.335-14.267Q-13.223-13.987-13.223-13.673Q-13.223-13.273-13.420-12.912Q-13.617-12.552-13.953-12.340Q-14.290-12.128-14.700-12.128M-14.700-12.617Q-14.293-12.617-14.039-12.962Q-13.784-13.307-13.784-13.731Q-13.784-13.987-13.902-14.221Q-14.020-14.455-14.230-14.601Q-14.440-14.746-14.700-14.746Q-14.967-14.746-15.175-14.601Q-15.384-14.455-15.502-14.221Q-15.619-13.987-15.619-13.731Q-15.619-13.310-15.363-12.964Q-15.107-12.617-14.700-12.617M-12.191-12.911L-12.191-14.688L-12.560-14.688Q-12.742-14.708-12.779-14.900L-12.779-14.975Q-12.738-15.160-12.560-15.180L-11.846-15.180Q-11.675-15.160-11.631-14.975L-11.631-12.938Q-11.631-12.733-11.482-12.675Q-11.333-12.617-11.084-12.617Q-10.903-12.617-10.732-12.683Q-10.561-12.750-10.452-12.881Q-10.342-13.013-10.342-13.198L-10.342-14.688L-10.711-14.688Q-10.896-14.708-10.930-14.900L-10.930-14.975Q-10.896-15.160-10.711-15.180L-10-15.180Q-9.826-15.160-9.782-14.975L-9.782-12.651L-9.409-12.651Q-9.228-12.630-9.194-12.449L-9.194-12.370Q-9.228-12.183-9.409-12.162L-10.123-12.162Q-10.298-12.183-10.342-12.357Q-10.694-12.128-11.139-12.128Q-11.344-12.128-11.532-12.164Q-11.720-12.200-11.865-12.288Q-12.010-12.377-12.101-12.533Q-12.191-12.688-12.191-12.911M-8.076-13.129L-8.076-14.688L-8.732-14.688Q-8.907-14.708-8.951-14.900L-8.951-14.975Q-8.907-15.160-8.732-15.180L-8.076-15.180L-8.076-15.836Q-8.032-16.017-7.857-16.041L-7.731-16.041Q-7.560-16.017-7.515-15.836L-7.515-15.180L-6.326-15.180Q-6.159-15.163-6.107-14.975L-6.107-14.900Q-6.155-14.708-6.326-14.688L-7.515-14.688L-7.515-13.157Q-7.515-12.617-7.013-12.617Q-6.794-12.617-6.651-12.779Q-6.507-12.941-6.507-13.157Q-6.507-13.239-6.444-13.300Q-6.381-13.362-6.292-13.372L-6.165-13.372Q-5.991-13.351-5.947-13.170L-5.947-13.129Q-5.947-12.846-6.107-12.615Q-6.268-12.384-6.524-12.256Q-6.781-12.128-7.061-12.128Q-7.509-12.128-7.792-12.400Q-8.076-12.671-8.076-13.129M-5.348-10.812L-5.348-10.887Q-5.311-11.079-5.130-11.099L-4.761-11.099L-4.761-14.688L-5.130-14.688Q-5.311-14.708-5.348-14.900L-5.348-14.975Q-5.307-15.160-5.130-15.180L-4.415-15.180Q-4.244-15.163-4.200-14.975L-4.200-14.913Q-4.015-15.060-3.785-15.137Q-3.554-15.214-3.318-15.214Q-3.021-15.214-2.761-15.088Q-2.501-14.961-2.313-14.741Q-2.125-14.520-2.025-14.247Q-1.924-13.974-1.924-13.673Q-1.924-13.266-2.122-12.907Q-2.320-12.548-2.659-12.338Q-2.997-12.128-3.407-12.128Q-3.862-12.128-4.200-12.449L-4.200-11.099L-3.827-11.099Q-3.646-11.079-3.612-10.887L-3.612-10.812Q-3.646-10.627-3.827-10.607L-5.130-10.607Q-5.307-10.627-5.348-10.812M-3.445-12.617Q-3.175-12.617-2.956-12.765Q-2.737-12.914-2.611-13.160Q-2.484-13.406-2.484-13.673Q-2.484-13.926-2.594-14.170Q-2.703-14.414-2.906-14.570Q-3.110-14.725-3.373-14.725Q-3.653-14.725-3.882-14.563Q-4.111-14.401-4.200-14.138L-4.200-13.392Q-4.121-13.071-3.928-12.844Q-3.735-12.617-3.445-12.617M-1.045-12.911L-1.045-14.688L-1.414-14.688Q-1.596-14.708-1.633-14.900L-1.633-14.975Q-1.592-15.160-1.414-15.180L-0.700-15.180Q-0.529-15.160-0.485-14.975L-0.485-12.938Q-0.485-12.733-0.336-12.675Q-0.187-12.617 0.062-12.617Q0.243-12.617 0.414-12.683Q0.585-12.750 0.694-12.881Q0.804-13.013 0.804-13.198L0.804-14.688L0.435-14.688Q0.250-14.708 0.216-14.900L0.216-14.975Q0.250-15.160 0.435-15.180L1.146-15.180Q1.320-15.160 1.364-14.975L1.364-12.651L1.737-12.651Q1.918-12.630 1.952-12.449L1.952-12.370Q1.918-12.183 1.737-12.162L1.023-12.162Q0.848-12.183 0.804-12.357Q0.452-12.128 0.007-12.128Q-0.198-12.128-0.386-12.164Q-0.574-12.200-0.719-12.288Q-0.864-12.377-0.955-12.533Q-1.045-12.688-1.045-12.911M3.070-13.129L3.070-14.688L2.414-14.688Q2.239-14.708 2.195-14.900L2.195-14.975Q2.239-15.160 2.414-15.180L3.070-15.180L3.070-15.836Q3.114-16.017 3.289-16.041L3.415-16.041Q3.586-16.017 3.631-15.836L3.631-15.180L4.820-15.180Q4.987-15.163 5.039-14.975L5.039-14.900Q4.991-14.708 4.820-14.688L3.631-14.688L3.631-13.157Q3.631-12.617 4.133-12.617Q4.352-12.617 4.495-12.779Q4.639-12.941 4.639-13.157Q4.639-13.239 4.702-13.300Q4.765-13.362 4.854-13.372L4.981-13.372Q5.155-13.351 5.199-13.170L5.199-13.129Q5.199-12.846 5.039-12.615Q4.878-12.384 4.622-12.256Q4.365-12.128 4.085-12.128Q3.637-12.128 3.354-12.400Q3.070-12.671 3.070-13.129\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M185.458 2.715v-9.231\"\u002F>\u003Cpath stroke=\"none\" d=\"m185.458-9.116-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M185.458-26.588v-5.536\"\u002F>\u003Cpath stroke=\"none\" d=\"m185.458-34.724-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M282.198 1.507v-8.023\"\u002F>\u003Cpath stroke=\"none\" d=\"m282.198-9.116-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M282.198-26.588v-5.536\"\u002F>\u003Cpath stroke=\"none\" d=\"m282.198-34.724-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M282.198-52.196v-5.178\"\u002F>\u003Cpath stroke=\"none\" d=\"m282.198-59.974-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M214.11-43.46h36.835\"\u002F>\u003Cpath stroke=\"none\" d=\"m253.545-43.46-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M233.828-43.46v25.608h17.117\"\u002F>\u003Cpath stroke=\"none\" d=\"m253.545-17.852-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(218.508 45.124)\">\u003Cpath d=\"M-13.044-13.650L-15.486-13.650Q-15.431-13.373-15.234-13.150Q-15.036-12.928-14.759-12.805Q-14.482-12.682-14.197-12.682Q-13.724-12.682-13.501-12.971Q-13.494-12.982-13.437-13.088Q-13.380-13.193-13.331-13.236Q-13.283-13.279-13.189-13.291L-13.044-13.291Q-12.853-13.271-12.794-13.057L-12.794-13.002Q-12.861-12.701-13.091-12.504Q-13.322-12.307-13.634-12.215Q-13.947-12.123-14.251-12.123Q-14.736-12.123-15.175-12.351Q-15.615-12.580-15.882-12.980Q-16.150-13.381-16.150-13.873L-16.150-13.932Q-16.150-14.400-15.904-14.803Q-15.658-15.205-15.249-15.439Q-14.841-15.674-14.372-15.674Q-13.869-15.674-13.515-15.451Q-13.161-15.228-12.978-14.840Q-12.794-14.451-12.794-13.947L-12.794-13.889Q-12.853-13.674-13.044-13.650M-15.478-14.201L-13.451-14.201Q-13.497-14.611-13.736-14.863Q-13.974-15.115-14.372-15.115Q-14.767-15.115-15.074-14.853Q-15.380-14.592-15.478-14.201M-12.240-12.400L-12.240-12.490Q-12.197-12.697-11.990-12.721L-11.568-12.721L-11.568-15.049L-11.990-15.049Q-12.197-15.072-12.240-15.291L-12.240-15.377Q-12.193-15.588-11.990-15.611L-11.173-15.611Q-10.978-15.588-10.927-15.377L-10.927-15.291L-10.935-15.267Q-10.708-15.447-10.435-15.549Q-10.161-15.650-9.869-15.650Q-9.521-15.650-9.283-15.510Q-9.044-15.369-8.929-15.111Q-8.814-14.853-8.814-14.498L-8.814-12.721L-8.388-12.721Q-8.181-12.697-8.142-12.490L-8.142-12.400Q-8.181-12.185-8.388-12.162L-9.783-12.162Q-9.978-12.185-10.029-12.400L-10.029-12.490Q-9.978-12.701-9.783-12.721L-9.454-12.721L-9.454-14.467Q-9.454-14.775-9.544-14.933Q-9.634-15.092-9.927-15.092Q-10.197-15.092-10.425-14.961Q-10.654-14.830-10.790-14.601Q-10.927-14.373-10.927-14.107L-10.927-12.721L-10.501-12.721Q-10.294-12.697-10.255-12.490L-10.255-12.400Q-10.294-12.185-10.501-12.162L-11.990-12.162Q-12.197-12.185-12.240-12.400M-7.505-13.889Q-7.505-14.369-7.261-14.783Q-7.017-15.197-6.601-15.435Q-6.185-15.674-5.704-15.674Q-5.150-15.674-4.771-15.564Q-4.392-15.455-4.392-15.049Q-4.392-14.881-4.505-14.758Q-4.619-14.635-4.790-14.635Q-4.962-14.635-5.081-14.750Q-5.201-14.865-5.201-15.033L-5.201-15.092Q-5.361-15.115-5.697-15.115Q-6.025-15.115-6.292-14.945Q-6.560-14.775-6.712-14.492Q-6.865-14.209-6.865-13.889Q-6.865-13.568-6.693-13.287Q-6.521-13.006-6.236-12.844Q-5.951-12.682-5.622-12.682Q-5.310-12.682-5.183-12.785Q-5.056-12.889-4.939-13.078Q-4.822-13.267-4.704-13.283L-4.536-13.283Q-4.431-13.271-4.367-13.203Q-4.302-13.135-4.302-13.033Q-4.302-12.986-4.322-12.947Q-4.431-12.654-4.634-12.475Q-4.837-12.295-5.113-12.209Q-5.388-12.123-5.704-12.123Q-6.189-12.123-6.605-12.361Q-7.021-12.600-7.263-13.002Q-7.505-13.404-7.505-13.889M-1.697-12.123Q-2.169-12.123-2.554-12.367Q-2.939-12.611-3.161-13.021Q-3.384-13.432-3.384-13.889Q-3.384-14.232-3.259-14.555Q-3.134-14.877-2.904-15.131Q-2.673-15.385-2.367-15.529Q-2.060-15.674-1.697-15.674Q-1.333-15.674-1.021-15.527Q-0.708-15.381-0.486-15.135Q-0.263-14.889-0.136-14.568Q-0.009-14.248-0.009-13.889Q-0.009-13.432-0.234-13.019Q-0.458-12.607-0.843-12.365Q-1.228-12.123-1.697-12.123M-1.697-12.682Q-1.232-12.682-0.941-13.076Q-0.650-13.471-0.650-13.955Q-0.650-14.248-0.785-14.516Q-0.919-14.783-1.160-14.949Q-1.400-15.115-1.697-15.115Q-2.001-15.115-2.240-14.949Q-2.478-14.783-2.613-14.516Q-2.747-14.248-2.747-13.955Q-2.747-13.475-2.454-13.078Q-2.161-12.682-1.697-12.682M2.292-12.123Q1.827-12.123 1.462-12.373Q1.096-12.623 0.891-13.027Q0.686-13.432 0.686-13.889Q0.686-14.232 0.811-14.553Q0.936-14.873 1.169-15.123Q1.401-15.373 1.706-15.512Q2.010-15.650 2.366-15.650Q2.878-15.650 3.284-15.330L3.284-16.490L2.862-16.490Q2.651-16.514 2.612-16.728L2.612-16.818Q2.651-17.025 2.862-17.049L3.674-17.049Q3.874-17.025 3.924-16.818L3.924-12.721L4.350-12.721Q4.557-12.697 4.596-12.490L4.596-12.400Q4.557-12.185 4.350-12.162L3.534-12.162Q3.335-12.185 3.284-12.400L3.284-12.529Q3.089-12.338 2.827-12.230Q2.565-12.123 2.292-12.123M2.331-12.682Q2.690-12.682 2.942-12.951Q3.194-13.221 3.284-13.596L3.284-14.428Q3.225-14.615 3.098-14.766Q2.971-14.916 2.794-15.004Q2.616-15.092 2.421-15.092Q2.112-15.092 1.862-14.922Q1.612-14.752 1.467-14.467Q1.323-14.182 1.323-13.881Q1.323-13.432 1.608-13.057Q1.893-12.682 2.331-12.682M8.186-13.650L5.745-13.650Q5.799-13.373 5.997-13.150Q6.194-12.928 6.471-12.805Q6.749-12.682 7.034-12.682Q7.506-12.682 7.729-12.971Q7.737-12.982 7.794-13.088Q7.850-13.193 7.899-13.236Q7.948-13.279 8.042-13.291L8.186-13.291Q8.378-13.271 8.436-13.057L8.436-13.002Q8.370-12.701 8.139-12.504Q7.909-12.307 7.596-12.215Q7.284-12.123 6.979-12.123Q6.495-12.123 6.055-12.351Q5.616-12.580 5.348-12.980Q5.081-13.381 5.081-13.873L5.081-13.932Q5.081-14.400 5.327-14.803Q5.573-15.205 5.981-15.439Q6.389-15.674 6.858-15.674Q7.362-15.674 7.715-15.451Q8.069-15.228 8.253-14.840Q8.436-14.451 8.436-13.947L8.436-13.889Q8.378-13.674 8.186-13.650M5.753-14.201L7.780-14.201Q7.733-14.611 7.495-14.863Q7.256-15.115 6.858-15.115Q6.464-15.115 6.157-14.853Q5.850-14.592 5.753-14.201M9.143-12.400L9.143-12.490Q9.202-12.697 9.393-12.721L10.104-12.721L10.104-15.049L9.393-15.049Q9.198-15.072 9.143-15.291L9.143-15.377Q9.202-15.588 9.393-15.611L10.495-15.611Q10.694-15.592 10.745-15.377L10.745-15.049Q11.006-15.334 11.362-15.492Q11.717-15.650 12.104-15.650Q12.397-15.650 12.631-15.516Q12.866-15.381 12.866-15.115Q12.866-14.947 12.756-14.830Q12.647-14.713 12.479-14.713Q12.327-14.713 12.212-14.824Q12.096-14.935 12.096-15.092Q11.721-15.092 11.407-14.891Q11.092-14.689 10.919-14.355Q10.745-14.021 10.745-13.642L10.745-12.721L11.690-12.721Q11.897-12.697 11.936-12.490L11.936-12.400Q11.897-12.185 11.690-12.162L9.393-12.162Q9.202-12.185 9.143-12.400M16.663-14.299L13.921-14.299Q13.796-14.310 13.710-14.396Q13.624-14.482 13.624-14.611Q13.624-14.740 13.710-14.822Q13.796-14.904 13.921-14.916L16.663-14.916Q16.788-14.904 16.870-14.822Q16.952-14.740 16.952-14.611Q16.952-14.482 16.870-14.396Q16.788-14.310 16.663-14.299M19.276-12.123Q18.811-12.123 18.446-12.373Q18.081-12.623 17.876-13.027Q17.671-13.432 17.671-13.889Q17.671-14.232 17.796-14.553Q17.921-14.873 18.153-15.123Q18.385-15.373 18.690-15.512Q18.995-15.650 19.350-15.650Q19.862-15.650 20.268-15.330L20.268-16.490L19.846-16.490Q19.635-16.514 19.596-16.728L19.596-16.818Q19.635-17.025 19.846-17.049L20.659-17.049Q20.858-17.025 20.909-16.818L20.909-12.721L21.335-12.721Q21.542-12.697 21.581-12.490L21.581-12.400Q21.542-12.185 21.335-12.162L20.518-12.162Q20.319-12.185 20.268-12.400L20.268-12.529Q20.073-12.338 19.811-12.230Q19.549-12.123 19.276-12.123M19.315-12.682Q19.674-12.682 19.926-12.951Q20.178-13.221 20.268-13.596L20.268-14.428Q20.210-14.615 20.083-14.766Q19.956-14.916 19.778-15.004Q19.600-15.092 19.405-15.092Q19.096-15.092 18.846-14.922Q18.596-14.752 18.452-14.467Q18.307-14.182 18.307-13.881Q18.307-13.432 18.592-13.057Q18.878-12.682 19.315-12.682M25.171-13.650L22.729-13.650Q22.784-13.373 22.981-13.150Q23.178-12.928 23.456-12.805Q23.733-12.682 24.018-12.682Q24.491-12.682 24.714-12.971Q24.721-12.982 24.778-13.088Q24.835-13.193 24.883-13.236Q24.932-13.279 25.026-13.291L25.171-13.291Q25.362-13.271 25.421-13.057L25.421-13.002Q25.354-12.701 25.124-12.504Q24.893-12.307 24.581-12.215Q24.268-12.123 23.964-12.123Q23.479-12.123 23.040-12.351Q22.600-12.580 22.333-12.980Q22.065-13.381 22.065-13.873L22.065-13.932Q22.065-14.400 22.311-14.803Q22.557-15.205 22.965-15.439Q23.374-15.674 23.842-15.674Q24.346-15.674 24.700-15.451Q25.053-15.228 25.237-14.840Q25.421-14.451 25.421-13.947L25.421-13.889Q25.362-13.674 25.171-13.650M22.737-14.201L24.764-14.201Q24.717-14.611 24.479-14.863Q24.241-15.115 23.842-15.115Q23.448-15.115 23.141-14.853Q22.835-14.592 22.737-14.201M26.464-13.889Q26.464-14.369 26.708-14.783Q26.952-15.197 27.368-15.435Q27.784-15.674 28.264-15.674Q28.819-15.674 29.198-15.564Q29.577-15.455 29.577-15.049Q29.577-14.881 29.464-14.758Q29.350-14.635 29.178-14.635Q29.006-14.635 28.887-14.750Q28.768-14.865 28.768-15.033L28.768-15.092Q28.608-15.115 28.272-15.115Q27.944-15.115 27.676-14.945Q27.409-14.775 27.256-14.492Q27.104-14.209 27.104-13.889Q27.104-13.568 27.276-13.287Q27.448-13.006 27.733-12.844Q28.018-12.682 28.346-12.682Q28.659-12.682 28.786-12.785Q28.913-12.889 29.030-13.078Q29.147-13.267 29.264-13.283L29.432-13.283Q29.538-13.271 29.602-13.203Q29.667-13.135 29.667-13.033Q29.667-12.986 29.647-12.947Q29.538-12.654 29.335-12.475Q29.131-12.295 28.856-12.209Q28.581-12.123 28.264-12.123Q27.780-12.123 27.364-12.361Q26.948-12.600 26.706-13.002Q26.464-13.404 26.464-13.889M32.272-12.123Q31.799-12.123 31.415-12.367Q31.030-12.611 30.807-13.021Q30.585-13.432 30.585-13.889Q30.585-14.232 30.710-14.555Q30.835-14.877 31.065-15.131Q31.296-15.385 31.602-15.529Q31.909-15.674 32.272-15.674Q32.635-15.674 32.948-15.527Q33.260-15.381 33.483-15.135Q33.706-14.889 33.833-14.568Q33.960-14.248 33.960-13.889Q33.960-13.432 33.735-13.019Q33.510-12.607 33.126-12.365Q32.741-12.123 32.272-12.123M32.272-12.682Q32.737-12.682 33.028-13.076Q33.319-13.471 33.319-13.955Q33.319-14.248 33.184-14.516Q33.049-14.783 32.809-14.949Q32.569-15.115 32.272-15.115Q31.967-15.115 31.729-14.949Q31.491-14.783 31.356-14.516Q31.221-14.248 31.221-13.955Q31.221-13.475 31.514-13.078Q31.807-12.682 32.272-12.682M36.260-12.123Q35.796-12.123 35.430-12.373Q35.065-12.623 34.860-13.027Q34.655-13.432 34.655-13.889Q34.655-14.232 34.780-14.553Q34.905-14.873 35.137-15.123Q35.370-15.373 35.674-15.512Q35.979-15.650 36.335-15.650Q36.846-15.650 37.253-15.330L37.253-16.490L36.831-16.490Q36.620-16.514 36.581-16.728L36.581-16.818Q36.620-17.025 36.831-17.049L37.643-17.049Q37.842-17.025 37.893-16.818L37.893-12.721L38.319-12.721Q38.526-12.697 38.565-12.490L38.565-12.400Q38.526-12.185 38.319-12.162L37.503-12.162Q37.303-12.185 37.253-12.400L37.253-12.529Q37.057-12.338 36.796-12.230Q36.534-12.123 36.260-12.123M36.299-12.682Q36.659-12.682 36.911-12.951Q37.163-13.221 37.253-13.596L37.253-14.428Q37.194-14.615 37.067-14.766Q36.940-14.916 36.762-15.004Q36.585-15.092 36.389-15.092Q36.081-15.092 35.831-14.922Q35.581-14.752 35.436-14.467Q35.292-14.182 35.292-13.881Q35.292-13.432 35.577-13.057Q35.862-12.682 36.299-12.682M42.155-13.650L39.714-13.650Q39.768-13.373 39.965-13.150Q40.163-12.928 40.440-12.805Q40.717-12.682 41.003-12.682Q41.475-12.682 41.698-12.971Q41.706-12.982 41.762-13.088Q41.819-13.193 41.868-13.236Q41.917-13.279 42.010-13.291L42.155-13.291Q42.346-13.271 42.405-13.057L42.405-13.002Q42.339-12.701 42.108-12.504Q41.878-12.307 41.565-12.215Q41.253-12.123 40.948-12.123Q40.464-12.123 40.024-12.351Q39.585-12.580 39.317-12.980Q39.049-13.381 39.049-13.873L39.049-13.932Q39.049-14.400 39.296-14.803Q39.542-15.205 39.950-15.439Q40.358-15.674 40.827-15.674Q41.331-15.674 41.684-15.451Q42.038-15.228 42.221-14.840Q42.405-14.451 42.405-13.947L42.405-13.889Q42.346-13.674 42.155-13.650M39.721-14.201L41.749-14.201Q41.702-14.611 41.464-14.863Q41.225-15.115 40.827-15.115Q40.432-15.115 40.126-14.853Q39.819-14.592 39.721-14.201M43.112-12.400L43.112-12.490Q43.171-12.697 43.362-12.721L44.073-12.721L44.073-15.049L43.362-15.049Q43.167-15.072 43.112-15.291L43.112-15.377Q43.171-15.588 43.362-15.611L44.464-15.611Q44.663-15.592 44.714-15.377L44.714-15.049Q44.975-15.334 45.331-15.492Q45.686-15.650 46.073-15.650Q46.366-15.650 46.600-15.516Q46.835-15.381 46.835-15.115Q46.835-14.947 46.725-14.830Q46.616-14.713 46.448-14.713Q46.296-14.713 46.180-14.824Q46.065-14.935 46.065-15.092Q45.690-15.092 45.376-14.891Q45.061-14.689 44.887-14.355Q44.714-14.021 44.714-13.642L44.714-12.721L45.659-12.721Q45.866-12.697 45.905-12.490L45.905-12.400Q45.866-12.185 45.659-12.162L43.362-12.162Q43.171-12.185 43.112-12.400\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"7\">\u003Cg transform=\"translate(226.212 58.558)\">\u003Cpath d=\"M-13.832-11.601Q-14.297-11.871-14.647-12.299Q-14.997-12.726-15.182-13.245Q-15.367-13.765-15.367-14.305Q-15.367-14.845-15.184-15.360Q-15.001-15.874-14.654-16.294Q-14.307-16.715-13.839-16.998Q-13.777-17.019-13.750-17.019L-13.671-17.019Q-13.586-17.009-13.528-16.951Q-13.470-16.892-13.470-16.804Q-13.470-16.677-13.558-16.622Q-13.952-16.370-14.237-16.006Q-14.522-15.641-14.664-15.211Q-14.806-14.780-14.806-14.305Q-14.806-13.950-14.722-13.611Q-14.639-13.273-14.483-12.979Q-14.327-12.685-14.100-12.437Q-13.873-12.189-13.569-11.988Q-13.470-11.919-13.470-11.800Q-13.470-11.714-13.528-11.653Q-13.586-11.591-13.671-11.581L-13.750-11.581Q-13.801-11.581-13.832-11.601M-11.911-12.370L-11.911-12.449Q-11.860-12.630-11.692-12.651L-11.265-12.651L-11.265-15.949L-12.092-15.949L-12.092-15.501Q-12.133-15.313-12.307-15.289L-12.434-15.289Q-12.608-15.313-12.653-15.501L-12.653-16.236Q-12.608-16.417-12.434-16.438L-9.535-16.438Q-9.365-16.421-9.320-16.236L-9.320-15.501Q-9.361-15.313-9.535-15.289L-9.662-15.289Q-9.836-15.313-9.881-15.501L-9.881-15.949L-10.704-15.949L-10.704-12.651L-10.277-12.651Q-10.106-12.630-10.062-12.449L-10.062-12.370Q-10.106-12.183-10.277-12.162L-11.692-12.162Q-11.860-12.183-11.911-12.370M-8.131-12.931Q-8.028-12.753-7.823-12.668Q-7.618-12.582-7.389-12.582Q-7.129-12.582-6.890-12.695Q-6.651-12.808-6.499-13.015Q-6.347-13.222-6.347-13.485Q-6.347-13.707-6.451-13.919Q-6.555-14.131-6.743-14.259Q-6.931-14.387-7.167-14.387Q-7.697-14.387-7.991-14.107Q-8.059-14.032-8.107-13.991Q-8.155-13.950-8.230-13.939L-8.319-13.939Q-8.493-13.960-8.537-14.151L-8.537-16.236Q-8.493-16.417-8.319-16.438L-6.254-16.438Q-6.083-16.421-6.039-16.236L-6.039-16.158Q-6.083-15.970-6.254-15.949L-7.977-15.949L-7.977-14.702Q-7.621-14.879-7.167-14.879Q-6.791-14.879-6.471-14.690Q-6.152-14.500-5.969-14.177Q-5.786-13.854-5.786-13.485Q-5.786-13.071-6.017-12.757Q-6.247-12.442-6.618-12.268Q-6.989-12.094-7.389-12.094Q-7.611-12.094-7.854-12.159Q-8.097-12.224-8.302-12.360Q-8.507-12.497-8.630-12.702Q-8.753-12.907-8.753-13.157Q-8.753-13.304-8.652-13.411Q-8.551-13.519-8.397-13.519Q-8.326-13.519-8.264-13.493Q-8.202-13.468-8.153-13.420Q-8.103-13.372-8.076-13.305Q-8.049-13.239-8.049-13.170Q-8.049-13.030-8.131-12.931M-3.906-11.188Q-4.005-11.188-4.084-11.266Q-4.162-11.345-4.162-11.441Q-4.162-11.595-3.995-11.660Q-3.804-11.704-3.653-11.842Q-3.503-11.981-3.445-12.176Q-3.465-12.176-3.493-12.162L-3.547-12.162Q-3.749-12.162-3.894-12.304Q-4.039-12.446-4.039-12.651Q-4.039-12.856-3.896-12.996Q-3.752-13.136-3.547-13.136Q-3.363-13.136-3.219-13.030Q-3.076-12.924-2.997-12.755Q-2.918-12.586-2.918-12.401Q-2.918-11.984-3.180-11.644Q-3.441-11.304-3.848-11.195Q-3.869-11.188-3.906-11.188\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(226.212 58.558)\">\u003Cpath d=\"M2.551-12.336L2.551-13.136Q2.575-13.317 2.759-13.338L2.906-13.338Q3.050-13.317 3.101-13.177Q3.279-12.617 3.914-12.617Q4.096-12.617 4.296-12.647Q4.496-12.678 4.642-12.779Q4.789-12.880 4.789-13.058Q4.789-13.242 4.595-13.341Q4.400-13.440 4.161-13.478L3.549-13.577Q2.551-13.762 2.551-14.394Q2.551-14.647 2.677-14.813Q2.804-14.978 3.014-15.072Q3.224-15.166 3.448-15.201Q3.672-15.235 3.914-15.235Q4.133-15.235 4.302-15.209Q4.472-15.183 4.615-15.115Q4.684-15.218 4.796-15.235L4.865-15.235Q4.950-15.225 5.005-15.170Q5.059-15.115 5.070-15.033L5.070-14.414Q5.059-14.332 5.005-14.274Q4.950-14.216 4.865-14.206L4.718-14.206Q4.636-14.216 4.578-14.274Q4.519-14.332 4.509-14.414Q4.509-14.746 3.901-14.746Q3.597-14.746 3.318-14.674Q3.039-14.602 3.039-14.387Q3.039-14.155 3.627-14.059L4.243-13.953Q4.666-13.881 4.972-13.664Q5.278-13.447 5.278-13.058Q5.278-12.716 5.071-12.504Q4.865-12.292 4.559-12.210Q4.253-12.128 3.914-12.128Q3.409-12.128 3.060-12.350Q2.998-12.241 2.956-12.191Q2.913-12.141 2.821-12.128L2.759-12.128Q2.571-12.148 2.551-12.336M8.826-13.464L6.690-13.464Q6.738-13.222 6.910-13.027Q7.083-12.832 7.326-12.724Q7.568-12.617 7.818-12.617Q8.231-12.617 8.426-12.870Q8.433-12.880 8.483-12.972Q8.532-13.064 8.575-13.102Q8.618-13.140 8.700-13.150L8.826-13.150Q8.994-13.133 9.045-12.945L9.045-12.897Q8.987-12.634 8.785-12.461Q8.583-12.288 8.310-12.208Q8.037-12.128 7.770-12.128Q7.346-12.128 6.962-12.328Q6.577-12.528 6.343-12.878Q6.109-13.228 6.109-13.659L6.109-13.710Q6.109-14.120 6.324-14.473Q6.539-14.825 6.897-15.030Q7.254-15.235 7.664-15.235Q8.105-15.235 8.414-15.040Q8.724-14.845 8.884-14.505Q9.045-14.165 9.045-13.724L9.045-13.673Q8.994-13.485 8.826-13.464M6.697-13.946L8.471-13.946Q8.430-14.305 8.221-14.526Q8.013-14.746 7.664-14.746Q7.319-14.746 7.050-14.517Q6.782-14.288 6.697-13.946M11.492-10.812L11.492-10.887Q11.537-11.079 11.707-11.099L12.114-11.099L12.114-12.497Q11.718-12.128 11.184-12.128Q10.873-12.128 10.607-12.253Q10.340-12.377 10.137-12.596Q9.934-12.815 9.824-13.097Q9.715-13.379 9.715-13.673Q9.715-14.097 9.923-14.447Q10.132-14.797 10.487-15.006Q10.843-15.214 11.260-15.214Q11.752-15.214 12.114-14.872L12.114-15.013Q12.159-15.197 12.333-15.214L12.456-15.214Q12.630-15.194 12.675-15.013L12.675-11.099L13.081-11.099Q13.252-11.079 13.297-10.887L13.297-10.812Q13.252-10.627 13.081-10.607L11.707-10.607Q11.537-10.627 11.492-10.812M11.226-12.617Q11.550-12.617 11.791-12.839Q12.032-13.061 12.114-13.379L12.114-13.919Q12.077-14.127 11.969-14.314Q11.861-14.500 11.689-14.613Q11.516-14.725 11.304-14.725Q11.027-14.725 10.790-14.580Q10.552-14.435 10.414-14.189Q10.275-13.943 10.275-13.666Q10.275-13.259 10.550-12.938Q10.826-12.617 11.226-12.617M13.557-12.370L13.557-12.435Q13.584-12.582 13.673-12.623L14.801-13.557Q15.091-13.799 15.250-13.933Q15.409-14.066 15.580-14.259Q15.751-14.452 15.857-14.671Q15.963-14.890 15.963-15.122Q15.963-15.406 15.809-15.611Q15.655-15.816 15.411-15.917Q15.166-16.017 14.886-16.017Q14.661-16.017 14.461-15.910Q14.261-15.802 14.172-15.614Q14.261-15.498 14.261-15.368Q14.261-15.228 14.156-15.120Q14.052-15.013 13.912-15.013Q13.758-15.013 13.657-15.122Q13.557-15.231 13.557-15.382Q13.557-15.638 13.674-15.850Q13.792-16.062 14.001-16.212Q14.209-16.363 14.444-16.436Q14.678-16.510 14.934-16.510Q15.354-16.510 15.718-16.344Q16.082-16.178 16.303-15.862Q16.523-15.546 16.523-15.122Q16.523-14.821 16.407-14.556Q16.291-14.291 16.094-14.064Q15.898-13.837 15.628-13.608Q15.358-13.379 15.173-13.225L14.466-12.651L15.963-12.651L15.963-12.777Q16.007-12.962 16.182-12.982L16.305-12.982Q16.479-12.965 16.523-12.777L16.523-12.370Q16.479-12.183 16.305-12.162L13.772-12.162Q13.601-12.179 13.557-12.370M17.412-12.336L17.412-13.136Q17.436-13.317 17.621-13.338L17.767-13.338Q17.911-13.317 17.962-13.177Q18.140-12.617 18.776-12.617Q18.957-12.617 19.157-12.647Q19.357-12.678 19.504-12.779Q19.651-12.880 19.651-13.058Q19.651-13.242 19.456-13.341Q19.261-13.440 19.022-13.478L18.410-13.577Q17.412-13.762 17.412-14.394Q17.412-14.647 17.538-14.813Q17.665-14.978 17.875-15.072Q18.085-15.166 18.309-15.201Q18.533-15.235 18.776-15.235Q18.995-15.235 19.164-15.209Q19.333-15.183 19.476-15.115Q19.545-15.218 19.658-15.235L19.726-15.235Q19.811-15.225 19.866-15.170Q19.921-15.115 19.931-15.033L19.931-14.414Q19.921-14.332 19.866-14.274Q19.811-14.216 19.726-14.206L19.579-14.206Q19.497-14.216 19.439-14.274Q19.381-14.332 19.371-14.414Q19.371-14.746 18.762-14.746Q18.458-14.746 18.179-14.674Q17.901-14.602 17.901-14.387Q17.901-14.155 18.489-14.059L19.104-13.953Q19.528-13.881 19.834-13.664Q20.140-13.447 20.140-13.058Q20.140-12.716 19.933-12.504Q19.726-12.292 19.420-12.210Q19.114-12.128 18.776-12.128Q18.270-12.128 17.921-12.350Q17.860-12.241 17.817-12.191Q17.774-12.141 17.682-12.128L17.621-12.128Q17.433-12.148 17.412-12.336M23.687-13.464L21.551-13.464Q21.599-13.222 21.772-13.027Q21.944-12.832 22.187-12.724Q22.430-12.617 22.679-12.617Q23.093-12.617 23.288-12.870Q23.294-12.880 23.344-12.972Q23.393-13.064 23.436-13.102Q23.479-13.140 23.561-13.150L23.687-13.150Q23.855-13.133 23.906-12.945L23.906-12.897Q23.848-12.634 23.646-12.461Q23.445-12.288 23.171-12.208Q22.898-12.128 22.631-12.128Q22.207-12.128 21.823-12.328Q21.438-12.528 21.204-12.878Q20.970-13.228 20.970-13.659L20.970-13.710Q20.970-14.120 21.185-14.473Q21.401-14.825 21.758-15.030Q22.115-15.235 22.525-15.235Q22.966-15.235 23.276-15.040Q23.585-14.845 23.746-14.505Q23.906-14.165 23.906-13.724L23.906-13.673Q23.855-13.485 23.687-13.464M21.558-13.946L23.332-13.946Q23.291-14.305 23.082-14.526Q22.874-14.746 22.525-14.746Q22.180-14.746 21.912-14.517Q21.643-14.288 21.558-13.946M26.353-10.812L26.353-10.887Q26.398-11.079 26.569-11.099L26.976-11.099L26.976-12.497Q26.579-12.128 26.046-12.128Q25.735-12.128 25.468-12.253Q25.202-12.377 24.998-12.596Q24.795-12.815 24.685-13.097Q24.576-13.379 24.576-13.673Q24.576-14.097 24.785-14.447Q24.993-14.797 25.349-15.006Q25.704-15.214 26.121-15.214Q26.613-15.214 26.976-14.872L26.976-15.013Q27.020-15.197 27.194-15.214L27.317-15.214Q27.492-15.194 27.536-15.013L27.536-11.099L27.943-11.099Q28.114-11.079 28.158-10.887L28.158-10.812Q28.114-10.627 27.943-10.607L26.569-10.607Q26.398-10.627 26.353-10.812M26.087-12.617Q26.412-12.617 26.653-12.839Q26.893-13.061 26.976-13.379L26.976-13.919Q26.938-14.127 26.830-14.314Q26.723-14.500 26.550-14.613Q26.377-14.725 26.165-14.725Q25.889-14.725 25.651-14.580Q25.413-14.435 25.275-14.189Q25.137-13.943 25.137-13.666Q25.137-13.259 25.412-12.938Q25.687-12.617 26.087-12.617M28.955-11.581L28.879-11.581Q28.787-11.591 28.727-11.654Q28.667-11.718 28.667-11.800Q28.667-11.923 28.760-11.981Q29.054-12.169 29.289-12.422Q29.525-12.675 29.686-12.979Q29.847-13.283 29.925-13.615Q30.004-13.946 30.004-14.305Q30.004-14.777 29.860-15.207Q29.717-15.638 29.438-16Q29.160-16.363 28.773-16.616Q28.667-16.687 28.667-16.804Q28.667-16.889 28.727-16.949Q28.787-17.009 28.879-17.019L28.955-17.019Q29.002-17.019 29.033-16.998Q29.371-16.804 29.669-16.499Q29.966-16.195 30.159-15.850Q30.352-15.505 30.458-15.115Q30.564-14.725 30.564-14.305Q30.564-13.881 30.458-13.486Q30.352-13.092 30.156-12.745Q29.959-12.398 29.676-12.106Q29.392-11.813 29.040-11.601Q28.978-11.581 28.955-11.581\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">The three families. Encoder-only (BERT) attends bidirectionally; decoder-only (GPT) masks causally; encoder–decoder (T5) joins both halves by cross-attention (green).\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:247.809px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 185.857 291.985\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cpath fill=\"none\" d=\"M-29.187 195.915V-54.47\" style=\"stroke-width:7.398\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"rotate(-90 -70.165 164.827)\">\u003Cpath d=\"M-28.964 184.296L-28.964 184.206Q-28.906 183.999-28.714 183.975L-28.003 183.975L-28.003 181.647L-28.714 181.647Q-28.910 181.624-28.964 181.405L-28.964 181.319Q-28.906 181.108-28.714 181.085L-27.613 181.085Q-27.414 181.104-27.363 181.319L-27.363 181.647Q-27.101 181.362-26.746 181.204Q-26.390 181.046-26.003 181.046Q-25.710 181.046-25.476 181.180Q-25.242 181.315-25.242 181.581Q-25.242 181.749-25.351 181.866Q-25.460 181.983-25.628 181.983Q-25.781 181.983-25.896 181.872Q-26.011 181.761-26.011 181.604Q-26.386 181.604-26.701 181.805Q-27.015 182.007-27.189 182.341Q-27.363 182.675-27.363 183.054L-27.363 183.975L-26.417 183.975Q-26.210 183.999-26.171 184.206L-26.171 184.296Q-26.210 184.511-26.417 184.534L-28.714 184.534Q-28.906 184.511-28.964 184.296M-21.429 183.046L-23.871 183.046Q-23.816 183.323-23.619 183.546Q-23.421 183.768-23.144 183.891Q-22.867 184.014-22.582 184.014Q-22.109 184.014-21.886 183.725Q-21.878 183.714-21.822 183.608Q-21.765 183.503-21.716 183.460Q-21.667 183.417-21.574 183.405L-21.429 183.405Q-21.238 183.425-21.179 183.639L-21.179 183.694Q-21.246 183.995-21.476 184.192Q-21.707 184.389-22.019 184.481Q-22.332 184.573-22.636 184.573Q-23.121 184.573-23.560 184.345Q-24 184.116-24.267 183.716Q-24.535 183.315-24.535 182.823L-24.535 182.764Q-24.535 182.296-24.289 181.893Q-24.042 181.491-23.634 181.257Q-23.226 181.022-22.757 181.022Q-22.253 181.022-21.900 181.245Q-21.546 181.468-21.363 181.856Q-21.179 182.245-21.179 182.749L-21.179 182.807Q-21.238 183.022-21.429 183.046M-23.863 182.495L-21.835 182.495Q-21.882 182.085-22.121 181.833Q-22.359 181.581-22.757 181.581Q-23.152 181.581-23.458 181.843Q-23.765 182.104-23.863 182.495M-20.109 184.335L-20.109 183.421Q-20.082 183.214-19.871 183.190L-19.703 183.190Q-19.539 183.214-19.480 183.374Q-19.277 184.014-18.550 184.014Q-18.343 184.014-18.115 183.979Q-17.886 183.944-17.718 183.829Q-17.550 183.714-17.550 183.511Q-17.550 183.300-17.773 183.186Q-17.996 183.073-18.269 183.030L-18.968 182.917Q-20.109 182.706-20.109 181.983Q-20.109 181.694-19.964 181.505Q-19.820 181.315-19.580 181.208Q-19.339 181.100-19.083 181.061Q-18.828 181.022-18.550 181.022Q-18.300 181.022-18.107 181.052Q-17.914 181.081-17.750 181.159Q-17.671 181.042-17.542 181.022L-17.464 181.022Q-17.367 181.034-17.304 181.096Q-17.242 181.159-17.230 181.253L-17.230 181.960Q-17.242 182.054-17.304 182.120Q-17.367 182.186-17.464 182.198L-17.632 182.198Q-17.726 182.186-17.792 182.120Q-17.859 182.054-17.871 181.960Q-17.871 181.581-18.566 181.581Q-18.914 181.581-19.232 181.663Q-19.550 181.745-19.550 181.991Q-19.550 182.257-18.878 182.366L-18.175 182.487Q-17.691 182.569-17.341 182.817Q-16.992 183.065-16.992 183.511Q-16.992 183.901-17.228 184.143Q-17.464 184.386-17.814 184.479Q-18.164 184.573-18.550 184.573Q-19.128 184.573-19.527 184.319Q-19.597 184.444-19.646 184.501Q-19.695 184.557-19.800 184.573L-19.871 184.573Q-20.085 184.550-20.109 184.335M-15.832 184.296L-15.832 184.206Q-15.781 183.999-15.585 183.975L-14.546 183.975L-14.546 181.647L-15.519 181.647Q-15.718 181.624-15.769 181.405L-15.769 181.319Q-15.718 181.108-15.519 181.085L-14.152 181.085Q-13.957 181.104-13.906 181.319L-13.906 183.975L-12.992 183.975Q-12.796 183.999-12.746 184.206L-12.746 184.296Q-12.796 184.511-12.992 184.534L-15.585 184.534Q-15.781 184.511-15.832 184.296M-14.800 180.108L-14.800 180.054Q-14.800 179.882-14.664 179.761Q-14.527 179.639-14.351 179.639Q-14.179 179.639-14.042 179.761Q-13.906 179.882-13.906 180.054L-13.906 180.108Q-13.906 180.284-14.042 180.405Q-14.179 180.526-14.351 180.526Q-14.527 180.526-14.664 180.405Q-14.800 180.284-14.800 180.108M-10.339 184.573Q-10.804 184.573-11.169 184.323Q-11.535 184.073-11.740 183.669Q-11.945 183.264-11.945 182.807Q-11.945 182.464-11.820 182.143Q-11.695 181.823-11.462 181.573Q-11.230 181.323-10.925 181.184Q-10.621 181.046-10.265 181.046Q-9.753 181.046-9.347 181.366L-9.347 180.206L-9.769 180.206Q-9.980 180.182-10.019 179.968L-10.019 179.878Q-9.980 179.671-9.769 179.647L-8.957 179.647Q-8.757 179.671-8.707 179.878L-8.707 183.975L-8.281 183.975Q-8.074 183.999-8.035 184.206L-8.035 184.296Q-8.074 184.511-8.281 184.534L-9.097 184.534Q-9.296 184.511-9.347 184.296L-9.347 184.167Q-9.542 184.358-9.804 184.466Q-10.066 184.573-10.339 184.573M-10.300 184.014Q-9.941 184.014-9.689 183.745Q-9.437 183.475-9.347 183.100L-9.347 182.268Q-9.406 182.081-9.533 181.930Q-9.660 181.780-9.837 181.692Q-10.015 181.604-10.210 181.604Q-10.519 181.604-10.769 181.774Q-11.019 181.944-11.164 182.229Q-11.308 182.514-11.308 182.815Q-11.308 183.264-11.023 183.639Q-10.738 184.014-10.300 184.014M-7.214 183.679L-7.214 181.647L-7.636 181.647Q-7.843 181.624-7.886 181.405L-7.886 181.319Q-7.839 181.108-7.636 181.085L-6.820 181.085Q-6.625 181.108-6.574 181.319L-6.574 183.647Q-6.574 183.882-6.404 183.948Q-6.234 184.014-5.949 184.014Q-5.742 184.014-5.546 183.938Q-5.351 183.862-5.226 183.712Q-5.101 183.561-5.101 183.350L-5.101 181.647L-5.523 181.647Q-5.734 181.624-5.773 181.405L-5.773 181.319Q-5.734 181.108-5.523 181.085L-4.710 181.085Q-4.511 181.108-4.460 181.319L-4.460 183.975L-4.035 183.975Q-3.828 183.999-3.789 184.206L-3.789 184.296Q-3.828 184.511-4.035 184.534L-4.851 184.534Q-5.050 184.511-5.101 184.311Q-5.503 184.573-6.011 184.573Q-6.246 184.573-6.460 184.532Q-6.675 184.491-6.841 184.389Q-7.007 184.288-7.111 184.110Q-7.214 183.932-7.214 183.679M-3.304 183.421Q-3.304 182.975-2.890 182.718Q-2.476 182.460-1.935 182.360Q-1.394 182.261-0.886 182.253Q-0.886 182.038-1.021 181.886Q-1.156 181.733-1.363 181.657Q-1.570 181.581-1.781 181.581Q-2.125 181.581-2.285 181.604L-2.285 181.663Q-2.285 181.831-2.404 181.946Q-2.523 182.061-2.687 182.061Q-2.863 182.061-2.978 181.938Q-3.093 181.815-3.093 181.647Q-3.093 181.241-2.712 181.132Q-2.332 181.022-1.773 181.022Q-1.503 181.022-1.236 181.100Q-0.968 181.179-0.744 181.329Q-0.519 181.479-0.382 181.700Q-0.246 181.921-0.246 182.198L-0.246 183.917Q-0.246 183.975 0.282 183.975Q0.477 183.995 0.528 184.206L0.528 184.296Q0.477 184.511 0.282 184.534L0.137 184.534Q-0.207 184.534-0.435 184.487Q-0.664 184.440-0.808 184.253Q-1.269 184.573-1.976 184.573Q-2.312 184.573-2.617 184.432Q-2.921 184.292-3.113 184.030Q-3.304 183.768-3.304 183.421M-2.664 183.429Q-2.664 183.702-2.421 183.858Q-2.179 184.014-1.894 184.014Q-1.675 184.014-1.443 183.956Q-1.210 183.897-1.048 183.759Q-0.886 183.620-0.886 183.397L-0.886 182.807Q-1.167 182.807-1.583 182.864Q-2 182.921-2.332 183.059Q-2.664 183.198-2.664 183.429M0.985 184.296L0.985 184.206Q1.036 183.999 1.231 183.975L2.336 183.975L2.336 180.206L1.231 180.206Q1.036 180.182 0.985 179.968L0.985 179.878Q1.036 179.671 1.231 179.647L2.727 179.647Q2.918 179.671 2.977 179.878L2.977 183.975L4.079 183.975Q4.278 183.999 4.329 184.206L4.329 184.296Q4.278 184.511 4.079 184.534L1.231 184.534Q1.036 184.511 0.985 184.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"rotate(-90 -70.165 164.827)\">\u003Cpath d=\"M9.650 184.335L9.650 183.421Q9.677 183.214 9.888 183.190L10.056 183.190Q10.220 183.214 10.279 183.374Q10.482 184.014 11.209 184.014Q11.416 184.014 11.644 183.979Q11.873 183.944 12.041 183.829Q12.209 183.714 12.209 183.511Q12.209 183.300 11.986 183.186Q11.763 183.073 11.490 183.030L10.791 182.917Q9.650 182.706 9.650 181.983Q9.650 181.694 9.794 181.505Q9.939 181.315 10.179 181.208Q10.419 181.100 10.675 181.061Q10.931 181.022 11.209 181.022Q11.459 181.022 11.652 181.052Q11.845 181.081 12.009 181.159Q12.087 181.042 12.216 181.022L12.294 181.022Q12.392 181.034 12.455 181.096Q12.517 181.159 12.529 181.253L12.529 181.960Q12.517 182.054 12.455 182.120Q12.392 182.186 12.294 182.198L12.127 182.198Q12.033 182.186 11.966 182.120Q11.900 182.054 11.888 181.960Q11.888 181.581 11.193 181.581Q10.845 181.581 10.527 181.663Q10.209 181.745 10.209 181.991Q10.209 182.257 10.880 182.366L11.584 182.487Q12.068 182.569 12.418 182.817Q12.767 183.065 12.767 183.511Q12.767 183.901 12.531 184.143Q12.294 184.386 11.945 184.479Q11.595 184.573 11.209 184.573Q10.630 184.573 10.232 184.319Q10.162 184.444 10.113 184.501Q10.064 184.557 9.959 184.573L9.888 184.573Q9.673 184.550 9.650 184.335M14.509 183.429L14.509 181.647L13.759 181.647Q13.560 181.624 13.509 181.405L13.509 181.319Q13.560 181.108 13.759 181.085L14.509 181.085L14.509 180.335Q14.560 180.128 14.759 180.100L14.904 180.100Q15.099 180.128 15.150 180.335L15.150 181.085L16.509 181.085Q16.701 181.104 16.759 181.319L16.759 181.405Q16.705 181.624 16.509 181.647L15.150 181.647L15.150 183.397Q15.150 184.014 15.724 184.014Q15.974 184.014 16.138 183.829Q16.302 183.643 16.302 183.397Q16.302 183.304 16.375 183.233Q16.447 183.163 16.548 183.151L16.693 183.151Q16.892 183.175 16.943 183.382L16.943 183.429Q16.943 183.753 16.759 184.016Q16.576 184.280 16.283 184.427Q15.990 184.573 15.669 184.573Q15.158 184.573 14.834 184.263Q14.509 183.952 14.509 183.429M17.779 184.296L17.779 184.206Q17.837 183.999 18.029 183.975L18.740 183.975L18.740 181.647L18.029 181.647Q17.834 181.624 17.779 181.405L17.779 181.319Q17.837 181.108 18.029 181.085L19.130 181.085Q19.330 181.104 19.380 181.319L19.380 181.647Q19.642 181.362 19.998 181.204Q20.353 181.046 20.740 181.046Q21.033 181.046 21.267 181.180Q21.502 181.315 21.502 181.581Q21.502 181.749 21.392 181.866Q21.283 181.983 21.115 181.983Q20.962 181.983 20.847 181.872Q20.732 181.761 20.732 181.604Q20.357 181.604 20.043 181.805Q19.728 182.007 19.554 182.341Q19.380 182.675 19.380 183.054L19.380 183.975L20.326 183.975Q20.533 183.999 20.572 184.206L20.572 184.296Q20.533 184.511 20.326 184.534L18.029 184.534Q17.837 184.511 17.779 184.296M25.314 183.046L22.873 183.046Q22.927 183.323 23.125 183.546Q23.322 183.768 23.599 183.891Q23.877 184.014 24.162 184.014Q24.634 184.014 24.857 183.725Q24.865 183.714 24.921 183.608Q24.978 183.503 25.027 183.460Q25.076 183.417 25.169 183.405L25.314 183.405Q25.505 183.425 25.564 183.639L25.564 183.694Q25.498 183.995 25.267 184.192Q25.037 184.389 24.724 184.481Q24.412 184.573 24.107 184.573Q23.623 184.573 23.183 184.345Q22.744 184.116 22.476 183.716Q22.209 183.315 22.209 182.823L22.209 182.764Q22.209 182.296 22.455 181.893Q22.701 181.491 23.109 181.257Q23.517 181.022 23.986 181.022Q24.490 181.022 24.843 181.245Q25.197 181.468 25.380 181.856Q25.564 182.245 25.564 182.749L25.564 182.807Q25.505 183.022 25.314 183.046M22.880 182.495L24.908 182.495Q24.861 182.085 24.623 181.833Q24.384 181.581 23.986 181.581Q23.591 181.581 23.285 181.843Q22.978 182.104 22.880 182.495M26.455 183.421Q26.455 182.975 26.869 182.718Q27.283 182.460 27.824 182.360Q28.365 182.261 28.873 182.253Q28.873 182.038 28.738 181.886Q28.603 181.733 28.396 181.657Q28.189 181.581 27.978 181.581Q27.634 181.581 27.474 181.604L27.474 181.663Q27.474 181.831 27.355 181.946Q27.236 182.061 27.072 182.061Q26.896 182.061 26.781 181.938Q26.666 181.815 26.666 181.647Q26.666 181.241 27.046 181.132Q27.427 181.022 27.986 181.022Q28.255 181.022 28.523 181.100Q28.791 181.179 29.015 181.329Q29.240 181.479 29.377 181.700Q29.513 181.921 29.513 182.198L29.513 183.917Q29.513 183.975 30.041 183.975Q30.236 183.995 30.287 184.206L30.287 184.296Q30.236 184.511 30.041 184.534L29.896 184.534Q29.552 184.534 29.324 184.487Q29.095 184.440 28.951 184.253Q28.490 184.573 27.783 184.573Q27.447 184.573 27.142 184.432Q26.837 184.292 26.646 184.030Q26.455 183.768 26.455 183.421M27.095 183.429Q27.095 183.702 27.337 183.858Q27.580 184.014 27.865 184.014Q28.084 184.014 28.316 183.956Q28.548 183.897 28.710 183.759Q28.873 183.620 28.873 183.397L28.873 182.807Q28.591 182.807 28.175 182.864Q27.759 182.921 27.427 183.059Q27.095 183.198 27.095 183.429M30.240 184.296L30.240 184.206Q30.291 183.995 30.486 183.975L30.685 183.975L30.685 181.647L30.486 181.647Q30.279 181.624 30.240 181.405L30.240 181.319Q30.291 181.104 30.486 181.085L30.966 181.085Q31.158 181.108 31.216 181.319Q31.537 181.046 31.951 181.046Q32.142 181.046 32.310 181.155Q32.478 181.264 32.552 181.436Q32.728 181.245 32.951 181.145Q33.173 181.046 33.416 181.046Q33.834 181.046 33.988 181.388Q34.142 181.729 34.142 182.198L34.142 183.975L34.341 183.975Q34.552 183.999 34.591 184.206L34.591 184.296Q34.541 184.511 34.341 184.534L33.525 184.534Q33.330 184.511 33.279 184.296L33.279 184.206Q33.330 183.999 33.525 183.975L33.615 183.975L33.615 182.229Q33.615 181.604 33.365 181.604Q33.033 181.604 32.855 181.915Q32.677 182.225 32.677 182.589L32.677 183.975L32.880 183.975Q33.087 183.999 33.127 184.206L33.127 184.296Q33.076 184.511 32.880 184.534L32.064 184.534Q31.865 184.511 31.814 184.296L31.814 184.206Q31.865 183.999 32.064 183.975L32.150 183.975L32.150 182.229Q32.150 181.604 31.904 181.604Q31.572 181.604 31.394 181.917Q31.216 182.229 31.216 182.589L31.216 183.975L31.416 183.975Q31.623 183.999 31.662 184.206L31.662 184.296Q31.611 184.514 31.416 184.534L30.486 184.534Q30.279 184.511 30.240 184.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"rotate(-90 -70.165 164.827)\">\u003Cpath d=\"M41.927 185.175Q41.396 184.866 40.996 184.378Q40.595 183.889 40.384 183.296Q40.173 182.702 40.173 182.085Q40.173 181.468 40.382 180.880Q40.591 180.292 40.988 179.811Q41.384 179.331 41.919 179.007Q41.990 178.983 42.021 178.983L42.111 178.983Q42.209 178.995 42.275 179.061Q42.341 179.128 42.341 179.229Q42.341 179.374 42.240 179.436Q41.791 179.725 41.464 180.141Q41.138 180.557 40.976 181.050Q40.814 181.542 40.814 182.085Q40.814 182.491 40.910 182.878Q41.005 183.264 41.183 183.600Q41.361 183.936 41.621 184.220Q41.880 184.503 42.228 184.733Q42.341 184.811 42.341 184.948Q42.341 185.046 42.275 185.116Q42.209 185.186 42.111 185.198L42.021 185.198Q41.962 185.198 41.927 185.175M44.068 184.311L43.603 181.647L43.443 181.647Q43.236 181.624 43.197 181.405L43.197 181.319Q43.236 181.108 43.443 181.085L44.611 181.085Q44.822 181.108 44.861 181.319L44.861 181.405Q44.822 181.624 44.611 181.647L44.138 181.647Q44.252 182.292 44.330 182.737Q44.408 183.182 44.459 183.501Q44.509 183.819 44.509 183.893Q44.517 183.721 44.802 182.725Q44.841 182.612 44.939 182.538Q45.037 182.464 45.158 182.464L45.236 182.464Q45.357 182.464 45.455 182.538Q45.552 182.612 45.587 182.725Q45.697 183.108 45.779 183.432Q45.861 183.757 45.861 183.893Q45.873 183.604 46.220 181.647L45.748 181.647Q45.541 181.624 45.502 181.405L45.502 181.319Q45.541 181.108 45.748 181.085L46.923 181.085Q47.115 181.108 47.173 181.319L47.173 181.405Q47.119 181.624 46.923 181.647L46.755 181.647L46.291 184.311Q46.267 184.429 46.179 184.501Q46.091 184.573 45.970 184.573L45.830 184.573Q45.709 184.573 45.613 184.501Q45.517 184.429 45.474 184.311Q45.427 184.132 45.355 183.876Q45.283 183.620 45.240 183.411Q45.197 183.202 45.197 183.100Q45.189 183.382 44.908 184.311Q44.880 184.421 44.783 184.497Q44.685 184.573 44.564 184.573L44.388 184.573Q44.267 184.573 44.179 184.501Q44.091 184.429 44.068 184.311M47.923 184.296L47.923 184.206Q47.974 183.999 48.169 183.975L49.209 183.975L49.209 181.647L48.236 181.647Q48.037 181.624 47.986 181.405L47.986 181.319Q48.037 181.108 48.236 181.085L49.603 181.085Q49.798 181.104 49.849 181.319L49.849 183.975L50.763 183.975Q50.959 183.999 51.009 184.206L51.009 184.296Q50.959 184.511 50.763 184.534L48.169 184.534Q47.974 184.511 47.923 184.296M48.955 180.108L48.955 180.054Q48.955 179.882 49.091 179.761Q49.228 179.639 49.404 179.639Q49.576 179.639 49.712 179.761Q49.849 179.882 49.849 180.054L49.849 180.108Q49.849 180.284 49.712 180.405Q49.576 180.526 49.404 180.526Q49.228 180.526 49.091 180.405Q48.955 180.284 48.955 180.108M53.416 184.573Q52.951 184.573 52.585 184.323Q52.220 184.073 52.015 183.669Q51.810 183.264 51.810 182.807Q51.810 182.464 51.935 182.143Q52.060 181.823 52.293 181.573Q52.525 181.323 52.830 181.184Q53.134 181.046 53.490 181.046Q54.002 181.046 54.408 181.366L54.408 180.206L53.986 180.206Q53.775 180.182 53.736 179.968L53.736 179.878Q53.775 179.671 53.986 179.647L54.798 179.647Q54.998 179.671 55.048 179.878L55.048 183.975L55.474 183.975Q55.681 183.999 55.720 184.206L55.720 184.296Q55.681 184.511 55.474 184.534L54.658 184.534Q54.459 184.511 54.408 184.296L54.408 184.167Q54.212 184.358 53.951 184.466Q53.689 184.573 53.416 184.573M53.455 184.014Q53.814 184.014 54.066 183.745Q54.318 183.475 54.408 183.100L54.408 182.268Q54.349 182.081 54.222 181.930Q54.095 181.780 53.918 181.692Q53.740 181.604 53.544 181.604Q53.236 181.604 52.986 181.774Q52.736 181.944 52.591 182.229Q52.447 182.514 52.447 182.815Q52.447 183.264 52.732 183.639Q53.017 184.014 53.455 184.014M56.998 183.429L56.998 181.647L56.248 181.647Q56.048 181.624 55.998 181.405L55.998 181.319Q56.048 181.108 56.248 181.085L56.998 181.085L56.998 180.335Q57.048 180.128 57.248 180.100L57.392 180.100Q57.587 180.128 57.638 180.335L57.638 181.085L58.998 181.085Q59.189 181.104 59.248 181.319L59.248 181.405Q59.193 181.624 58.998 181.647L57.638 181.647L57.638 183.397Q57.638 184.014 58.212 184.014Q58.462 184.014 58.627 183.829Q58.791 183.643 58.791 183.397Q58.791 183.304 58.863 183.233Q58.935 183.163 59.037 183.151L59.181 183.151Q59.380 183.175 59.431 183.382L59.431 183.429Q59.431 183.753 59.248 184.016Q59.064 184.280 58.771 184.427Q58.478 184.573 58.158 184.573Q57.646 184.573 57.322 184.263Q56.998 183.952 56.998 183.429M60.115 184.296L60.115 184.206Q60.158 183.999 60.365 183.975L60.787 183.975L60.787 180.206L60.365 180.206Q60.158 180.182 60.115 179.968L60.115 179.878Q60.158 179.671 60.365 179.647L61.181 179.647Q61.377 179.671 61.427 179.878L61.427 181.429Q61.888 181.046 62.486 181.046Q62.834 181.046 63.072 181.186Q63.310 181.327 63.425 181.585Q63.541 181.843 63.541 182.198L63.541 183.975L63.966 183.975Q64.173 183.999 64.212 184.206L64.212 184.296Q64.173 184.511 63.966 184.534L62.572 184.534Q62.377 184.511 62.326 184.296L62.326 184.206Q62.377 183.995 62.572 183.975L62.900 183.975L62.900 182.229Q62.900 181.921 62.810 181.763Q62.720 181.604 62.427 181.604Q62.158 181.604 61.929 181.735Q61.701 181.866 61.564 182.095Q61.427 182.323 61.427 182.589L61.427 183.975L61.853 183.975Q62.060 183.999 62.099 184.206L62.099 184.296Q62.060 184.511 61.853 184.534L60.365 184.534Q60.158 184.511 60.115 184.296\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"rotate(-90 -70.165 164.827)\">\u003Cpath d=\"M70.428 184.573Q69.963 184.573 69.598 184.323Q69.233 184.073 69.028 183.669Q68.823 183.264 68.823 182.807Q68.823 182.464 68.948 182.143Q69.073 181.823 69.305 181.573Q69.538 181.323 69.842 181.184Q70.147 181.046 70.502 181.046Q71.014 181.046 71.420 181.366L71.420 180.206L70.999 180.206Q70.788 180.182 70.749 179.968L70.749 179.878Q70.788 179.671 70.999 179.647L71.811 179.647Q72.010 179.671 72.061 179.878L72.061 183.975L72.487 183.975Q72.694 183.999 72.733 184.206L72.733 184.296Q72.694 184.511 72.487 184.534L71.670 184.534Q71.471 184.511 71.420 184.296L71.420 184.167Q71.225 184.358 70.963 184.466Q70.702 184.573 70.428 184.573M70.467 184.014Q70.827 184.014 71.079 183.745Q71.331 183.475 71.420 183.100L71.420 182.268Q71.362 182.081 71.235 181.930Q71.108 181.780 70.930 181.692Q70.752 181.604 70.557 181.604Q70.249 181.604 69.999 181.774Q69.749 181.944 69.604 182.229Q69.460 182.514 69.460 182.815Q69.460 183.264 69.745 183.639Q70.030 184.014 70.467 184.014M73.850 185.198L73.764 185.198Q73.659 185.186 73.590 185.114Q73.522 185.042 73.522 184.948Q73.522 184.807 73.627 184.741Q73.963 184.526 74.233 184.237Q74.502 183.948 74.686 183.600Q74.870 183.253 74.960 182.874Q75.049 182.495 75.049 182.085Q75.049 181.546 74.885 181.054Q74.721 180.561 74.403 180.147Q74.085 179.733 73.643 179.444Q73.522 179.362 73.522 179.229Q73.522 179.132 73.590 179.063Q73.659 178.995 73.764 178.983L73.850 178.983Q73.905 178.983 73.940 179.007Q74.327 179.229 74.667 179.577Q75.006 179.925 75.227 180.319Q75.448 180.714 75.569 181.159Q75.690 181.604 75.690 182.085Q75.690 182.569 75.569 183.020Q75.448 183.471 75.223 183.868Q74.999 184.264 74.674 184.598Q74.350 184.932 73.948 185.175Q73.877 185.198 73.850 185.198\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-23.375 24.071)\">\u003Cpath d=\"M-25.675 183.046L-28.117 183.046Q-28.062 183.323-27.865 183.546Q-27.667 183.768-27.390 183.891Q-27.113 184.014-26.828 184.014Q-26.355 184.014-26.132 183.725Q-26.125 183.714-26.068 183.608Q-26.011 183.503-25.962 183.460Q-25.914 183.417-25.820 183.405L-25.675 183.405Q-25.484 183.425-25.425 183.639L-25.425 183.694Q-25.492 183.995-25.722 184.192Q-25.953 184.389-26.265 184.481Q-26.578 184.573-26.882 184.573Q-27.367 184.573-27.806 184.345Q-28.246 184.116-28.513 183.716Q-28.781 183.315-28.781 182.823L-28.781 182.764Q-28.781 182.296-28.535 181.893Q-28.289 181.491-27.880 181.257Q-27.472 181.022-27.003 181.022Q-26.500 181.022-26.146 181.245Q-25.792 181.468-25.609 181.856Q-25.425 182.245-25.425 182.749L-25.425 182.807Q-25.484 183.022-25.675 183.046M-28.109 182.495L-26.082 182.495Q-26.128 182.085-26.367 181.833Q-26.605 181.581-27.003 181.581Q-27.398 181.581-27.705 181.843Q-28.011 182.104-28.109 182.495M-24.996 184.296L-24.996 184.206Q-24.945 183.995-24.750 183.975L-24.550 183.975L-24.550 181.647L-24.750 181.647Q-24.957 181.624-24.996 181.405L-24.996 181.319Q-24.945 181.104-24.750 181.085L-24.269 181.085Q-24.078 181.108-24.019 181.319Q-23.699 181.046-23.285 181.046Q-23.093 181.046-22.925 181.155Q-22.757 181.264-22.683 181.436Q-22.507 181.245-22.285 181.145Q-22.062 181.046-21.820 181.046Q-21.402 181.046-21.248 181.388Q-21.093 181.729-21.093 182.198L-21.093 183.975L-20.894 183.975Q-20.683 183.999-20.644 184.206L-20.644 184.296Q-20.695 184.511-20.894 184.534L-21.710 184.534Q-21.906 184.511-21.957 184.296L-21.957 184.206Q-21.906 183.999-21.710 183.975L-21.621 183.975L-21.621 182.229Q-21.621 181.604-21.871 181.604Q-22.203 181.604-22.380 181.915Q-22.558 182.225-22.558 182.589L-22.558 183.975L-22.355 183.975Q-22.148 183.999-22.109 184.206L-22.109 184.296Q-22.160 184.511-22.355 184.534L-23.171 184.534Q-23.371 184.511-23.421 184.296L-23.421 184.206Q-23.371 183.999-23.171 183.975L-23.085 183.975L-23.085 182.229Q-23.085 181.604-23.332 181.604Q-23.664 181.604-23.841 181.917Q-24.019 182.229-24.019 182.589L-24.019 183.975L-23.820 183.975Q-23.613 183.999-23.574 184.206L-23.574 184.296Q-23.625 184.514-23.820 184.534L-24.750 184.534Q-24.957 184.511-24.996 184.296M-19.953 184.296L-19.953 180.206L-20.375 180.206Q-20.582 180.182-20.625 179.968L-20.625 179.878Q-20.582 179.671-20.375 179.647L-19.558 179.647Q-19.363 179.671-19.312 179.878L-19.312 181.389Q-19.101 181.221-18.837 181.134Q-18.574 181.046-18.304 181.046Q-17.964 181.046-17.667 181.190Q-17.371 181.335-17.156 181.587Q-16.941 181.839-16.826 182.151Q-16.710 182.464-16.710 182.807Q-16.710 183.272-16.937 183.682Q-17.164 184.093-17.550 184.333Q-17.937 184.573-18.406 184.573Q-18.925 184.573-19.312 184.206L-19.312 184.296Q-19.363 184.514-19.558 184.534L-19.703 184.534Q-19.894 184.511-19.953 184.296M-18.449 184.014Q-18.140 184.014-17.890 183.845Q-17.640 183.675-17.496 183.393Q-17.351 183.112-17.351 182.807Q-17.351 182.518-17.476 182.239Q-17.601 181.960-17.833 181.782Q-18.066 181.604-18.367 181.604Q-18.687 181.604-18.949 181.790Q-19.210 181.975-19.312 182.276L-19.312 183.128Q-19.222 183.495-19.001 183.755Q-18.781 184.014-18.449 184.014M-12.937 183.046L-15.378 183.046Q-15.324 183.323-15.126 183.546Q-14.929 183.768-14.652 183.891Q-14.375 184.014-14.089 184.014Q-13.617 184.014-13.394 183.725Q-13.386 183.714-13.330 183.608Q-13.273 183.503-13.224 183.460Q-13.175 183.417-13.082 183.405L-12.937 183.405Q-12.746 183.425-12.687 183.639L-12.687 183.694Q-12.753 183.995-12.984 184.192Q-13.214 184.389-13.527 184.481Q-13.839 184.573-14.144 184.573Q-14.628 184.573-15.068 184.345Q-15.507 184.116-15.775 183.716Q-16.042 183.315-16.042 182.823L-16.042 182.764Q-16.042 182.296-15.796 181.893Q-15.550 181.491-15.142 181.257Q-14.734 181.022-14.265 181.022Q-13.761 181.022-13.408 181.245Q-13.054 181.468-12.871 181.856Q-12.687 182.245-12.687 182.749L-12.687 182.807Q-12.746 183.022-12.937 183.046M-15.371 182.495L-13.343 182.495Q-13.390 182.085-13.628 181.833Q-13.867 181.581-14.265 181.581Q-14.660 181.581-14.966 181.843Q-15.273 182.104-15.371 182.495M-10.339 184.573Q-10.804 184.573-11.169 184.323Q-11.535 184.073-11.740 183.669Q-11.945 183.264-11.945 182.807Q-11.945 182.464-11.820 182.143Q-11.695 181.823-11.462 181.573Q-11.230 181.323-10.925 181.184Q-10.621 181.046-10.265 181.046Q-9.753 181.046-9.347 181.366L-9.347 180.206L-9.769 180.206Q-9.980 180.182-10.019 179.968L-10.019 179.878Q-9.980 179.671-9.769 179.647L-8.957 179.647Q-8.757 179.671-8.707 179.878L-8.707 183.975L-8.281 183.975Q-8.074 183.999-8.035 184.206L-8.035 184.296Q-8.074 184.511-8.281 184.534L-9.097 184.534Q-9.296 184.511-9.347 184.296L-9.347 184.167Q-9.542 184.358-9.804 184.466Q-10.066 184.573-10.339 184.573M-10.300 184.014Q-9.941 184.014-9.689 183.745Q-9.437 183.475-9.347 183.100L-9.347 182.268Q-9.406 182.081-9.533 181.930Q-9.660 181.780-9.837 181.692Q-10.015 181.604-10.210 181.604Q-10.519 181.604-10.769 181.774Q-11.019 181.944-11.164 182.229Q-11.308 182.514-11.308 182.815Q-11.308 183.264-11.023 183.639Q-10.738 184.014-10.300 184.014\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-23.375 24.071)\">\u003Cpath d=\"M-1.870 183.612L-1.870 182.397L-3.084 182.397Q-3.209 182.386-3.295 182.300Q-3.381 182.214-3.381 182.085Q-3.381 181.956-3.295 181.874Q-3.209 181.792-3.084 181.780L-1.870 181.780L-1.870 180.557Q-1.858 180.432-1.772 180.350Q-1.686 180.268-1.557 180.268Q-1.428 180.268-1.346 180.350Q-1.264 180.432-1.252 180.557L-1.252 181.780L-0.038 181.780Q0.087 181.792 0.169 181.874Q0.252 181.956 0.252 182.085Q0.252 182.214 0.169 182.300Q0.087 182.386-0.038 182.397L-1.252 182.397L-1.252 183.612Q-1.264 183.737-1.346 183.823Q-1.428 183.909-1.557 183.909Q-1.686 183.909-1.772 183.823Q-1.858 183.737-1.870 183.612\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-23.375 24.071)\">\u003Cpath d=\"M4.884 186.077L4.884 185.991Q4.927 185.772 5.134 185.749L5.556 185.749L5.556 181.647L5.134 181.647Q4.927 181.624 4.884 181.405L4.884 181.319Q4.931 181.108 5.134 181.085L5.951 181.085Q6.146 181.104 6.197 181.319L6.197 181.389Q6.408 181.221 6.671 181.134Q6.935 181.046 7.205 181.046Q7.544 181.046 7.841 181.190Q8.138 181.335 8.353 181.587Q8.568 181.839 8.683 182.151Q8.798 182.464 8.798 182.807Q8.798 183.272 8.572 183.682Q8.345 184.093 7.959 184.333Q7.572 184.573 7.103 184.573Q6.584 184.573 6.197 184.206L6.197 185.749L6.623 185.749Q6.830 185.772 6.869 185.991L6.869 186.077Q6.830 186.288 6.623 186.311L5.134 186.311Q4.931 186.288 4.884 186.077M7.060 184.014Q7.369 184.014 7.619 183.845Q7.869 183.675 8.013 183.393Q8.158 183.112 8.158 182.807Q8.158 182.518 8.033 182.239Q7.908 181.960 7.675 181.782Q7.443 181.604 7.142 181.604Q6.822 181.604 6.560 181.790Q6.298 181.975 6.197 182.276L6.197 183.128Q6.287 183.495 6.507 183.755Q6.728 184.014 7.060 184.014M11.181 184.573Q10.709 184.573 10.324 184.329Q9.939 184.085 9.716 183.675Q9.494 183.264 9.494 182.807Q9.494 182.464 9.619 182.141Q9.744 181.819 9.974 181.565Q10.205 181.311 10.511 181.167Q10.818 181.022 11.181 181.022Q11.544 181.022 11.857 181.169Q12.169 181.315 12.392 181.561Q12.615 181.807 12.742 182.128Q12.869 182.448 12.869 182.807Q12.869 183.264 12.644 183.677Q12.419 184.089 12.035 184.331Q11.650 184.573 11.181 184.573M11.181 184.014Q11.646 184.014 11.937 183.620Q12.228 183.225 12.228 182.741Q12.228 182.448 12.093 182.180Q11.959 181.913 11.718 181.747Q11.478 181.581 11.181 181.581Q10.877 181.581 10.638 181.747Q10.400 181.913 10.265 182.180Q10.130 182.448 10.130 182.741Q10.130 183.221 10.423 183.618Q10.716 184.014 11.181 184.014M13.892 184.335L13.892 183.421Q13.919 183.214 14.130 183.190L14.298 183.190Q14.462 183.214 14.521 183.374Q14.724 184.014 15.451 184.014Q15.658 184.014 15.886 183.979Q16.115 183.944 16.283 183.829Q16.451 183.714 16.451 183.511Q16.451 183.300 16.228 183.186Q16.005 183.073 15.732 183.030L15.033 182.917Q13.892 182.706 13.892 181.983Q13.892 181.694 14.037 181.505Q14.181 181.315 14.421 181.208Q14.662 181.100 14.918 181.061Q15.173 181.022 15.451 181.022Q15.701 181.022 15.894 181.052Q16.087 181.081 16.252 181.159Q16.330 181.042 16.459 181.022L16.537 181.022Q16.634 181.034 16.697 181.096Q16.759 181.159 16.771 181.253L16.771 181.960Q16.759 182.054 16.697 182.120Q16.634 182.186 16.537 182.198L16.369 182.198Q16.275 182.186 16.209 182.120Q16.142 182.054 16.130 181.960Q16.130 181.581 15.435 181.581Q15.087 181.581 14.769 181.663Q14.451 181.745 14.451 181.991Q14.451 182.257 15.123 182.366L15.826 182.487Q16.310 182.569 16.660 182.817Q17.009 183.065 17.009 183.511Q17.009 183.901 16.773 184.143Q16.537 184.386 16.187 184.479Q15.837 184.573 15.451 184.573Q14.873 184.573 14.474 184.319Q14.404 184.444 14.355 184.501Q14.306 184.557 14.201 184.573L14.130 184.573Q13.916 184.550 13.892 184.335\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(-29.75 -248.582)\">\u003Cpath d=\"M-27.988 183.429L-27.988 181.647L-28.738 181.647Q-28.937 181.624-28.988 181.405L-28.988 181.319Q-28.937 181.108-28.738 181.085L-27.988 181.085L-27.988 180.335Q-27.937 180.128-27.738 180.100L-27.593 180.100Q-27.398 180.128-27.347 180.335L-27.347 181.085L-25.988 181.085Q-25.796 181.104-25.738 181.319L-25.738 181.405Q-25.792 181.624-25.988 181.647L-27.347 181.647L-27.347 183.397Q-27.347 184.014-26.773 184.014Q-26.523 184.014-26.359 183.829Q-26.195 183.643-26.195 183.397Q-26.195 183.304-26.123 183.233Q-26.050 183.163-25.949 183.151L-25.804 183.151Q-25.605 183.175-25.554 183.382L-25.554 183.429Q-25.554 183.753-25.738 184.016Q-25.921 184.280-26.214 184.427Q-26.507 184.573-26.828 184.573Q-27.339 184.573-27.664 184.263Q-27.988 183.952-27.988 183.429M-22.820 184.573Q-23.292 184.573-23.677 184.329Q-24.062 184.085-24.285 183.675Q-24.507 183.264-24.507 182.807Q-24.507 182.464-24.382 182.141Q-24.257 181.819-24.027 181.565Q-23.796 181.311-23.490 181.167Q-23.183 181.022-22.820 181.022Q-22.457 181.022-22.144 181.169Q-21.832 181.315-21.609 181.561Q-21.386 181.807-21.259 182.128Q-21.132 182.448-21.132 182.807Q-21.132 183.264-21.357 183.677Q-21.582 184.089-21.966 184.331Q-22.351 184.573-22.820 184.573M-22.820 184.014Q-22.355 184.014-22.064 183.620Q-21.773 183.225-21.773 182.741Q-21.773 182.448-21.908 182.180Q-22.042 181.913-22.283 181.747Q-22.523 181.581-22.820 181.581Q-23.125 181.581-23.363 181.747Q-23.601 181.913-23.736 182.180Q-23.871 182.448-23.871 182.741Q-23.871 183.221-23.578 183.618Q-23.285 184.014-22.820 184.014\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-29.75 -248.582)\">\u003Cpath d=\"M-14.315 184.573Q-14.788 184.573-15.172 184.329Q-15.557 184.085-15.780 183.675Q-16.002 183.264-16.002 182.807Q-16.002 182.464-15.877 182.141Q-15.752 181.819-15.522 181.565Q-15.291 181.311-14.985 181.167Q-14.678 181.022-14.315 181.022Q-13.952 181.022-13.639 181.169Q-13.327 181.315-13.104 181.561Q-12.881 181.807-12.754 182.128Q-12.627 182.448-12.627 182.807Q-12.627 183.264-12.852 183.677Q-13.077 184.089-13.461 184.331Q-13.846 184.573-14.315 184.573M-14.315 184.014Q-13.850 184.014-13.559 183.620Q-13.268 183.225-13.268 182.741Q-13.268 182.448-13.403 182.180Q-13.538 181.913-13.778 181.747Q-14.018 181.581-14.315 181.581Q-14.620 181.581-14.858 181.747Q-15.096 181.913-15.231 182.180Q-15.366 182.448-15.366 182.741Q-15.366 183.221-15.073 183.618Q-14.780 184.014-14.315 184.014M-11.448 183.679L-11.448 181.647L-11.870 181.647Q-12.077 181.624-12.120 181.405L-12.120 181.319Q-12.073 181.108-11.870 181.085L-11.053 181.085Q-10.858 181.108-10.807 181.319L-10.807 183.647Q-10.807 183.882-10.637 183.948Q-10.467 184.014-10.182 184.014Q-9.975 184.014-9.780 183.938Q-9.584 183.862-9.459 183.712Q-9.334 183.561-9.334 183.350L-9.334 181.647L-9.756 181.647Q-9.967 181.624-10.006 181.405L-10.006 181.319Q-9.967 181.108-9.756 181.085L-8.944 181.085Q-8.745 181.108-8.694 181.319L-8.694 183.975L-8.268 183.975Q-8.061 183.999-8.022 184.206L-8.022 184.296Q-8.061 184.511-8.268 184.534L-9.084 184.534Q-9.284 184.511-9.334 184.311Q-9.737 184.573-10.245 184.573Q-10.479 184.573-10.694 184.532Q-10.909 184.491-11.075 184.389Q-11.241 184.288-11.344 184.110Q-11.448 183.932-11.448 183.679M-6.745 183.429L-6.745 181.647L-7.495 181.647Q-7.694 181.624-7.745 181.405L-7.745 181.319Q-7.694 181.108-7.495 181.085L-6.745 181.085L-6.745 180.335Q-6.694 180.128-6.495 180.100L-6.350 180.100Q-6.155 180.128-6.104 180.335L-6.104 181.085L-4.745 181.085Q-4.553 181.104-4.495 181.319L-4.495 181.405Q-4.549 181.624-4.745 181.647L-6.104 181.647L-6.104 183.397Q-6.104 184.014-5.530 184.014Q-5.280 184.014-5.116 183.829Q-4.952 183.643-4.952 183.397Q-4.952 183.304-4.879 183.233Q-4.807 183.163-4.706 183.151L-4.561 183.151Q-4.362 183.175-4.311 183.382L-4.311 183.429Q-4.311 183.753-4.495 184.016Q-4.678 184.280-4.971 184.427Q-5.264 184.573-5.584 184.573Q-6.096 184.573-6.420 184.263Q-6.745 183.952-6.745 183.429M-3.627 186.077L-3.627 185.991Q-3.584 185.772-3.377 185.749L-2.956 185.749L-2.956 181.647L-3.377 181.647Q-3.584 181.624-3.627 181.405L-3.627 181.319Q-3.581 181.108-3.377 181.085L-2.561 181.085Q-2.366 181.104-2.315 181.319L-2.315 181.389Q-2.104 181.221-1.840 181.134Q-1.577 181.046-1.307 181.046Q-0.967 181.046-0.670 181.190Q-0.373 181.335-0.159 181.587Q0.056 181.839 0.171 182.151Q0.287 182.464 0.287 182.807Q0.287 183.272 0.060 183.682Q-0.166 184.093-0.553 184.333Q-0.940 184.573-1.409 184.573Q-1.928 184.573-2.315 184.206L-2.315 185.749L-1.889 185.749Q-1.682 185.772-1.643 185.991L-1.643 186.077Q-1.682 186.288-1.889 186.311L-3.377 186.311Q-3.581 186.288-3.627 186.077M-1.452 184.014Q-1.143 184.014-0.893 183.845Q-0.643 183.675-0.498 183.393Q-0.354 183.112-0.354 182.807Q-0.354 182.518-0.479 182.239Q-0.604 181.960-0.836 181.782Q-1.069 181.604-1.370 181.604Q-1.690 181.604-1.952 181.790Q-2.213 181.975-2.315 182.276L-2.315 183.128Q-2.225 183.495-2.004 183.755Q-1.784 184.014-1.452 184.014M1.291 183.679L1.291 181.647L0.869 181.647Q0.662 181.624 0.619 181.405L0.619 181.319Q0.666 181.108 0.869 181.085L1.685 181.085Q1.880 181.108 1.931 181.319L1.931 183.647Q1.931 183.882 2.101 183.948Q2.271 184.014 2.556 184.014Q2.763 184.014 2.959 183.938Q3.154 183.862 3.279 183.712Q3.404 183.561 3.404 183.350L3.404 181.647L2.982 181.647Q2.771 181.624 2.732 181.405L2.732 181.319Q2.771 181.108 2.982 181.085L3.794 181.085Q3.994 181.108 4.044 181.319L4.044 183.975L4.470 183.975Q4.677 183.999 4.716 184.206L4.716 184.296Q4.677 184.511 4.470 184.534L3.654 184.534Q3.455 184.511 3.404 184.311Q3.002 184.573 2.494 184.573Q2.259 184.573 2.044 184.532Q1.830 184.491 1.664 184.389Q1.498 184.288 1.394 184.110Q1.291 183.932 1.291 183.679M5.994 183.429L5.994 181.647L5.244 181.647Q5.044 181.624 4.994 181.405L4.994 181.319Q5.044 181.108 5.244 181.085L5.994 181.085L5.994 180.335Q6.044 180.128 6.244 180.100L6.388 180.100Q6.584 180.128 6.634 180.335L6.634 181.085L7.994 181.085Q8.185 181.104 8.244 181.319L8.244 181.405Q8.189 181.624 7.994 181.647L6.634 181.647L6.634 183.397Q6.634 184.014 7.209 184.014Q7.459 184.014 7.623 183.829Q7.787 183.643 7.787 183.397Q7.787 183.304 7.859 183.233Q7.931 183.163 8.033 183.151L8.177 183.151Q8.377 183.175 8.427 183.382L8.427 183.429Q8.427 183.753 8.244 184.016Q8.060 184.280 7.767 184.427Q7.474 184.573 7.154 184.573Q6.642 184.573 6.318 184.263Q5.994 183.952 5.994 183.429\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-29.75 -248.582)\">\u003Cpath d=\"M13.384 184.296L13.384 184.206Q13.427 183.999 13.634 183.975L14.056 183.975L14.056 180.206L13.634 180.206Q13.427 180.182 13.384 179.968L13.384 179.878Q13.427 179.671 13.634 179.647L14.451 179.647Q14.646 179.671 14.697 179.878L14.697 181.429Q15.158 181.046 15.755 181.046Q16.103 181.046 16.341 181.186Q16.580 181.327 16.695 181.585Q16.810 181.843 16.810 182.198L16.810 183.975L17.236 183.975Q17.443 183.999 17.482 184.206L17.482 184.296Q17.443 184.511 17.236 184.534L15.841 184.534Q15.646 184.511 15.595 184.296L15.595 184.206Q15.646 183.995 15.841 183.975L16.169 183.975L16.169 182.229Q16.169 181.921 16.080 181.763Q15.990 181.604 15.697 181.604Q15.427 181.604 15.199 181.735Q14.970 181.866 14.834 182.095Q14.697 182.323 14.697 182.589L14.697 183.975L15.123 183.975Q15.330 183.999 15.369 184.206L15.369 184.296Q15.330 184.511 15.123 184.534L13.634 184.534Q13.427 184.511 13.384 184.296M21.072 183.046L18.630 183.046Q18.685 183.323 18.882 183.546Q19.080 183.768 19.357 183.891Q19.634 184.014 19.919 184.014Q20.392 184.014 20.615 183.725Q20.623 183.714 20.679 183.608Q20.736 183.503 20.785 183.460Q20.834 183.417 20.927 183.405L21.072 183.405Q21.263 183.425 21.322 183.639L21.322 183.694Q21.255 183.995 21.025 184.192Q20.794 184.389 20.482 184.481Q20.169 184.573 19.865 184.573Q19.380 184.573 18.941 184.345Q18.502 184.116 18.234 183.716Q17.966 183.315 17.966 182.823L17.966 182.764Q17.966 182.296 18.212 181.893Q18.459 181.491 18.867 181.257Q19.275 181.022 19.744 181.022Q20.248 181.022 20.601 181.245Q20.955 181.468 21.138 181.856Q21.322 182.245 21.322 182.749L21.322 182.807Q21.263 183.022 21.072 183.046M18.638 182.495L20.666 182.495Q20.619 182.085 20.380 181.833Q20.142 181.581 19.744 181.581Q19.349 181.581 19.043 181.843Q18.736 182.104 18.638 182.495M22.212 183.421Q22.212 182.975 22.627 182.718Q23.041 182.460 23.582 182.360Q24.123 182.261 24.630 182.253Q24.630 182.038 24.496 181.886Q24.361 181.733 24.154 181.657Q23.947 181.581 23.736 181.581Q23.392 181.581 23.232 181.604L23.232 181.663Q23.232 181.831 23.113 181.946Q22.994 182.061 22.830 182.061Q22.654 182.061 22.539 181.938Q22.423 181.815 22.423 181.647Q22.423 181.241 22.804 181.132Q23.185 181.022 23.744 181.022Q24.013 181.022 24.281 181.100Q24.548 181.179 24.773 181.329Q24.998 181.479 25.134 181.700Q25.271 181.921 25.271 182.198L25.271 183.917Q25.271 183.975 25.798 183.975Q25.994 183.995 26.044 184.206L26.044 184.296Q25.994 184.511 25.798 184.534L25.654 184.534Q25.310 184.534 25.082 184.487Q24.853 184.440 24.709 184.253Q24.248 184.573 23.541 184.573Q23.205 184.573 22.900 184.432Q22.595 184.292 22.404 184.030Q22.212 183.768 22.212 183.421M22.853 183.429Q22.853 183.702 23.095 183.858Q23.337 184.014 23.623 184.014Q23.841 184.014 24.074 183.956Q24.306 183.897 24.468 183.759Q24.630 183.620 24.630 183.397L24.630 182.807Q24.349 182.807 23.933 182.864Q23.517 182.921 23.185 183.059Q22.853 183.198 22.853 183.429M27.916 184.573Q27.451 184.573 27.085 184.323Q26.720 184.073 26.515 183.669Q26.310 183.264 26.310 182.807Q26.310 182.464 26.435 182.143Q26.560 181.823 26.793 181.573Q27.025 181.323 27.330 181.184Q27.634 181.046 27.990 181.046Q28.502 181.046 28.908 181.366L28.908 180.206L28.486 180.206Q28.275 180.182 28.236 179.968L28.236 179.878Q28.275 179.671 28.486 179.647L29.298 179.647Q29.498 179.671 29.548 179.878L29.548 183.975L29.974 183.975Q30.181 183.999 30.220 184.206L30.220 184.296Q30.181 184.511 29.974 184.534L29.158 184.534Q28.959 184.511 28.908 184.296L28.908 184.167Q28.712 184.358 28.451 184.466Q28.189 184.573 27.916 184.573M27.955 184.014Q28.314 184.014 28.566 183.745Q28.818 183.475 28.908 183.100L28.908 182.268Q28.849 182.081 28.722 181.930Q28.595 181.780 28.418 181.692Q28.240 181.604 28.044 181.604Q27.736 181.604 27.486 181.774Q27.236 181.944 27.091 182.229Q26.947 182.514 26.947 182.815Q26.947 183.264 27.232 183.639Q27.517 184.014 27.955 184.014\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M39.1 161.772h68.287v-22.763H39.1Z\"\u002F>\u003Cg transform=\"translate(72.68 -31.699)\">\u003Cpath d=\"M-28.601 184.335L-28.601 183.421Q-28.574 183.214-28.363 183.190L-28.195 183.190Q-28.031 183.214-27.972 183.374Q-27.769 184.014-27.042 184.014Q-26.835 184.014-26.607 183.979Q-26.378 183.944-26.210 183.829Q-26.042 183.714-26.042 183.511Q-26.042 183.300-26.265 183.186Q-26.488 183.073-26.761 183.030L-27.460 182.917Q-28.601 182.706-28.601 181.983Q-28.601 181.694-28.457 181.505Q-28.312 181.315-28.072 181.208Q-27.832 181.100-27.576 181.061Q-27.320 181.022-27.042 181.022Q-26.792 181.022-26.599 181.052Q-26.406 181.081-26.242 181.159Q-26.164 181.042-26.035 181.022L-25.957 181.022Q-25.859 181.034-25.796 181.096Q-25.734 181.159-25.722 181.253L-25.722 181.960Q-25.734 182.054-25.796 182.120Q-25.859 182.186-25.957 182.198L-26.125 182.198Q-26.218 182.186-26.285 182.120Q-26.351 182.054-26.363 181.960Q-26.363 181.581-27.058 181.581Q-27.406 181.581-27.724 181.663Q-28.042 181.745-28.042 181.991Q-28.042 182.257-27.371 182.366L-26.667 182.487Q-26.183 182.569-25.833 182.817Q-25.484 183.065-25.484 183.511Q-25.484 183.901-25.720 184.143Q-25.957 184.386-26.306 184.479Q-26.656 184.573-27.042 184.573Q-27.621 184.573-28.019 184.319Q-28.089 184.444-28.138 184.501Q-28.187 184.557-28.292 184.573L-28.363 184.573Q-28.578 184.550-28.601 184.335M-21.429 183.046L-23.871 183.046Q-23.816 183.323-23.619 183.546Q-23.421 183.768-23.144 183.891Q-22.867 184.014-22.582 184.014Q-22.109 184.014-21.886 183.725Q-21.878 183.714-21.822 183.608Q-21.765 183.503-21.716 183.460Q-21.667 183.417-21.574 183.405L-21.429 183.405Q-21.238 183.425-21.179 183.639L-21.179 183.694Q-21.246 183.995-21.476 184.192Q-21.707 184.389-22.019 184.481Q-22.332 184.573-22.636 184.573Q-23.121 184.573-23.560 184.345Q-24 184.116-24.267 183.716Q-24.535 183.315-24.535 182.823L-24.535 182.764Q-24.535 182.296-24.289 181.893Q-24.042 181.491-23.634 181.257Q-23.226 181.022-22.757 181.022Q-22.253 181.022-21.900 181.245Q-21.546 181.468-21.363 181.856Q-21.179 182.245-21.179 182.749L-21.179 182.807Q-21.238 183.022-21.429 183.046M-23.863 182.495L-21.835 182.495Q-21.882 182.085-22.121 181.833Q-22.359 181.581-22.757 181.581Q-23.152 181.581-23.458 181.843Q-23.765 182.104-23.863 182.495M-20.246 184.296L-20.246 184.206Q-20.195 183.999-20 183.975L-18.894 183.975L-18.894 180.206L-20 180.206Q-20.195 180.182-20.246 179.968L-20.246 179.878Q-20.195 179.671-20 179.647L-18.503 179.647Q-18.312 179.671-18.253 179.878L-18.253 183.975L-17.152 183.975Q-16.953 183.999-16.902 184.206L-16.902 184.296Q-16.953 184.511-17.152 184.534L-20 184.534Q-20.195 184.511-20.246 184.296M-16.128 184.296L-16.128 184.206Q-16.078 183.999-15.882 183.975L-15 183.975L-15 181.647L-15.855 181.647Q-16.054 181.624-16.105 181.405L-16.105 181.319Q-16.054 181.108-15.855 181.085L-15 181.085L-15 180.632Q-15 180.167-14.593 179.886Q-14.187 179.604-13.707 179.604Q-13.394 179.604-13.150 179.725Q-12.906 179.846-12.906 180.128Q-12.906 180.292-13.015 180.409Q-13.125 180.526-13.289 180.526Q-13.437 180.526-13.558 180.421Q-13.679 180.315-13.679 180.167L-13.761 180.167Q-13.914 180.167-14.050 180.227Q-14.187 180.288-14.273 180.403Q-14.359 180.518-14.359 180.663L-14.359 181.085L-13.328 181.085Q-13.132 181.104-13.082 181.319L-13.082 181.405Q-13.132 181.624-13.328 181.647L-14.359 181.647L-14.359 183.975L-13.480 183.975Q-13.285 183.999-13.234 184.206L-13.234 184.296Q-13.285 184.511-13.480 184.534L-15.882 184.534Q-16.078 184.511-16.128 184.296M-8.707 182.397L-11.449 182.397Q-11.574 182.386-11.660 182.300Q-11.746 182.214-11.746 182.085Q-11.746 181.956-11.660 181.874Q-11.574 181.792-11.449 181.780L-8.707 181.780Q-8.582 181.792-8.500 181.874Q-8.417 181.956-8.417 182.085Q-8.417 182.214-8.500 182.300Q-8.582 182.386-8.707 182.397M-7.550 183.421Q-7.550 182.975-7.136 182.718Q-6.722 182.460-6.181 182.360Q-5.640 182.261-5.132 182.253Q-5.132 182.038-5.267 181.886Q-5.402 181.733-5.609 181.657Q-5.816 181.581-6.027 181.581Q-6.371 181.581-6.531 181.604L-6.531 181.663Q-6.531 181.831-6.650 181.946Q-6.769 182.061-6.933 182.061Q-7.109 182.061-7.224 181.938Q-7.339 181.815-7.339 181.647Q-7.339 181.241-6.958 181.132Q-6.578 181.022-6.019 181.022Q-5.750 181.022-5.482 181.100Q-5.214 181.179-4.990 181.329Q-4.765 181.479-4.628 181.700Q-4.492 181.921-4.492 182.198L-4.492 183.917Q-4.492 183.975-3.964 183.975Q-3.769 183.995-3.718 184.206L-3.718 184.296Q-3.769 184.511-3.964 184.534L-4.109 184.534Q-4.453 184.534-4.681 184.487Q-4.910 184.440-5.054 184.253Q-5.515 184.573-6.222 184.573Q-6.558 184.573-6.863 184.432Q-7.167 184.292-7.359 184.030Q-7.550 183.768-7.550 183.421M-6.910 183.429Q-6.910 183.702-6.667 183.858Q-6.425 184.014-6.140 184.014Q-5.921 184.014-5.689 183.956Q-5.457 183.897-5.294 183.759Q-5.132 183.620-5.132 183.397L-5.132 182.807Q-5.414 182.807-5.830 182.864Q-6.246 182.921-6.578 183.059Q-6.910 183.198-6.910 183.429M-2.511 183.429L-2.511 181.647L-3.261 181.647Q-3.460 181.624-3.511 181.405L-3.511 181.319Q-3.460 181.108-3.261 181.085L-2.511 181.085L-2.511 180.335Q-2.460 180.128-2.261 180.100L-2.117 180.100Q-1.921 180.128-1.871 180.335L-1.871 181.085L-0.511 181.085Q-0.320 181.104-0.261 181.319L-0.261 181.405Q-0.316 181.624-0.511 181.647L-1.871 181.647L-1.871 183.397Q-1.871 184.014-1.296 184.014Q-1.046 184.014-0.882 183.829Q-0.718 183.643-0.718 183.397Q-0.718 183.304-0.646 183.233Q-0.574 183.163-0.472 183.151L-0.328 183.151Q-0.128 183.175-0.078 183.382L-0.078 183.429Q-0.078 183.753-0.261 184.016Q-0.445 184.280-0.738 184.427Q-1.031 184.573-1.351 184.573Q-1.863 184.573-2.187 184.263Q-2.511 183.952-2.511 183.429M1.735 183.429L1.735 181.647L0.985 181.647Q0.786 181.624 0.735 181.405L0.735 181.319Q0.786 181.108 0.985 181.085L1.735 181.085L1.735 180.335Q1.786 180.128 1.985 180.100L2.129 180.100Q2.325 180.128 2.375 180.335L2.375 181.085L3.735 181.085Q3.926 181.104 3.985 181.319L3.985 181.405Q3.930 181.624 3.735 181.647L2.375 181.647L2.375 183.397Q2.375 184.014 2.950 184.014Q3.200 184.014 3.364 183.829Q3.528 183.643 3.528 183.397Q3.528 183.304 3.600 183.233Q3.672 183.163 3.774 183.151L3.918 183.151Q4.118 183.175 4.168 183.382L4.168 183.429Q4.168 183.753 3.985 184.016Q3.801 184.280 3.508 184.427Q3.215 184.573 2.895 184.573Q2.383 184.573 2.059 184.263Q1.735 183.952 1.735 183.429M8.293 183.046L5.852 183.046Q5.907 183.323 6.104 183.546Q6.301 183.768 6.579 183.891Q6.856 184.014 7.141 184.014Q7.614 184.014 7.836 183.725Q7.844 183.714 7.901 183.608Q7.958 183.503 8.006 183.460Q8.055 183.417 8.149 183.405L8.293 183.405Q8.485 183.425 8.543 183.639L8.543 183.694Q8.477 183.995 8.247 184.192Q8.016 184.389 7.704 184.481Q7.391 184.573 7.086 184.573Q6.602 184.573 6.163 184.345Q5.723 184.116 5.456 183.716Q5.188 183.315 5.188 182.823L5.188 182.764Q5.188 182.296 5.434 181.893Q5.680 181.491 6.088 181.257Q6.497 181.022 6.965 181.022Q7.469 181.022 7.823 181.245Q8.176 181.468 8.360 181.856Q8.543 182.245 8.543 182.749L8.543 182.807Q8.485 183.022 8.293 183.046M5.860 182.495L7.887 182.495Q7.840 182.085 7.602 181.833Q7.364 181.581 6.965 181.581Q6.571 181.581 6.264 181.843Q5.958 182.104 5.860 182.495M9.098 184.296L9.098 184.206Q9.141 183.999 9.348 183.975L9.770 183.975L9.770 181.647L9.348 181.647Q9.141 181.624 9.098 181.405L9.098 181.319Q9.145 181.108 9.348 181.085L10.165 181.085Q10.360 181.108 10.411 181.319L10.411 181.405L10.403 181.429Q10.629 181.249 10.903 181.147Q11.176 181.046 11.469 181.046Q11.817 181.046 12.055 181.186Q12.293 181.327 12.409 181.585Q12.524 181.843 12.524 182.198L12.524 183.975L12.950 183.975Q13.157 183.999 13.196 184.206L13.196 184.296Q13.157 184.511 12.950 184.534L11.555 184.534Q11.360 184.511 11.309 184.296L11.309 184.206Q11.360 183.995 11.555 183.975L11.883 183.975L11.883 182.229Q11.883 181.921 11.793 181.763Q11.704 181.604 11.411 181.604Q11.141 181.604 10.913 181.735Q10.684 181.866 10.547 182.095Q10.411 182.323 10.411 182.589L10.411 183.975L10.836 183.975Q11.043 183.999 11.083 184.206L11.083 184.296Q11.043 184.511 10.836 184.534L9.348 184.534Q9.141 184.511 9.098 184.296M14.473 183.429L14.473 181.647L13.723 181.647Q13.524 181.624 13.473 181.405L13.473 181.319Q13.524 181.108 13.723 181.085L14.473 181.085L14.473 180.335Q14.524 180.128 14.723 180.100L14.868 180.100Q15.063 180.128 15.114 180.335L15.114 181.085L16.473 181.085Q16.665 181.104 16.723 181.319L16.723 181.405Q16.668 181.624 16.473 181.647L15.114 181.647L15.114 183.397Q15.114 184.014 15.688 184.014Q15.938 184.014 16.102 183.829Q16.266 183.643 16.266 183.397Q16.266 183.304 16.338 183.233Q16.411 183.163 16.512 183.151L16.657 183.151Q16.856 183.175 16.907 183.382L16.907 183.429Q16.907 183.753 16.723 184.016Q16.540 184.280 16.247 184.427Q15.954 184.573 15.633 184.573Q15.122 184.573 14.797 184.263Q14.473 183.952 14.473 183.429M18.137 184.296L18.137 184.206Q18.188 183.999 18.383 183.975L19.422 183.975L19.422 181.647L18.450 181.647Q18.250 181.624 18.200 181.405L18.200 181.319Q18.250 181.108 18.450 181.085L19.817 181.085Q20.012 181.104 20.063 181.319L20.063 183.975L20.977 183.975Q21.172 183.999 21.223 184.206L21.223 184.296Q21.172 184.511 20.977 184.534L18.383 184.534Q18.188 184.511 18.137 184.296M19.168 180.108L19.168 180.054Q19.168 179.882 19.305 179.761Q19.442 179.639 19.618 179.639Q19.790 179.639 19.926 179.761Q20.063 179.882 20.063 180.054L20.063 180.108Q20.063 180.284 19.926 180.405Q19.790 180.526 19.618 180.526Q19.442 180.526 19.305 180.405Q19.168 180.284 19.168 180.108M23.887 184.573Q23.415 184.573 23.030 184.329Q22.645 184.085 22.422 183.675Q22.200 183.264 22.200 182.807Q22.200 182.464 22.325 182.141Q22.450 181.819 22.680 181.565Q22.911 181.311 23.217 181.167Q23.524 181.022 23.887 181.022Q24.250 181.022 24.563 181.169Q24.875 181.315 25.098 181.561Q25.321 181.807 25.448 182.128Q25.575 182.448 25.575 182.807Q25.575 183.264 25.350 183.677Q25.125 184.089 24.741 184.331Q24.356 184.573 23.887 184.573M23.887 184.014Q24.352 184.014 24.643 183.620Q24.934 183.225 24.934 182.741Q24.934 182.448 24.799 182.180Q24.665 181.913 24.424 181.747Q24.184 181.581 23.887 181.581Q23.583 181.581 23.344 181.747Q23.106 181.913 22.971 182.180Q22.836 182.448 22.836 182.741Q22.836 183.221 23.129 183.618Q23.422 184.014 23.887 184.014M26.083 184.296L26.083 184.206Q26.125 183.999 26.333 183.975L26.754 183.975L26.754 181.647L26.333 181.647Q26.125 181.624 26.083 181.405L26.083 181.319Q26.129 181.108 26.333 181.085L27.149 181.085Q27.344 181.108 27.395 181.319L27.395 181.405L27.387 181.429Q27.614 181.249 27.887 181.147Q28.161 181.046 28.454 181.046Q28.801 181.046 29.040 181.186Q29.278 181.327 29.393 181.585Q29.508 181.843 29.508 182.198L29.508 183.975L29.934 183.975Q30.141 183.999 30.180 184.206L30.180 184.296Q30.141 184.511 29.934 184.534L28.540 184.534Q28.344 184.511 28.293 184.296L28.293 184.206Q28.344 183.995 28.540 183.975L28.868 183.975L28.868 182.229Q28.868 181.921 28.778 181.763Q28.688 181.604 28.395 181.604Q28.125 181.604 27.897 181.735Q27.668 181.866 27.532 182.095Q27.395 182.323 27.395 182.589L27.395 183.975L27.821 183.975Q28.028 183.999 28.067 184.206L28.067 184.296Q28.028 184.511 27.821 184.534L26.333 184.534Q26.125 184.511 26.083 184.296\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M39.1 104.866h68.287V82.104H39.1Z\"\u002F>\u003Cg transform=\"translate(76.93 -88.604)\">\u003Cpath d=\"M-28.867 184.296L-28.867 184.206Q-28.816 183.999-28.621 183.975L-27.738 183.975L-27.738 181.647L-28.593 181.647Q-28.792 181.624-28.843 181.405L-28.843 181.319Q-28.792 181.108-28.593 181.085L-27.738 181.085L-27.738 180.632Q-27.738 180.167-27.332 179.886Q-26.925 179.604-26.445 179.604Q-26.132 179.604-25.888 179.725Q-25.644 179.846-25.644 180.128Q-25.644 180.292-25.753 180.409Q-25.863 180.526-26.027 180.526Q-26.175 180.526-26.296 180.421Q-26.417 180.315-26.417 180.167L-26.500 180.167Q-26.652 180.167-26.789 180.227Q-26.925 180.288-27.011 180.403Q-27.097 180.518-27.097 180.663L-27.097 181.085L-26.066 181.085Q-25.871 181.104-25.820 181.319L-25.820 181.405Q-25.871 181.624-26.066 181.647L-27.097 181.647L-27.097 183.975L-26.218 183.975Q-26.023 183.999-25.972 184.206L-25.972 184.296Q-26.023 184.511-26.218 184.534L-28.621 184.534Q-28.816 184.511-28.867 184.296M-21.429 183.046L-23.871 183.046Q-23.816 183.323-23.619 183.546Q-23.421 183.768-23.144 183.891Q-22.867 184.014-22.582 184.014Q-22.109 184.014-21.886 183.725Q-21.878 183.714-21.822 183.608Q-21.765 183.503-21.716 183.460Q-21.667 183.417-21.574 183.405L-21.429 183.405Q-21.238 183.425-21.179 183.639L-21.179 183.694Q-21.246 183.995-21.476 184.192Q-21.707 184.389-22.019 184.481Q-22.332 184.573-22.636 184.573Q-23.121 184.573-23.560 184.345Q-24 184.116-24.267 183.716Q-24.535 183.315-24.535 182.823L-24.535 182.764Q-24.535 182.296-24.289 181.893Q-24.042 181.491-23.634 181.257Q-23.226 181.022-22.757 181.022Q-22.253 181.022-21.900 181.245Q-21.546 181.468-21.363 181.856Q-21.179 182.245-21.179 182.749L-21.179 182.807Q-21.238 183.022-21.429 183.046M-23.863 182.495L-21.835 182.495Q-21.882 182.085-22.121 181.833Q-22.359 181.581-22.757 181.581Q-23.152 181.581-23.458 181.843Q-23.765 182.104-23.863 182.495M-17.183 183.046L-19.625 183.046Q-19.570 183.323-19.373 183.546Q-19.175 183.768-18.898 183.891Q-18.621 184.014-18.335 184.014Q-17.863 184.014-17.640 183.725Q-17.632 183.714-17.576 183.608Q-17.519 183.503-17.470 183.460Q-17.421 183.417-17.328 183.405L-17.183 183.405Q-16.992 183.425-16.933 183.639L-16.933 183.694Q-17 183.995-17.230 184.192Q-17.460 184.389-17.773 184.481Q-18.085 184.573-18.390 184.573Q-18.875 184.573-19.314 184.345Q-19.753 184.116-20.021 183.716Q-20.289 183.315-20.289 182.823L-20.289 182.764Q-20.289 182.296-20.042 181.893Q-19.796 181.491-19.388 181.257Q-18.980 181.022-18.511 181.022Q-18.007 181.022-17.654 181.245Q-17.300 181.468-17.117 181.856Q-16.933 182.245-16.933 182.749L-16.933 182.807Q-16.992 183.022-17.183 183.046M-19.617 182.495L-17.589 182.495Q-17.636 182.085-17.875 181.833Q-18.113 181.581-18.511 181.581Q-18.906 181.581-19.212 181.843Q-19.519 182.104-19.617 182.495M-14.585 184.573Q-15.050 184.573-15.416 184.323Q-15.781 184.073-15.986 183.669Q-16.191 183.264-16.191 182.807Q-16.191 182.464-16.066 182.143Q-15.941 181.823-15.708 181.573Q-15.476 181.323-15.171 181.184Q-14.867 181.046-14.511 181.046Q-14 181.046-13.593 181.366L-13.593 180.206L-14.015 180.206Q-14.226 180.182-14.265 179.968L-14.265 179.878Q-14.226 179.671-14.015 179.647L-13.203 179.647Q-13.003 179.671-12.953 179.878L-12.953 183.975L-12.527 183.975Q-12.320 183.999-12.281 184.206L-12.281 184.296Q-12.320 184.511-12.527 184.534L-13.343 184.534Q-13.542 184.511-13.593 184.296L-13.593 184.167Q-13.789 184.358-14.050 184.466Q-14.312 184.573-14.585 184.573M-14.546 184.014Q-14.187 184.014-13.935 183.745Q-13.683 183.475-13.593 183.100L-13.593 182.268Q-13.652 182.081-13.779 181.930Q-13.906 181.780-14.083 181.692Q-14.261 181.604-14.457 181.604Q-14.765 181.604-15.015 181.774Q-15.265 181.944-15.410 182.229Q-15.554 182.514-15.554 182.815Q-15.554 183.264-15.269 183.639Q-14.984 184.014-14.546 184.014M-8.707 182.397L-11.449 182.397Q-11.574 182.386-11.660 182.300Q-11.746 182.214-11.746 182.085Q-11.746 181.956-11.660 181.874Q-11.574 181.792-11.449 181.780L-8.707 181.780Q-8.582 181.792-8.500 181.874Q-8.417 181.956-8.417 182.085Q-8.417 182.214-8.500 182.300Q-8.582 182.386-8.707 182.397M-7.636 184.296L-7.636 184.206Q-7.585 183.999-7.390 183.975L-6.507 183.975L-6.507 181.647L-7.363 181.647Q-7.562 181.624-7.613 181.405L-7.613 181.319Q-7.562 181.108-7.363 181.085L-6.507 181.085L-6.507 180.632Q-6.507 180.167-6.101 179.886Q-5.695 179.604-5.214 179.604Q-4.902 179.604-4.658 179.725Q-4.414 179.846-4.414 180.128Q-4.414 180.292-4.523 180.409Q-4.632 180.526-4.796 180.526Q-4.945 180.526-5.066 180.421Q-5.187 180.315-5.187 180.167L-5.269 180.167Q-5.421 180.167-5.558 180.227Q-5.695 180.288-5.781 180.403Q-5.867 180.518-5.867 180.663L-5.867 181.085L-4.835 181.085Q-4.640 181.104-4.589 181.319L-4.589 181.405Q-4.640 181.624-4.835 181.647L-5.867 181.647L-5.867 183.975L-4.988 183.975Q-4.792 183.999-4.742 184.206L-4.742 184.296Q-4.792 184.511-4.988 184.534L-7.390 184.534Q-7.585 184.511-7.636 184.296M-1.589 184.573Q-2.062 184.573-2.447 184.329Q-2.832 184.085-3.054 183.675Q-3.277 183.264-3.277 182.807Q-3.277 182.464-3.152 182.141Q-3.027 181.819-2.796 181.565Q-2.566 181.311-2.259 181.167Q-1.953 181.022-1.589 181.022Q-1.226 181.022-0.914 181.169Q-0.601 181.315-0.378 181.561Q-0.156 181.807-0.029 182.128Q0.098 182.448 0.098 182.807Q0.098 183.264-0.126 183.677Q-0.351 184.089-0.736 184.331Q-1.121 184.573-1.589 184.573M-1.589 184.014Q-1.125 184.014-0.833 183.620Q-0.542 183.225-0.542 182.741Q-0.542 182.448-0.677 182.180Q-0.812 181.913-1.052 181.747Q-1.292 181.581-1.589 181.581Q-1.894 181.581-2.132 181.747Q-2.371 181.913-2.505 182.180Q-2.640 182.448-2.640 182.741Q-2.640 183.221-2.347 183.618Q-2.054 184.014-1.589 184.014M0.758 184.296L0.758 184.206Q0.817 183.999 1.008 183.975L1.719 183.975L1.719 181.647L1.008 181.647Q0.813 181.624 0.758 181.405L0.758 181.319Q0.817 181.108 1.008 181.085L2.110 181.085Q2.309 181.104 2.360 181.319L2.360 181.647Q2.622 181.362 2.977 181.204Q3.333 181.046 3.719 181.046Q4.012 181.046 4.247 181.180Q4.481 181.315 4.481 181.581Q4.481 181.749 4.372 181.866Q4.262 181.983 4.094 181.983Q3.942 181.983 3.827 181.872Q3.711 181.761 3.711 181.604Q3.336 181.604 3.022 181.805Q2.708 182.007 2.534 182.341Q2.360 182.675 2.360 183.054L2.360 183.975L3.305 183.975Q3.512 183.999 3.551 184.206L3.551 184.296Q3.512 184.511 3.305 184.534L1.008 184.534Q0.817 184.511 0.758 184.296M5.790 184.311L5.325 181.647L5.165 181.647Q4.958 181.624 4.918 181.405L4.918 181.319Q4.958 181.108 5.165 181.085L6.333 181.085Q6.543 181.108 6.583 181.319L6.583 181.405Q6.543 181.624 6.333 181.647L5.860 181.647Q5.973 182.292 6.051 182.737Q6.129 183.182 6.180 183.501Q6.231 183.819 6.231 183.893Q6.239 183.721 6.524 182.725Q6.563 182.612 6.661 182.538Q6.758 182.464 6.879 182.464L6.958 182.464Q7.079 182.464 7.176 182.538Q7.274 182.612 7.309 182.725Q7.418 183.108 7.500 183.432Q7.583 183.757 7.583 183.893Q7.594 183.604 7.942 181.647L7.469 181.647Q7.262 181.624 7.223 181.405L7.223 181.319Q7.262 181.108 7.469 181.085L8.645 181.085Q8.836 181.108 8.895 181.319L8.895 181.405Q8.840 181.624 8.645 181.647L8.477 181.647L8.012 184.311Q7.989 184.429 7.901 184.501Q7.813 184.573 7.692 184.573L7.551 184.573Q7.430 184.573 7.334 184.501Q7.239 184.429 7.196 184.311Q7.149 184.132 7.077 183.876Q7.004 183.620 6.961 183.411Q6.918 183.202 6.918 183.100Q6.911 183.382 6.629 184.311Q6.602 184.421 6.504 184.497Q6.407 184.573 6.286 184.573L6.110 184.573Q5.989 184.573 5.901 184.501Q5.813 184.429 5.790 184.311M9.434 183.421Q9.434 182.975 9.848 182.718Q10.262 182.460 10.803 182.360Q11.344 182.261 11.852 182.253Q11.852 182.038 11.717 181.886Q11.583 181.733 11.375 181.657Q11.168 181.581 10.958 181.581Q10.614 181.581 10.454 181.604L10.454 181.663Q10.454 181.831 10.334 181.946Q10.215 182.061 10.051 182.061Q9.875 182.061 9.760 181.938Q9.645 181.815 9.645 181.647Q9.645 181.241 10.026 181.132Q10.407 181.022 10.965 181.022Q11.235 181.022 11.502 181.100Q11.770 181.179 11.995 181.329Q12.219 181.479 12.356 181.700Q12.493 181.921 12.493 182.198L12.493 183.917Q12.493 183.975 13.020 183.975Q13.215 183.995 13.266 184.206L13.266 184.296Q13.215 184.511 13.020 184.534L12.875 184.534Q12.532 184.534 12.303 184.487Q12.075 184.440 11.930 184.253Q11.469 184.573 10.762 184.573Q10.426 184.573 10.122 184.432Q9.817 184.292 9.625 184.030Q9.434 183.768 9.434 183.421M10.075 183.429Q10.075 183.702 10.317 183.858Q10.559 184.014 10.844 184.014Q11.063 184.014 11.295 183.956Q11.528 183.897 11.690 183.759Q11.852 183.620 11.852 183.397L11.852 182.807Q11.571 182.807 11.155 182.864Q10.739 182.921 10.407 183.059Q10.075 183.198 10.075 183.429M13.497 184.296L13.497 184.206Q13.555 183.999 13.747 183.975L14.458 183.975L14.458 181.647L13.747 181.647Q13.551 181.624 13.497 181.405L13.497 181.319Q13.555 181.108 13.747 181.085L14.848 181.085Q15.047 181.104 15.098 181.319L15.098 181.647Q15.360 181.362 15.715 181.204Q16.071 181.046 16.458 181.046Q16.750 181.046 16.985 181.180Q17.219 181.315 17.219 181.581Q17.219 181.749 17.110 181.866Q17 181.983 16.833 181.983Q16.680 181.983 16.565 181.872Q16.450 181.761 16.450 181.604Q16.075 181.604 15.760 181.805Q15.446 182.007 15.272 182.341Q15.098 182.675 15.098 183.054L15.098 183.975L16.043 183.975Q16.250 183.999 16.290 184.206L16.290 184.296Q16.250 184.511 16.043 184.534L13.747 184.534Q13.555 184.511 13.497 184.296M19.383 184.573Q18.918 184.573 18.553 184.323Q18.188 184.073 17.983 183.669Q17.778 183.264 17.778 182.807Q17.778 182.464 17.903 182.143Q18.028 181.823 18.260 181.573Q18.493 181.323 18.797 181.184Q19.102 181.046 19.458 181.046Q19.969 181.046 20.375 181.366L20.375 180.206L19.954 180.206Q19.743 180.182 19.704 179.968L19.704 179.878Q19.743 179.671 19.954 179.647L20.766 179.647Q20.965 179.671 21.016 179.878L21.016 183.975L21.442 183.975Q21.649 183.999 21.688 184.206L21.688 184.296Q21.649 184.511 21.442 184.534L20.625 184.534Q20.426 184.511 20.375 184.296L20.375 184.167Q20.180 184.358 19.918 184.466Q19.657 184.573 19.383 184.573M19.422 184.014Q19.782 184.014 20.034 183.745Q20.286 183.475 20.375 183.100L20.375 182.268Q20.317 182.081 20.190 181.930Q20.063 181.780 19.885 181.692Q19.708 181.604 19.512 181.604Q19.204 181.604 18.954 181.774Q18.704 181.944 18.559 182.229Q18.415 182.514 18.415 182.815Q18.415 183.264 18.700 183.639Q18.985 184.014 19.422 184.014\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M39.1 47.96h68.287V25.199H39.1Z\"\u002F>\u003Cg transform=\"translate(72.68 -145.51)\">\u003Cpath d=\"M-28.601 184.335L-28.601 183.421Q-28.574 183.214-28.363 183.190L-28.195 183.190Q-28.031 183.214-27.972 183.374Q-27.769 184.014-27.042 184.014Q-26.835 184.014-26.607 183.979Q-26.378 183.944-26.210 183.829Q-26.042 183.714-26.042 183.511Q-26.042 183.300-26.265 183.186Q-26.488 183.073-26.761 183.030L-27.460 182.917Q-28.601 182.706-28.601 181.983Q-28.601 181.694-28.457 181.505Q-28.312 181.315-28.072 181.208Q-27.832 181.100-27.576 181.061Q-27.320 181.022-27.042 181.022Q-26.792 181.022-26.599 181.052Q-26.406 181.081-26.242 181.159Q-26.164 181.042-26.035 181.022L-25.957 181.022Q-25.859 181.034-25.796 181.096Q-25.734 181.159-25.722 181.253L-25.722 181.960Q-25.734 182.054-25.796 182.120Q-25.859 182.186-25.957 182.198L-26.125 182.198Q-26.218 182.186-26.285 182.120Q-26.351 182.054-26.363 181.960Q-26.363 181.581-27.058 181.581Q-27.406 181.581-27.724 181.663Q-28.042 181.745-28.042 181.991Q-28.042 182.257-27.371 182.366L-26.667 182.487Q-26.183 182.569-25.833 182.817Q-25.484 183.065-25.484 183.511Q-25.484 183.901-25.720 184.143Q-25.957 184.386-26.306 184.479Q-26.656 184.573-27.042 184.573Q-27.621 184.573-28.019 184.319Q-28.089 184.444-28.138 184.501Q-28.187 184.557-28.292 184.573L-28.363 184.573Q-28.578 184.550-28.601 184.335M-21.429 183.046L-23.871 183.046Q-23.816 183.323-23.619 183.546Q-23.421 183.768-23.144 183.891Q-22.867 184.014-22.582 184.014Q-22.109 184.014-21.886 183.725Q-21.878 183.714-21.822 183.608Q-21.765 183.503-21.716 183.460Q-21.667 183.417-21.574 183.405L-21.429 183.405Q-21.238 183.425-21.179 183.639L-21.179 183.694Q-21.246 183.995-21.476 184.192Q-21.707 184.389-22.019 184.481Q-22.332 184.573-22.636 184.573Q-23.121 184.573-23.560 184.345Q-24 184.116-24.267 183.716Q-24.535 183.315-24.535 182.823L-24.535 182.764Q-24.535 182.296-24.289 181.893Q-24.042 181.491-23.634 181.257Q-23.226 181.022-22.757 181.022Q-22.253 181.022-21.900 181.245Q-21.546 181.468-21.363 181.856Q-21.179 182.245-21.179 182.749L-21.179 182.807Q-21.238 183.022-21.429 183.046M-23.863 182.495L-21.835 182.495Q-21.882 182.085-22.121 181.833Q-22.359 181.581-22.757 181.581Q-23.152 181.581-23.458 181.843Q-23.765 182.104-23.863 182.495M-20.246 184.296L-20.246 184.206Q-20.195 183.999-20 183.975L-18.894 183.975L-18.894 180.206L-20 180.206Q-20.195 180.182-20.246 179.968L-20.246 179.878Q-20.195 179.671-20 179.647L-18.503 179.647Q-18.312 179.671-18.253 179.878L-18.253 183.975L-17.152 183.975Q-16.953 183.999-16.902 184.206L-16.902 184.296Q-16.953 184.511-17.152 184.534L-20 184.534Q-20.195 184.511-20.246 184.296M-16.128 184.296L-16.128 184.206Q-16.078 183.999-15.882 183.975L-15 183.975L-15 181.647L-15.855 181.647Q-16.054 181.624-16.105 181.405L-16.105 181.319Q-16.054 181.108-15.855 181.085L-15 181.085L-15 180.632Q-15 180.167-14.593 179.886Q-14.187 179.604-13.707 179.604Q-13.394 179.604-13.150 179.725Q-12.906 179.846-12.906 180.128Q-12.906 180.292-13.015 180.409Q-13.125 180.526-13.289 180.526Q-13.437 180.526-13.558 180.421Q-13.679 180.315-13.679 180.167L-13.761 180.167Q-13.914 180.167-14.050 180.227Q-14.187 180.288-14.273 180.403Q-14.359 180.518-14.359 180.663L-14.359 181.085L-13.328 181.085Q-13.132 181.104-13.082 181.319L-13.082 181.405Q-13.132 181.624-13.328 181.647L-14.359 181.647L-14.359 183.975L-13.480 183.975Q-13.285 183.999-13.234 184.206L-13.234 184.296Q-13.285 184.511-13.480 184.534L-15.882 184.534Q-16.078 184.511-16.128 184.296M-8.707 182.397L-11.449 182.397Q-11.574 182.386-11.660 182.300Q-11.746 182.214-11.746 182.085Q-11.746 181.956-11.660 181.874Q-11.574 181.792-11.449 181.780L-8.707 181.780Q-8.582 181.792-8.500 181.874Q-8.417 181.956-8.417 182.085Q-8.417 182.214-8.500 182.300Q-8.582 182.386-8.707 182.397M-7.550 183.421Q-7.550 182.975-7.136 182.718Q-6.722 182.460-6.181 182.360Q-5.640 182.261-5.132 182.253Q-5.132 182.038-5.267 181.886Q-5.402 181.733-5.609 181.657Q-5.816 181.581-6.027 181.581Q-6.371 181.581-6.531 181.604L-6.531 181.663Q-6.531 181.831-6.650 181.946Q-6.769 182.061-6.933 182.061Q-7.109 182.061-7.224 181.938Q-7.339 181.815-7.339 181.647Q-7.339 181.241-6.958 181.132Q-6.578 181.022-6.019 181.022Q-5.750 181.022-5.482 181.100Q-5.214 181.179-4.990 181.329Q-4.765 181.479-4.628 181.700Q-4.492 181.921-4.492 182.198L-4.492 183.917Q-4.492 183.975-3.964 183.975Q-3.769 183.995-3.718 184.206L-3.718 184.296Q-3.769 184.511-3.964 184.534L-4.109 184.534Q-4.453 184.534-4.681 184.487Q-4.910 184.440-5.054 184.253Q-5.515 184.573-6.222 184.573Q-6.558 184.573-6.863 184.432Q-7.167 184.292-7.359 184.030Q-7.550 183.768-7.550 183.421M-6.910 183.429Q-6.910 183.702-6.667 183.858Q-6.425 184.014-6.140 184.014Q-5.921 184.014-5.689 183.956Q-5.457 183.897-5.294 183.759Q-5.132 183.620-5.132 183.397L-5.132 182.807Q-5.414 182.807-5.830 182.864Q-6.246 182.921-6.578 183.059Q-6.910 183.198-6.910 183.429M-2.511 183.429L-2.511 181.647L-3.261 181.647Q-3.460 181.624-3.511 181.405L-3.511 181.319Q-3.460 181.108-3.261 181.085L-2.511 181.085L-2.511 180.335Q-2.460 180.128-2.261 180.100L-2.117 180.100Q-1.921 180.128-1.871 180.335L-1.871 181.085L-0.511 181.085Q-0.320 181.104-0.261 181.319L-0.261 181.405Q-0.316 181.624-0.511 181.647L-1.871 181.647L-1.871 183.397Q-1.871 184.014-1.296 184.014Q-1.046 184.014-0.882 183.829Q-0.718 183.643-0.718 183.397Q-0.718 183.304-0.646 183.233Q-0.574 183.163-0.472 183.151L-0.328 183.151Q-0.128 183.175-0.078 183.382L-0.078 183.429Q-0.078 183.753-0.261 184.016Q-0.445 184.280-0.738 184.427Q-1.031 184.573-1.351 184.573Q-1.863 184.573-2.187 184.263Q-2.511 183.952-2.511 183.429M1.735 183.429L1.735 181.647L0.985 181.647Q0.786 181.624 0.735 181.405L0.735 181.319Q0.786 181.108 0.985 181.085L1.735 181.085L1.735 180.335Q1.786 180.128 1.985 180.100L2.129 180.100Q2.325 180.128 2.375 180.335L2.375 181.085L3.735 181.085Q3.926 181.104 3.985 181.319L3.985 181.405Q3.930 181.624 3.735 181.647L2.375 181.647L2.375 183.397Q2.375 184.014 2.950 184.014Q3.200 184.014 3.364 183.829Q3.528 183.643 3.528 183.397Q3.528 183.304 3.600 183.233Q3.672 183.163 3.774 183.151L3.918 183.151Q4.118 183.175 4.168 183.382L4.168 183.429Q4.168 183.753 3.985 184.016Q3.801 184.280 3.508 184.427Q3.215 184.573 2.895 184.573Q2.383 184.573 2.059 184.263Q1.735 183.952 1.735 183.429M8.293 183.046L5.852 183.046Q5.907 183.323 6.104 183.546Q6.301 183.768 6.579 183.891Q6.856 184.014 7.141 184.014Q7.614 184.014 7.836 183.725Q7.844 183.714 7.901 183.608Q7.958 183.503 8.006 183.460Q8.055 183.417 8.149 183.405L8.293 183.405Q8.485 183.425 8.543 183.639L8.543 183.694Q8.477 183.995 8.247 184.192Q8.016 184.389 7.704 184.481Q7.391 184.573 7.086 184.573Q6.602 184.573 6.163 184.345Q5.723 184.116 5.456 183.716Q5.188 183.315 5.188 182.823L5.188 182.764Q5.188 182.296 5.434 181.893Q5.680 181.491 6.088 181.257Q6.497 181.022 6.965 181.022Q7.469 181.022 7.823 181.245Q8.176 181.468 8.360 181.856Q8.543 182.245 8.543 182.749L8.543 182.807Q8.485 183.022 8.293 183.046M5.860 182.495L7.887 182.495Q7.840 182.085 7.602 181.833Q7.364 181.581 6.965 181.581Q6.571 181.581 6.264 181.843Q5.958 182.104 5.860 182.495M9.098 184.296L9.098 184.206Q9.141 183.999 9.348 183.975L9.770 183.975L9.770 181.647L9.348 181.647Q9.141 181.624 9.098 181.405L9.098 181.319Q9.145 181.108 9.348 181.085L10.165 181.085Q10.360 181.108 10.411 181.319L10.411 181.405L10.403 181.429Q10.629 181.249 10.903 181.147Q11.176 181.046 11.469 181.046Q11.817 181.046 12.055 181.186Q12.293 181.327 12.409 181.585Q12.524 181.843 12.524 182.198L12.524 183.975L12.950 183.975Q13.157 183.999 13.196 184.206L13.196 184.296Q13.157 184.511 12.950 184.534L11.555 184.534Q11.360 184.511 11.309 184.296L11.309 184.206Q11.360 183.995 11.555 183.975L11.883 183.975L11.883 182.229Q11.883 181.921 11.793 181.763Q11.704 181.604 11.411 181.604Q11.141 181.604 10.913 181.735Q10.684 181.866 10.547 182.095Q10.411 182.323 10.411 182.589L10.411 183.975L10.836 183.975Q11.043 183.999 11.083 184.206L11.083 184.296Q11.043 184.511 10.836 184.534L9.348 184.534Q9.141 184.511 9.098 184.296M14.473 183.429L14.473 181.647L13.723 181.647Q13.524 181.624 13.473 181.405L13.473 181.319Q13.524 181.108 13.723 181.085L14.473 181.085L14.473 180.335Q14.524 180.128 14.723 180.100L14.868 180.100Q15.063 180.128 15.114 180.335L15.114 181.085L16.473 181.085Q16.665 181.104 16.723 181.319L16.723 181.405Q16.668 181.624 16.473 181.647L15.114 181.647L15.114 183.397Q15.114 184.014 15.688 184.014Q15.938 184.014 16.102 183.829Q16.266 183.643 16.266 183.397Q16.266 183.304 16.338 183.233Q16.411 183.163 16.512 183.151L16.657 183.151Q16.856 183.175 16.907 183.382L16.907 183.429Q16.907 183.753 16.723 184.016Q16.540 184.280 16.247 184.427Q15.954 184.573 15.633 184.573Q15.122 184.573 14.797 184.263Q14.473 183.952 14.473 183.429M18.137 184.296L18.137 184.206Q18.188 183.999 18.383 183.975L19.422 183.975L19.422 181.647L18.450 181.647Q18.250 181.624 18.200 181.405L18.200 181.319Q18.250 181.108 18.450 181.085L19.817 181.085Q20.012 181.104 20.063 181.319L20.063 183.975L20.977 183.975Q21.172 183.999 21.223 184.206L21.223 184.296Q21.172 184.511 20.977 184.534L18.383 184.534Q18.188 184.511 18.137 184.296M19.168 180.108L19.168 180.054Q19.168 179.882 19.305 179.761Q19.442 179.639 19.618 179.639Q19.790 179.639 19.926 179.761Q20.063 179.882 20.063 180.054L20.063 180.108Q20.063 180.284 19.926 180.405Q19.790 180.526 19.618 180.526Q19.442 180.526 19.305 180.405Q19.168 180.284 19.168 180.108M23.887 184.573Q23.415 184.573 23.030 184.329Q22.645 184.085 22.422 183.675Q22.200 183.264 22.200 182.807Q22.200 182.464 22.325 182.141Q22.450 181.819 22.680 181.565Q22.911 181.311 23.217 181.167Q23.524 181.022 23.887 181.022Q24.250 181.022 24.563 181.169Q24.875 181.315 25.098 181.561Q25.321 181.807 25.448 182.128Q25.575 182.448 25.575 182.807Q25.575 183.264 25.350 183.677Q25.125 184.089 24.741 184.331Q24.356 184.573 23.887 184.573M23.887 184.014Q24.352 184.014 24.643 183.620Q24.934 183.225 24.934 182.741Q24.934 182.448 24.799 182.180Q24.665 181.913 24.424 181.747Q24.184 181.581 23.887 181.581Q23.583 181.581 23.344 181.747Q23.106 181.913 22.971 182.180Q22.836 182.448 22.836 182.741Q22.836 183.221 23.129 183.618Q23.422 184.014 23.887 184.014M26.083 184.296L26.083 184.206Q26.125 183.999 26.333 183.975L26.754 183.975L26.754 181.647L26.333 181.647Q26.125 181.624 26.083 181.405L26.083 181.319Q26.129 181.108 26.333 181.085L27.149 181.085Q27.344 181.108 27.395 181.319L27.395 181.405L27.387 181.429Q27.614 181.249 27.887 181.147Q28.161 181.046 28.454 181.046Q28.801 181.046 29.040 181.186Q29.278 181.327 29.393 181.585Q29.508 181.843 29.508 182.198L29.508 183.975L29.934 183.975Q30.141 183.999 30.180 184.206L30.180 184.296Q30.141 184.511 29.934 184.534L28.540 184.534Q28.344 184.511 28.293 184.296L28.293 184.206Q28.344 183.995 28.540 183.975L28.868 183.975L28.868 182.229Q28.868 181.921 28.778 181.763Q28.688 181.604 28.395 181.604Q28.125 181.604 27.897 181.735Q27.668 181.866 27.532 182.095Q27.395 182.323 27.395 182.589L27.395 183.975L27.821 183.975Q28.028 183.999 28.067 184.206L28.067 184.296Q28.028 184.511 27.821 184.534L26.333 184.534Q26.125 184.511 26.083 184.296\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg stroke=\"var(--tk-accent)\">\u003Cpath fill=\"none\" d=\"M39.1-8.945h68.287v-22.762H39.1Z\"\u002F>\u003Cg transform=\"translate(76.93 -202.415)\">\u003Cpath d=\"M-28.867 184.296L-28.867 184.206Q-28.816 183.999-28.621 183.975L-27.738 183.975L-27.738 181.647L-28.593 181.647Q-28.792 181.624-28.843 181.405L-28.843 181.319Q-28.792 181.108-28.593 181.085L-27.738 181.085L-27.738 180.632Q-27.738 180.167-27.332 179.886Q-26.925 179.604-26.445 179.604Q-26.132 179.604-25.888 179.725Q-25.644 179.846-25.644 180.128Q-25.644 180.292-25.753 180.409Q-25.863 180.526-26.027 180.526Q-26.175 180.526-26.296 180.421Q-26.417 180.315-26.417 180.167L-26.500 180.167Q-26.652 180.167-26.789 180.227Q-26.925 180.288-27.011 180.403Q-27.097 180.518-27.097 180.663L-27.097 181.085L-26.066 181.085Q-25.871 181.104-25.820 181.319L-25.820 181.405Q-25.871 181.624-26.066 181.647L-27.097 181.647L-27.097 183.975L-26.218 183.975Q-26.023 183.999-25.972 184.206L-25.972 184.296Q-26.023 184.511-26.218 184.534L-28.621 184.534Q-28.816 184.511-28.867 184.296M-21.429 183.046L-23.871 183.046Q-23.816 183.323-23.619 183.546Q-23.421 183.768-23.144 183.891Q-22.867 184.014-22.582 184.014Q-22.109 184.014-21.886 183.725Q-21.878 183.714-21.822 183.608Q-21.765 183.503-21.716 183.460Q-21.667 183.417-21.574 183.405L-21.429 183.405Q-21.238 183.425-21.179 183.639L-21.179 183.694Q-21.246 183.995-21.476 184.192Q-21.707 184.389-22.019 184.481Q-22.332 184.573-22.636 184.573Q-23.121 184.573-23.560 184.345Q-24 184.116-24.267 183.716Q-24.535 183.315-24.535 182.823L-24.535 182.764Q-24.535 182.296-24.289 181.893Q-24.042 181.491-23.634 181.257Q-23.226 181.022-22.757 181.022Q-22.253 181.022-21.900 181.245Q-21.546 181.468-21.363 181.856Q-21.179 182.245-21.179 182.749L-21.179 182.807Q-21.238 183.022-21.429 183.046M-23.863 182.495L-21.835 182.495Q-21.882 182.085-22.121 181.833Q-22.359 181.581-22.757 181.581Q-23.152 181.581-23.458 181.843Q-23.765 182.104-23.863 182.495M-17.183 183.046L-19.625 183.046Q-19.570 183.323-19.373 183.546Q-19.175 183.768-18.898 183.891Q-18.621 184.014-18.335 184.014Q-17.863 184.014-17.640 183.725Q-17.632 183.714-17.576 183.608Q-17.519 183.503-17.470 183.460Q-17.421 183.417-17.328 183.405L-17.183 183.405Q-16.992 183.425-16.933 183.639L-16.933 183.694Q-17 183.995-17.230 184.192Q-17.460 184.389-17.773 184.481Q-18.085 184.573-18.390 184.573Q-18.875 184.573-19.314 184.345Q-19.753 184.116-20.021 183.716Q-20.289 183.315-20.289 182.823L-20.289 182.764Q-20.289 182.296-20.042 181.893Q-19.796 181.491-19.388 181.257Q-18.980 181.022-18.511 181.022Q-18.007 181.022-17.654 181.245Q-17.300 181.468-17.117 181.856Q-16.933 182.245-16.933 182.749L-16.933 182.807Q-16.992 183.022-17.183 183.046M-19.617 182.495L-17.589 182.495Q-17.636 182.085-17.875 181.833Q-18.113 181.581-18.511 181.581Q-18.906 181.581-19.212 181.843Q-19.519 182.104-19.617 182.495M-14.585 184.573Q-15.050 184.573-15.416 184.323Q-15.781 184.073-15.986 183.669Q-16.191 183.264-16.191 182.807Q-16.191 182.464-16.066 182.143Q-15.941 181.823-15.708 181.573Q-15.476 181.323-15.171 181.184Q-14.867 181.046-14.511 181.046Q-14 181.046-13.593 181.366L-13.593 180.206L-14.015 180.206Q-14.226 180.182-14.265 179.968L-14.265 179.878Q-14.226 179.671-14.015 179.647L-13.203 179.647Q-13.003 179.671-12.953 179.878L-12.953 183.975L-12.527 183.975Q-12.320 183.999-12.281 184.206L-12.281 184.296Q-12.320 184.511-12.527 184.534L-13.343 184.534Q-13.542 184.511-13.593 184.296L-13.593 184.167Q-13.789 184.358-14.050 184.466Q-14.312 184.573-14.585 184.573M-14.546 184.014Q-14.187 184.014-13.935 183.745Q-13.683 183.475-13.593 183.100L-13.593 182.268Q-13.652 182.081-13.779 181.930Q-13.906 181.780-14.083 181.692Q-14.261 181.604-14.457 181.604Q-14.765 181.604-15.015 181.774Q-15.265 181.944-15.410 182.229Q-15.554 182.514-15.554 182.815Q-15.554 183.264-15.269 183.639Q-14.984 184.014-14.546 184.014M-8.707 182.397L-11.449 182.397Q-11.574 182.386-11.660 182.300Q-11.746 182.214-11.746 182.085Q-11.746 181.956-11.660 181.874Q-11.574 181.792-11.449 181.780L-8.707 181.780Q-8.582 181.792-8.500 181.874Q-8.417 181.956-8.417 182.085Q-8.417 182.214-8.500 182.300Q-8.582 182.386-8.707 182.397M-7.636 184.296L-7.636 184.206Q-7.585 183.999-7.390 183.975L-6.507 183.975L-6.507 181.647L-7.363 181.647Q-7.562 181.624-7.613 181.405L-7.613 181.319Q-7.562 181.108-7.363 181.085L-6.507 181.085L-6.507 180.632Q-6.507 180.167-6.101 179.886Q-5.695 179.604-5.214 179.604Q-4.902 179.604-4.658 179.725Q-4.414 179.846-4.414 180.128Q-4.414 180.292-4.523 180.409Q-4.632 180.526-4.796 180.526Q-4.945 180.526-5.066 180.421Q-5.187 180.315-5.187 180.167L-5.269 180.167Q-5.421 180.167-5.558 180.227Q-5.695 180.288-5.781 180.403Q-5.867 180.518-5.867 180.663L-5.867 181.085L-4.835 181.085Q-4.640 181.104-4.589 181.319L-4.589 181.405Q-4.640 181.624-4.835 181.647L-5.867 181.647L-5.867 183.975L-4.988 183.975Q-4.792 183.999-4.742 184.206L-4.742 184.296Q-4.792 184.511-4.988 184.534L-7.390 184.534Q-7.585 184.511-7.636 184.296M-1.589 184.573Q-2.062 184.573-2.447 184.329Q-2.832 184.085-3.054 183.675Q-3.277 183.264-3.277 182.807Q-3.277 182.464-3.152 182.141Q-3.027 181.819-2.796 181.565Q-2.566 181.311-2.259 181.167Q-1.953 181.022-1.589 181.022Q-1.226 181.022-0.914 181.169Q-0.601 181.315-0.378 181.561Q-0.156 181.807-0.029 182.128Q0.098 182.448 0.098 182.807Q0.098 183.264-0.126 183.677Q-0.351 184.089-0.736 184.331Q-1.121 184.573-1.589 184.573M-1.589 184.014Q-1.125 184.014-0.833 183.620Q-0.542 183.225-0.542 182.741Q-0.542 182.448-0.677 182.180Q-0.812 181.913-1.052 181.747Q-1.292 181.581-1.589 181.581Q-1.894 181.581-2.132 181.747Q-2.371 181.913-2.505 182.180Q-2.640 182.448-2.640 182.741Q-2.640 183.221-2.347 183.618Q-2.054 184.014-1.589 184.014M0.758 184.296L0.758 184.206Q0.817 183.999 1.008 183.975L1.719 183.975L1.719 181.647L1.008 181.647Q0.813 181.624 0.758 181.405L0.758 181.319Q0.817 181.108 1.008 181.085L2.110 181.085Q2.309 181.104 2.360 181.319L2.360 181.647Q2.622 181.362 2.977 181.204Q3.333 181.046 3.719 181.046Q4.012 181.046 4.247 181.180Q4.481 181.315 4.481 181.581Q4.481 181.749 4.372 181.866Q4.262 181.983 4.094 181.983Q3.942 181.983 3.827 181.872Q3.711 181.761 3.711 181.604Q3.336 181.604 3.022 181.805Q2.708 182.007 2.534 182.341Q2.360 182.675 2.360 183.054L2.360 183.975L3.305 183.975Q3.512 183.999 3.551 184.206L3.551 184.296Q3.512 184.511 3.305 184.534L1.008 184.534Q0.817 184.511 0.758 184.296M5.790 184.311L5.325 181.647L5.165 181.647Q4.958 181.624 4.918 181.405L4.918 181.319Q4.958 181.108 5.165 181.085L6.333 181.085Q6.543 181.108 6.583 181.319L6.583 181.405Q6.543 181.624 6.333 181.647L5.860 181.647Q5.973 182.292 6.051 182.737Q6.129 183.182 6.180 183.501Q6.231 183.819 6.231 183.893Q6.239 183.721 6.524 182.725Q6.563 182.612 6.661 182.538Q6.758 182.464 6.879 182.464L6.958 182.464Q7.079 182.464 7.176 182.538Q7.274 182.612 7.309 182.725Q7.418 183.108 7.500 183.432Q7.583 183.757 7.583 183.893Q7.594 183.604 7.942 181.647L7.469 181.647Q7.262 181.624 7.223 181.405L7.223 181.319Q7.262 181.108 7.469 181.085L8.645 181.085Q8.836 181.108 8.895 181.319L8.895 181.405Q8.840 181.624 8.645 181.647L8.477 181.647L8.012 184.311Q7.989 184.429 7.901 184.501Q7.813 184.573 7.692 184.573L7.551 184.573Q7.430 184.573 7.334 184.501Q7.239 184.429 7.196 184.311Q7.149 184.132 7.077 183.876Q7.004 183.620 6.961 183.411Q6.918 183.202 6.918 183.100Q6.911 183.382 6.629 184.311Q6.602 184.421 6.504 184.497Q6.407 184.573 6.286 184.573L6.110 184.573Q5.989 184.573 5.901 184.501Q5.813 184.429 5.790 184.311M9.434 183.421Q9.434 182.975 9.848 182.718Q10.262 182.460 10.803 182.360Q11.344 182.261 11.852 182.253Q11.852 182.038 11.717 181.886Q11.583 181.733 11.375 181.657Q11.168 181.581 10.958 181.581Q10.614 181.581 10.454 181.604L10.454 181.663Q10.454 181.831 10.334 181.946Q10.215 182.061 10.051 182.061Q9.875 182.061 9.760 181.938Q9.645 181.815 9.645 181.647Q9.645 181.241 10.026 181.132Q10.407 181.022 10.965 181.022Q11.235 181.022 11.502 181.100Q11.770 181.179 11.995 181.329Q12.219 181.479 12.356 181.700Q12.493 181.921 12.493 182.198L12.493 183.917Q12.493 183.975 13.020 183.975Q13.215 183.995 13.266 184.206L13.266 184.296Q13.215 184.511 13.020 184.534L12.875 184.534Q12.532 184.534 12.303 184.487Q12.075 184.440 11.930 184.253Q11.469 184.573 10.762 184.573Q10.426 184.573 10.122 184.432Q9.817 184.292 9.625 184.030Q9.434 183.768 9.434 183.421M10.075 183.429Q10.075 183.702 10.317 183.858Q10.559 184.014 10.844 184.014Q11.063 184.014 11.295 183.956Q11.528 183.897 11.690 183.759Q11.852 183.620 11.852 183.397L11.852 182.807Q11.571 182.807 11.155 182.864Q10.739 182.921 10.407 183.059Q10.075 183.198 10.075 183.429M13.497 184.296L13.497 184.206Q13.555 183.999 13.747 183.975L14.458 183.975L14.458 181.647L13.747 181.647Q13.551 181.624 13.497 181.405L13.497 181.319Q13.555 181.108 13.747 181.085L14.848 181.085Q15.047 181.104 15.098 181.319L15.098 181.647Q15.360 181.362 15.715 181.204Q16.071 181.046 16.458 181.046Q16.750 181.046 16.985 181.180Q17.219 181.315 17.219 181.581Q17.219 181.749 17.110 181.866Q17 181.983 16.833 181.983Q16.680 181.983 16.565 181.872Q16.450 181.761 16.450 181.604Q16.075 181.604 15.760 181.805Q15.446 182.007 15.272 182.341Q15.098 182.675 15.098 183.054L15.098 183.975L16.043 183.975Q16.250 183.999 16.290 184.206L16.290 184.296Q16.250 184.511 16.043 184.534L13.747 184.534Q13.555 184.511 13.497 184.296M19.383 184.573Q18.918 184.573 18.553 184.323Q18.188 184.073 17.983 183.669Q17.778 183.264 17.778 182.807Q17.778 182.464 17.903 182.143Q18.028 181.823 18.260 181.573Q18.493 181.323 18.797 181.184Q19.102 181.046 19.458 181.046Q19.969 181.046 20.375 181.366L20.375 180.206L19.954 180.206Q19.743 180.182 19.704 179.968L19.704 179.878Q19.743 179.671 19.954 179.647L20.766 179.647Q20.965 179.671 21.016 179.878L21.016 183.975L21.442 183.975Q21.649 183.999 21.688 184.206L21.688 184.296Q21.649 184.511 21.442 184.534L20.625 184.534Q20.426 184.511 20.375 184.296L20.375 184.167Q20.180 184.358 19.918 184.466Q19.657 184.573 19.383 184.573M19.422 184.014Q19.782 184.014 20.034 183.745Q20.286 183.475 20.375 183.100L20.375 182.268Q20.317 182.081 20.190 181.930Q20.063 181.780 19.885 181.692Q19.708 181.604 19.512 181.604Q19.204 181.604 18.954 181.774Q18.704 181.944 18.559 182.229Q18.415 182.514 18.415 182.815Q18.415 183.264 18.700 183.639Q18.985 184.014 19.422 184.014\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-24.634 166.04H36.3\"\u002F>\u003Cpath stroke=\"none\" d=\"m38.9 166.04-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M38.9 134.741h-60.934\"\u002F>\u003Cpath stroke=\"none\" d=\"m-24.634 134.741 4.16 2.08-1.56-2.08 1.56-2.08\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-24.634 109.134H36.3\"\u002F>\u003Cpath stroke=\"none\" d=\"m38.9 109.134-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M38.9 77.836h-60.934\"\u002F>\u003Cpath stroke=\"none\" d=\"m-24.634 77.836 4.16 2.08-1.56-2.08 1.56-2.08\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-24.634 52.229H36.3\"\u002F>\u003Cpath stroke=\"none\" d=\"m38.9 52.229-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M38.9 20.93h-60.934\"\u002F>\u003Cpath stroke=\"none\" d=\"m-24.634 20.93 4.16 2.08-1.56-2.08 1.56-2.08\"\u002F>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-24.634-4.677H36.3\"\u002F>\u003Cpath stroke=\"none\" d=\"m38.9-4.677-4.16-2.08 1.56 2.08-1.56 2.08\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M38.9-35.975h-60.934\"\u002F>\u003Cpath stroke=\"none\" d=\"m-24.634-35.975 4.16 2.08-1.56-2.08 1.56-2.08\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(45.56 -23.45)\">\u003Cpath d=\"M-28.964 184.296L-28.964 184.206Q-28.906 183.999-28.714 183.975L-28.003 183.975L-28.003 181.647L-28.714 181.647Q-28.910 181.624-28.964 181.405L-28.964 181.319Q-28.906 181.108-28.714 181.085L-27.613 181.085Q-27.414 181.104-27.363 181.319L-27.363 181.647Q-27.101 181.362-26.746 181.204Q-26.390 181.046-26.003 181.046Q-25.710 181.046-25.476 181.180Q-25.242 181.315-25.242 181.581Q-25.242 181.749-25.351 181.866Q-25.460 181.983-25.628 181.983Q-25.781 181.983-25.896 181.872Q-26.011 181.761-26.011 181.604Q-26.386 181.604-26.701 181.805Q-27.015 182.007-27.189 182.341Q-27.363 182.675-27.363 183.054L-27.363 183.975L-26.417 183.975Q-26.210 183.999-26.171 184.206L-26.171 184.296Q-26.210 184.511-26.417 184.534L-28.714 184.534Q-28.906 184.511-28.964 184.296M-21.429 183.046L-23.871 183.046Q-23.816 183.323-23.619 183.546Q-23.421 183.768-23.144 183.891Q-22.867 184.014-22.582 184.014Q-22.109 184.014-21.886 183.725Q-21.878 183.714-21.822 183.608Q-21.765 183.503-21.716 183.460Q-21.667 183.417-21.574 183.405L-21.429 183.405Q-21.238 183.425-21.179 183.639L-21.179 183.694Q-21.246 183.995-21.476 184.192Q-21.707 184.389-22.019 184.481Q-22.332 184.573-22.636 184.573Q-23.121 184.573-23.560 184.345Q-24 184.116-24.267 183.716Q-24.535 183.315-24.535 182.823L-24.535 182.764Q-24.535 182.296-24.289 181.893Q-24.042 181.491-23.634 181.257Q-23.226 181.022-22.757 181.022Q-22.253 181.022-21.900 181.245Q-21.546 181.468-21.363 181.856Q-21.179 182.245-21.179 182.749L-21.179 182.807Q-21.238 183.022-21.429 183.046M-23.863 182.495L-21.835 182.495Q-21.882 182.085-22.121 181.833Q-22.359 181.581-22.757 181.581Q-23.152 181.581-23.458 181.843Q-23.765 182.104-23.863 182.495M-20.289 183.421Q-20.289 182.975-19.875 182.718Q-19.460 182.460-18.919 182.360Q-18.378 182.261-17.871 182.253Q-17.871 182.038-18.005 181.886Q-18.140 181.733-18.347 181.657Q-18.554 181.581-18.765 181.581Q-19.109 181.581-19.269 181.604L-19.269 181.663Q-19.269 181.831-19.388 181.946Q-19.507 182.061-19.671 182.061Q-19.847 182.061-19.962 181.938Q-20.078 181.815-20.078 181.647Q-20.078 181.241-19.697 181.132Q-19.316 181.022-18.757 181.022Q-18.488 181.022-18.220 181.100Q-17.953 181.179-17.728 181.329Q-17.503 181.479-17.367 181.700Q-17.230 181.921-17.230 182.198L-17.230 183.917Q-17.230 183.975-16.703 183.975Q-16.507 183.995-16.457 184.206L-16.457 184.296Q-16.507 184.511-16.703 184.534L-16.847 184.534Q-17.191 184.534-17.419 184.487Q-17.648 184.440-17.792 184.253Q-18.253 184.573-18.960 184.573Q-19.296 184.573-19.601 184.432Q-19.906 184.292-20.097 184.030Q-20.289 183.768-20.289 183.421M-19.648 183.429Q-19.648 183.702-19.406 183.858Q-19.164 184.014-18.878 184.014Q-18.660 184.014-18.427 183.956Q-18.195 183.897-18.033 183.759Q-17.871 183.620-17.871 183.397L-17.871 182.807Q-18.152 182.807-18.568 182.864Q-18.984 182.921-19.316 183.059Q-19.648 183.198-19.648 183.429M-14.585 184.573Q-15.050 184.573-15.416 184.323Q-15.781 184.073-15.986 183.669Q-16.191 183.264-16.191 182.807Q-16.191 182.464-16.066 182.143Q-15.941 181.823-15.708 181.573Q-15.476 181.323-15.171 181.184Q-14.867 181.046-14.511 181.046Q-14 181.046-13.593 181.366L-13.593 180.206L-14.015 180.206Q-14.226 180.182-14.265 179.968L-14.265 179.878Q-14.226 179.671-14.015 179.647L-13.203 179.647Q-13.003 179.671-12.953 179.878L-12.953 183.975L-12.527 183.975Q-12.320 183.999-12.281 184.206L-12.281 184.296Q-12.320 184.511-12.527 184.534L-13.343 184.534Q-13.542 184.511-13.593 184.296L-13.593 184.167Q-13.789 184.358-14.050 184.466Q-14.312 184.573-14.585 184.573M-14.546 184.014Q-14.187 184.014-13.935 183.745Q-13.683 183.475-13.593 183.100L-13.593 182.268Q-13.652 182.081-13.779 181.930Q-13.906 181.780-14.083 181.692Q-14.261 181.604-14.457 181.604Q-14.765 181.604-15.015 181.774Q-15.265 181.944-15.410 182.229Q-15.554 182.514-15.554 182.815Q-15.554 183.264-15.269 183.639Q-14.984 184.014-14.546 184.014\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\">\u003Cg fill=\"var(--tk-good)\" stroke=\"none\" font-family=\"cmtt8\" font-size=\"8\">\u003Cg transform=\"translate(30.685 -227.554)\">\u003Cpath d=\"M-28.179 184.311L-28.644 181.647L-28.804 181.647Q-29.011 181.624-29.050 181.405L-29.050 181.319Q-29.011 181.108-28.804 181.085L-27.636 181.085Q-27.425 181.108-27.386 181.319L-27.386 181.405Q-27.425 181.624-27.636 181.647L-28.109 181.647Q-27.996 182.292-27.917 182.737Q-27.839 183.182-27.789 183.501Q-27.738 183.819-27.738 183.893Q-27.730 183.721-27.445 182.725Q-27.406 182.612-27.308 182.538Q-27.210 182.464-27.089 182.464L-27.011 182.464Q-26.890 182.464-26.792 182.538Q-26.695 182.612-26.660 182.725Q-26.550 183.108-26.468 183.432Q-26.386 183.757-26.386 183.893Q-26.375 183.604-26.027 181.647L-26.500 181.647Q-26.707 181.624-26.746 181.405L-26.746 181.319Q-26.707 181.108-26.500 181.085L-25.324 181.085Q-25.132 181.108-25.074 181.319L-25.074 181.405Q-25.128 181.624-25.324 181.647L-25.492 181.647L-25.957 184.311Q-25.980 184.429-26.068 184.501Q-26.156 184.573-26.277 184.573L-26.417 184.573Q-26.539 184.573-26.634 184.501Q-26.730 184.429-26.773 184.311Q-26.820 184.132-26.892 183.876Q-26.964 183.620-27.007 183.411Q-27.050 183.202-27.050 183.100Q-27.058 183.382-27.339 184.311Q-27.367 184.421-27.464 184.497Q-27.562 184.573-27.683 184.573L-27.859 184.573Q-27.980 184.573-28.068 184.501Q-28.156 184.429-28.179 184.311M-24.718 184.296L-24.718 184.206Q-24.660 183.999-24.468 183.975L-23.757 183.975L-23.757 181.647L-24.468 181.647Q-24.664 181.624-24.718 181.405L-24.718 181.319Q-24.660 181.108-24.468 181.085L-23.367 181.085Q-23.167 181.104-23.117 181.319L-23.117 181.647Q-22.855 181.362-22.500 181.204Q-22.144 181.046-21.757 181.046Q-21.464 181.046-21.230 181.180Q-20.996 181.315-20.996 181.581Q-20.996 181.749-21.105 181.866Q-21.214 181.983-21.382 181.983Q-21.535 181.983-21.650 181.872Q-21.765 181.761-21.765 181.604Q-22.140 181.604-22.455 181.805Q-22.769 182.007-22.943 182.341Q-23.117 182.675-23.117 183.054L-23.117 183.975L-22.171 183.975Q-21.964 183.999-21.925 184.206L-21.925 184.296Q-21.964 184.511-22.171 184.534L-24.468 184.534Q-24.660 184.511-24.718 184.296M-20.078 184.296L-20.078 184.206Q-20.027 183.999-19.832 183.975L-18.792 183.975L-18.792 181.647L-19.765 181.647Q-19.964 181.624-20.015 181.405L-20.015 181.319Q-19.964 181.108-19.765 181.085L-18.398 181.085Q-18.203 181.104-18.152 181.319L-18.152 183.975L-17.238 183.975Q-17.042 183.999-16.992 184.206L-16.992 184.296Q-17.042 184.511-17.238 184.534L-19.832 184.534Q-20.027 184.511-20.078 184.296M-19.046 180.108L-19.046 180.054Q-19.046 179.882-18.910 179.761Q-18.773 179.639-18.597 179.639Q-18.425 179.639-18.289 179.761Q-18.152 179.882-18.152 180.054L-18.152 180.108Q-18.152 180.284-18.289 180.405Q-18.425 180.526-18.597 180.526Q-18.773 180.526-18.910 180.405Q-19.046 180.284-19.046 180.108M-15.250 183.429L-15.250 181.647L-16 181.647Q-16.199 181.624-16.250 181.405L-16.250 181.319Q-16.199 181.108-16 181.085L-15.250 181.085L-15.250 180.335Q-15.199 180.128-15 180.100L-14.855 180.100Q-14.660 180.128-14.609 180.335L-14.609 181.085L-13.250 181.085Q-13.058 181.104-13 181.319L-13 181.405Q-13.054 181.624-13.250 181.647L-14.609 181.647L-14.609 183.397Q-14.609 184.014-14.035 184.014Q-13.785 184.014-13.621 183.829Q-13.457 183.643-13.457 183.397Q-13.457 183.304-13.384 183.233Q-13.312 183.163-13.210 183.151L-13.066 183.151Q-12.867 183.175-12.816 183.382L-12.816 183.429Q-12.816 183.753-13 184.016Q-13.183 184.280-13.476 184.427Q-13.769 184.573-14.089 184.573Q-14.601 184.573-14.925 184.263Q-15.250 183.952-15.250 183.429M-8.691 183.046L-11.132 183.046Q-11.078 183.323-10.880 183.546Q-10.683 183.768-10.406 183.891Q-10.128 184.014-9.843 184.014Q-9.371 184.014-9.148 183.725Q-9.140 183.714-9.083 183.608Q-9.027 183.503-8.978 183.460Q-8.929 183.417-8.835 183.405L-8.691 183.405Q-8.500 183.425-8.441 183.639L-8.441 183.694Q-8.507 183.995-8.738 184.192Q-8.968 184.389-9.281 184.481Q-9.593 184.573-9.898 184.573Q-10.382 184.573-10.822 184.345Q-11.261 184.116-11.529 183.716Q-11.796 183.315-11.796 182.823L-11.796 182.764Q-11.796 182.296-11.550 181.893Q-11.304 181.491-10.896 181.257Q-10.488 181.022-10.019 181.022Q-9.515 181.022-9.162 181.245Q-8.808 181.468-8.625 181.856Q-8.441 182.245-8.441 182.749L-8.441 182.807Q-8.500 183.022-8.691 183.046M-11.125 182.495L-9.097 182.495Q-9.144 182.085-9.382 181.833Q-9.621 181.581-10.019 181.581Q-10.414 181.581-10.720 181.843Q-11.027 182.104-11.125 182.495\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(30.685 -227.554)\">\u003Cpath d=\"M-0.573 185.175Q-1.104 184.866-1.504 184.378Q-1.905 183.889-2.116 183.296Q-2.327 182.702-2.327 182.085Q-2.327 181.468-2.118 180.880Q-1.909 180.292-1.512 179.811Q-1.116 179.331-0.581 179.007Q-0.510 178.983-0.479 178.983L-0.389 178.983Q-0.291 178.995-0.225 179.061Q-0.159 179.128-0.159 179.229Q-0.159 179.374-0.260 179.436Q-0.709 179.725-1.036 180.141Q-1.362 180.557-1.524 181.050Q-1.686 181.542-1.686 182.085Q-1.686 182.491-1.590 182.878Q-1.495 183.264-1.317 183.600Q-1.139 183.936-0.879 184.220Q-0.620 184.503-0.272 184.733Q-0.159 184.811-0.159 184.948Q-0.159 185.046-0.225 185.116Q-0.291 185.186-0.389 185.198L-0.479 185.198Q-0.538 185.198-0.573 185.175M0.966 183.421Q0.966 182.975 1.380 182.718Q1.794 182.460 2.335 182.360Q2.877 182.261 3.384 182.253Q3.384 182.038 3.250 181.886Q3.115 181.733 2.908 181.657Q2.701 181.581 2.490 181.581Q2.146 181.581 1.986 181.604L1.986 181.663Q1.986 181.831 1.867 181.946Q1.748 182.061 1.584 182.061Q1.408 182.061 1.293 181.938Q1.177 181.815 1.177 181.647Q1.177 181.241 1.558 181.132Q1.939 181.022 2.498 181.022Q2.767 181.022 3.035 181.100Q3.302 181.179 3.527 181.329Q3.752 181.479 3.888 181.700Q4.025 181.921 4.025 182.198L4.025 183.917Q4.025 183.975 4.552 183.975Q4.748 183.995 4.798 184.206L4.798 184.296Q4.748 184.511 4.552 184.534L4.408 184.534Q4.064 184.534 3.835 184.487Q3.607 184.440 3.462 184.253Q3.002 184.573 2.294 184.573Q1.959 184.573 1.654 184.432Q1.349 184.292 1.158 184.030Q0.966 183.768 0.966 183.421M1.607 183.429Q1.607 183.702 1.849 183.858Q2.091 184.014 2.377 184.014Q2.595 184.014 2.828 183.956Q3.060 183.897 3.222 183.759Q3.384 183.620 3.384 183.397L3.384 182.807Q3.103 182.807 2.687 182.864Q2.271 182.921 1.939 183.059Q1.607 183.198 1.607 183.429M6.669 184.573Q6.205 184.573 5.839 184.323Q5.474 184.073 5.269 183.669Q5.064 183.264 5.064 182.807Q5.064 182.464 5.189 182.143Q5.314 181.823 5.546 181.573Q5.779 181.323 6.084 181.184Q6.388 181.046 6.744 181.046Q7.255 181.046 7.662 181.366L7.662 180.206L7.240 180.206Q7.029 180.182 6.990 179.968L6.990 179.878Q7.029 179.671 7.240 179.647L8.052 179.647Q8.252 179.671 8.302 179.878L8.302 183.975L8.728 183.975Q8.935 183.999 8.974 184.206L8.974 184.296Q8.935 184.511 8.728 184.534L7.912 184.534Q7.712 184.511 7.662 184.296L7.662 184.167Q7.466 184.358 7.205 184.466Q6.943 184.573 6.669 184.573M6.709 184.014Q7.068 184.014 7.320 183.745Q7.572 183.475 7.662 183.100L7.662 182.268Q7.603 182.081 7.476 181.930Q7.349 181.780 7.171 181.692Q6.994 181.604 6.798 181.604Q6.490 181.604 6.240 181.774Q5.990 181.944 5.845 182.229Q5.701 182.514 5.701 182.815Q5.701 183.264 5.986 183.639Q6.271 184.014 6.709 184.014M10.916 184.573Q10.451 184.573 10.085 184.323Q9.720 184.073 9.515 183.669Q9.310 183.264 9.310 182.807Q9.310 182.464 9.435 182.143Q9.560 181.823 9.793 181.573Q10.025 181.323 10.330 181.184Q10.634 181.046 10.990 181.046Q11.502 181.046 11.908 181.366L11.908 180.206L11.486 180.206Q11.275 180.182 11.236 179.968L11.236 179.878Q11.275 179.671 11.486 179.647L12.298 179.647Q12.498 179.671 12.548 179.878L12.548 183.975L12.974 183.975Q13.181 183.999 13.220 184.206L13.220 184.296Q13.181 184.511 12.974 184.534L12.158 184.534Q11.959 184.511 11.908 184.296L11.908 184.167Q11.712 184.358 11.451 184.466Q11.189 184.573 10.916 184.573M10.955 184.014Q11.314 184.014 11.566 183.745Q11.818 183.475 11.908 183.100L11.908 182.268Q11.849 182.081 11.722 181.930Q11.595 181.780 11.418 181.692Q11.240 181.604 11.044 181.604Q10.736 181.604 10.486 181.774Q10.236 181.944 10.091 182.229Q9.947 182.514 9.947 182.815Q9.947 183.264 10.232 183.639Q10.517 184.014 10.955 184.014M14.337 185.198L14.252 185.198Q14.146 185.186 14.078 185.114Q14.009 185.042 14.009 184.948Q14.009 184.807 14.115 184.741Q14.451 184.526 14.720 184.237Q14.990 183.948 15.173 183.600Q15.357 183.253 15.447 182.874Q15.537 182.495 15.537 182.085Q15.537 181.546 15.373 181.054Q15.209 180.561 14.890 180.147Q14.572 179.733 14.130 179.444Q14.009 179.362 14.009 179.229Q14.009 179.132 14.078 179.063Q14.146 178.995 14.252 178.983L14.337 178.983Q14.392 178.983 14.427 179.007Q14.814 179.229 15.154 179.577Q15.494 179.925 15.714 180.319Q15.935 180.714 16.056 181.159Q16.177 181.604 16.177 182.085Q16.177 182.569 16.056 183.020Q15.935 183.471 15.710 183.868Q15.486 184.264 15.162 184.598Q14.837 184.932 14.435 185.175Q14.365 185.198 14.337 185.198\" fill=\"var(--tk-good)\" stroke=\"var(--tk-good)\" class=\"tikz-text\" style=\"stroke-width:0.240\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">The residual stream. A fixed-width bus (black) runs up the stack; each block reads a normalized view (black) and writes an additive update back (green), never overwriting it.\u003C\u002Ffigcaption>","\u003Csvg style=\"width:100%;max-width:337.286px;height:auto\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"-75 -75 252.965 161.898\">\u003Cg stroke=\"currentColor\" style=\"stroke-miterlimit:10;stroke-width:.4\">\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-48.888 71.9h196.57\"\u002F>\u003Cpath stroke=\"none\" d=\"m150.282 71.9-4.16-2.079 1.56 2.08-1.56 2.08\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(202.902 1.75)\">\u003Cpath d=\"M-46.906 71.901L-48.509 71.901L-48.509 71.621Q-48.283 71.621-48.134 71.587Q-47.986 71.552-47.986 71.412L-47.986 67.793Q-47.986 67.523-48.093 67.461Q-48.201 67.400-48.509 67.400L-48.509 67.119L-47.432 67.044L-47.432 71.412Q-47.432 71.549-47.282 71.585Q-47.131 71.621-46.906 71.621L-46.906 71.901M-46.352 70.418Q-46.352 70.076-46.217 69.777Q-46.082 69.478-45.843 69.254Q-45.603 69.030-45.285 68.905Q-44.968 68.780-44.636 68.780Q-44.192 68.780-43.792 68.996Q-43.392 69.211-43.158 69.589Q-42.924 69.966-42.924 70.418Q-42.924 70.759-43.065 71.043Q-43.207 71.327-43.452 71.534Q-43.696 71.740-44.005 71.855Q-44.315 71.969-44.636 71.969Q-45.067 71.969-45.468 71.768Q-45.870 71.566-46.111 71.214Q-46.352 70.862-46.352 70.418M-44.636 71.720Q-44.034 71.720-43.811 71.342Q-43.587 70.964-43.587 70.332Q-43.587 69.720-43.821 69.361Q-44.055 69.003-44.636 69.003Q-45.689 69.003-45.689 70.332Q-45.689 70.964-45.463 71.342Q-45.238 71.720-44.636 71.720M-42.370 72.434Q-42.370 72.188-42.173 72.004Q-41.977 71.819-41.721 71.740Q-41.857 71.628-41.929 71.467Q-42.001 71.306-42.001 71.125Q-42.001 70.804-41.789 70.558Q-42.124 70.260-42.124 69.850Q-42.124 69.389-41.734 69.102Q-41.345 68.815-40.866 68.815Q-40.394 68.815-40.059 69.061Q-39.885 68.907-39.675 68.825Q-39.465 68.743-39.236 68.743Q-39.072 68.743-38.950 68.850Q-38.829 68.958-38.829 69.122Q-38.829 69.218-38.901 69.290Q-38.972 69.361-39.065 69.361Q-39.164 69.361-39.234 69.288Q-39.304 69.214-39.304 69.115Q-39.304 69.061-39.290 69.030L-39.284 69.016Q-39.277 68.996-39.268 68.985Q-39.260 68.975-39.256 68.968Q-39.612 68.968-39.899 69.191Q-39.612 69.484-39.612 69.850Q-39.612 70.165-39.796 70.397Q-39.981 70.630-40.270 70.758Q-40.558 70.886-40.866 70.886Q-41.068 70.886-41.259 70.836Q-41.450 70.787-41.628 70.677Q-41.721 70.804-41.721 70.947Q-41.721 71.129-41.592 71.264Q-41.464 71.399-41.280 71.399L-40.647 71.399Q-40.200 71.399-39.830 71.470Q-39.461 71.542-39.201 71.771Q-38.942 72-38.942 72.434Q-38.942 72.755-39.237 72.957Q-39.533 73.159-39.936 73.248Q-40.340 73.337-40.654 73.337Q-40.972 73.337-41.375 73.248Q-41.779 73.159-42.074 72.957Q-42.370 72.755-42.370 72.434M-41.915 72.434Q-41.915 72.663-41.697 72.812Q-41.478 72.961-41.186 73.029Q-40.893 73.097-40.654 73.097Q-40.490 73.097-40.282 73.061Q-40.073 73.026-39.866 72.945Q-39.659 72.865-39.528 72.737Q-39.396 72.609-39.396 72.434Q-39.396 72.082-39.777 71.988Q-40.159 71.894-40.661 71.894L-41.280 71.894Q-41.519 71.894-41.717 72.045Q-41.915 72.195-41.915 72.434M-40.866 70.647Q-40.200 70.647-40.200 69.850Q-40.200 69.050-40.866 69.050Q-41.536 69.050-41.536 69.850Q-41.536 70.647-40.866 70.647\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(202.902 1.75)\">\u003Cpath d=\"M-33.961 71.901L-35.595 71.901L-35.595 71.621Q-35.366 71.621-35.217 71.587Q-35.068 71.552-35.068 71.412L-35.068 69.563Q-35.068 69.293-35.176 69.232Q-35.284 69.170-35.595 69.170L-35.595 68.890L-34.535 68.815L-34.535 69.464Q-34.364 69.156-34.060 68.985Q-33.756 68.815-33.411 68.815Q-32.905 68.815-32.621 69.038Q-32.337 69.262-32.337 69.758L-32.337 71.412Q-32.337 71.549-32.189 71.585Q-32.040 71.621-31.814 71.621L-31.814 71.901L-33.445 71.901L-33.445 71.621Q-33.216 71.621-33.067 71.587Q-32.918 71.552-32.918 71.412L-32.918 69.772Q-32.918 69.437-33.038 69.237Q-33.158 69.037-33.472 69.037Q-33.742 69.037-33.976 69.173Q-34.210 69.310-34.349 69.544Q-34.487 69.778-34.487 70.052L-34.487 71.412Q-34.487 71.549-34.337 71.585Q-34.186 71.621-33.961 71.621\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:.8\">\u003Cpath fill=\"none\" d=\"M-48.888 71.9V-56.381\"\u002F>\u003Cpath stroke=\"none\" d=\"m-48.888-58.982-2.08 4.16 2.08-1.56 2.08 1.56\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(-13.383 -135.977)\">\u003Cpath d=\"M-46.906 71.901L-48.509 71.901L-48.509 71.621Q-48.283 71.621-48.134 71.587Q-47.986 71.552-47.986 71.412L-47.986 67.793Q-47.986 67.523-48.093 67.461Q-48.201 67.400-48.509 67.400L-48.509 67.119L-47.432 67.044L-47.432 71.412Q-47.432 71.549-47.282 71.585Q-47.131 71.621-46.906 71.621L-46.906 71.901M-46.352 70.418Q-46.352 70.076-46.217 69.777Q-46.082 69.478-45.843 69.254Q-45.603 69.030-45.285 68.905Q-44.968 68.780-44.636 68.780Q-44.192 68.780-43.792 68.996Q-43.392 69.211-43.158 69.589Q-42.924 69.966-42.924 70.418Q-42.924 70.759-43.065 71.043Q-43.207 71.327-43.452 71.534Q-43.696 71.740-44.005 71.855Q-44.315 71.969-44.636 71.969Q-45.067 71.969-45.468 71.768Q-45.870 71.566-46.111 71.214Q-46.352 70.862-46.352 70.418M-44.636 71.720Q-44.034 71.720-43.811 71.342Q-43.587 70.964-43.587 70.332Q-43.587 69.720-43.821 69.361Q-44.055 69.003-44.636 69.003Q-45.689 69.003-45.689 70.332Q-45.689 70.964-45.463 71.342Q-45.238 71.720-44.636 71.720M-42.370 72.434Q-42.370 72.188-42.173 72.004Q-41.977 71.819-41.721 71.740Q-41.857 71.628-41.929 71.467Q-42.001 71.306-42.001 71.125Q-42.001 70.804-41.789 70.558Q-42.124 70.260-42.124 69.850Q-42.124 69.389-41.734 69.102Q-41.345 68.815-40.866 68.815Q-40.394 68.815-40.059 69.061Q-39.885 68.907-39.675 68.825Q-39.465 68.743-39.236 68.743Q-39.072 68.743-38.950 68.850Q-38.829 68.958-38.829 69.122Q-38.829 69.218-38.901 69.290Q-38.972 69.361-39.065 69.361Q-39.164 69.361-39.234 69.288Q-39.304 69.214-39.304 69.115Q-39.304 69.061-39.290 69.030L-39.284 69.016Q-39.277 68.996-39.268 68.985Q-39.260 68.975-39.256 68.968Q-39.612 68.968-39.899 69.191Q-39.612 69.484-39.612 69.850Q-39.612 70.165-39.796 70.397Q-39.981 70.630-40.270 70.758Q-40.558 70.886-40.866 70.886Q-41.068 70.886-41.259 70.836Q-41.450 70.787-41.628 70.677Q-41.721 70.804-41.721 70.947Q-41.721 71.129-41.592 71.264Q-41.464 71.399-41.280 71.399L-40.647 71.399Q-40.200 71.399-39.830 71.470Q-39.461 71.542-39.201 71.771Q-38.942 72-38.942 72.434Q-38.942 72.755-39.237 72.957Q-39.533 73.159-39.936 73.248Q-40.340 73.337-40.654 73.337Q-40.972 73.337-41.375 73.248Q-41.779 73.159-42.074 72.957Q-42.370 72.755-42.370 72.434M-41.915 72.434Q-41.915 72.663-41.697 72.812Q-41.478 72.961-41.186 73.029Q-40.893 73.097-40.654 73.097Q-40.490 73.097-40.282 73.061Q-40.073 73.026-39.866 72.945Q-39.659 72.865-39.528 72.737Q-39.396 72.609-39.396 72.434Q-39.396 72.082-39.777 71.988Q-40.159 71.894-40.661 71.894L-41.280 71.894Q-41.519 71.894-41.717 72.045Q-41.915 72.195-41.915 72.434M-40.866 70.647Q-40.200 70.647-40.200 69.850Q-40.200 69.050-40.866 69.050Q-41.536 69.050-41.536 69.850Q-41.536 70.647-40.866 70.647\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(-13.383 -135.977)\">\u003Cpath d=\"M-35.643 70.390Q-35.643 70.062-35.508 69.761Q-35.373 69.461-35.137 69.240Q-34.901 69.020-34.597 68.900Q-34.292 68.780-33.968 68.780Q-33.462 68.780-33.113 68.883Q-32.765 68.985-32.765 69.361Q-32.765 69.508-32.862 69.609Q-32.959 69.710-33.106 69.710Q-33.260 69.710-33.359 69.611Q-33.458 69.512-33.458 69.361Q-33.458 69.173-33.318 69.081Q-33.520 69.030-33.961 69.030Q-34.316 69.030-34.545 69.226Q-34.774 69.423-34.875 69.732Q-34.976 70.042-34.976 70.390Q-34.976 70.739-34.850 71.045Q-34.723 71.351-34.468 71.535Q-34.214 71.720-33.858 71.720Q-33.636 71.720-33.452 71.636Q-33.267 71.552-33.132 71.397Q-32.997 71.241-32.939 71.033Q-32.925 70.978-32.871 70.978L-32.758 70.978Q-32.727 70.978-32.705 71.002Q-32.683 71.026-32.683 71.060L-32.683 71.081Q-32.768 71.368-32.956 71.566Q-33.144 71.764-33.409 71.867Q-33.674 71.969-33.968 71.969Q-34.398 71.969-34.786 71.763Q-35.174 71.556-35.408 71.193Q-35.643 70.831-35.643 70.390M-32.136 70.418Q-32.136 70.076-32.001 69.777Q-31.866 69.478-31.626 69.254Q-31.387 69.030-31.069 68.905Q-30.751 68.780-30.420 68.780Q-29.976 68.780-29.576 68.996Q-29.176 69.211-28.942 69.589Q-28.707 69.966-28.707 70.418Q-28.707 70.759-28.849 71.043Q-28.991 71.327-29.236 71.534Q-29.480 71.740-29.789 71.855Q-30.099 71.969-30.420 71.969Q-30.851 71.969-31.252 71.768Q-31.654 71.566-31.895 71.214Q-32.136 70.862-32.136 70.418M-30.420 71.720Q-29.818 71.720-29.594 71.342Q-29.371 70.964-29.371 70.332Q-29.371 69.720-29.605 69.361Q-29.839 69.003-30.420 69.003Q-31.473 69.003-31.473 70.332Q-31.473 70.964-31.247 71.342Q-31.021 71.720-30.420 71.720M-28.113 71.894L-28.113 70.831Q-28.113 70.807-28.085 70.780Q-28.058 70.753-28.034 70.753L-27.925 70.753Q-27.860 70.753-27.846 70.811Q-27.750 71.245-27.504 71.496Q-27.258 71.747-26.845 71.747Q-26.503 71.747-26.250 71.614Q-25.997 71.481-25.997 71.173Q-25.997 71.016-26.091 70.901Q-26.185 70.787-26.323 70.718Q-26.462 70.650-26.629 70.612L-27.210 70.513Q-27.566 70.445-27.839 70.224Q-28.113 70.004-28.113 69.662Q-28.113 69.413-28.002 69.238Q-27.891 69.064-27.704 68.965Q-27.518 68.866-27.303 68.823Q-27.087 68.780-26.845 68.780Q-26.431 68.780-26.151 68.962L-25.936 68.787Q-25.925 68.784-25.918 68.782Q-25.912 68.780-25.901 68.780L-25.850 68.780Q-25.823 68.780-25.799 68.804Q-25.775 68.828-25.775 68.856L-25.775 69.703Q-25.775 69.724-25.799 69.751Q-25.823 69.778-25.850 69.778L-25.963 69.778Q-25.990 69.778-26.016 69.753Q-26.041 69.727-26.041 69.703Q-26.041 69.467-26.147 69.303Q-26.253 69.139-26.436 69.057Q-26.619 68.975-26.852 68.975Q-27.180 68.975-27.436 69.078Q-27.692 69.180-27.692 69.457Q-27.692 69.652-27.509 69.761Q-27.327 69.871-27.098 69.912L-26.523 70.018Q-26.277 70.066-26.064 70.194Q-25.850 70.322-25.713 70.525Q-25.577 70.729-25.577 70.978Q-25.577 71.491-25.942 71.730Q-26.308 71.969-26.845 71.969Q-27.340 71.969-27.672 71.675L-27.938 71.949Q-27.959 71.969-27.986 71.969L-28.034 71.969Q-28.058 71.969-28.085 71.942Q-28.113 71.915-28.113 71.894M-24.421 71.060L-24.421 69.163L-25.061 69.163L-25.061 68.941Q-24.743 68.941-24.526 68.731Q-24.309 68.521-24.208 68.211Q-24.107 67.902-24.107 67.594L-23.840 67.594L-23.840 68.883L-22.764 68.883L-22.764 69.163L-23.840 69.163L-23.840 71.047Q-23.840 71.323-23.736 71.522Q-23.632 71.720-23.372 71.720Q-23.215 71.720-23.109 71.616Q-23.003 71.511-22.953 71.358Q-22.904 71.204-22.904 71.047L-22.904 70.633L-22.637 70.633L-22.637 71.060Q-22.637 71.286-22.736 71.496Q-22.835 71.706-23.020 71.838Q-23.205 71.969-23.434 71.969Q-23.871 71.969-24.146 71.732Q-24.421 71.494-24.421 71.060\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003C\u002Fg>\u003Cg style=\"stroke-width:1.2\">\u003Cpath fill=\"none\" d=\"M-40.352 54.83 133.21-2.077\"\u002F>\u003Cg transform=\"translate(186.03 -71.547)\">\u003Cpath d=\"M-46.906 71.901L-48.509 71.901L-48.509 71.621Q-48.283 71.621-48.134 71.587Q-47.986 71.552-47.986 71.412L-47.986 67.793Q-47.986 67.523-48.093 67.461Q-48.201 67.400-48.509 67.400L-48.509 67.119L-47.432 67.044L-47.432 71.412Q-47.432 71.549-47.282 71.585Q-47.131 71.621-46.906 71.621L-46.906 71.901M-44.694 71.901L-46.246 71.901L-46.246 71.621Q-46.020 71.621-45.872 71.587Q-45.723 71.552-45.723 71.412L-45.723 69.563Q-45.723 69.375-45.771 69.291Q-45.819 69.208-45.916 69.189Q-46.013 69.170-46.225 69.170L-46.225 68.890L-45.169 68.815L-45.169 71.412Q-45.169 71.552-45.038 71.587Q-44.906 71.621-44.694 71.621L-44.694 71.901M-45.966 67.594Q-45.966 67.423-45.843 67.304Q-45.720 67.184-45.549 67.184Q-45.381 67.184-45.258 67.304Q-45.135 67.423-45.135 67.594Q-45.135 67.769-45.258 67.892Q-45.381 68.015-45.549 68.015Q-45.720 68.015-45.843 67.892Q-45.966 67.769-45.966 67.594M-42.367 71.901L-44 71.901L-44 71.621Q-43.771 71.621-43.623 71.587Q-43.474 71.552-43.474 71.412L-43.474 69.563Q-43.474 69.293-43.582 69.232Q-43.689 69.170-44 69.170L-44 68.890L-42.941 68.815L-42.941 69.464Q-42.770 69.156-42.466 68.985Q-42.161 68.815-41.816 68.815Q-41.310 68.815-41.027 69.038Q-40.743 69.262-40.743 69.758L-40.743 71.412Q-40.743 71.549-40.594 71.585Q-40.446 71.621-40.220 71.621L-40.220 71.901L-41.850 71.901L-41.850 71.621Q-41.621 71.621-41.473 71.587Q-41.324 71.552-41.324 71.412L-41.324 69.772Q-41.324 69.437-41.444 69.237Q-41.563 69.037-41.878 69.037Q-42.148 69.037-42.382 69.173Q-42.616 69.310-42.754 69.544Q-42.893 69.778-42.893 70.052L-42.893 71.412Q-42.893 71.549-42.742 71.585Q-42.592 71.621-42.367 71.621L-42.367 71.901M-39.673 70.366Q-39.673 70.045-39.548 69.756Q-39.424 69.467-39.198 69.244Q-38.972 69.020-38.677 68.900Q-38.381 68.780-38.063 68.780Q-37.735 68.780-37.474 68.880Q-37.212 68.979-37.036 69.161Q-36.860 69.344-36.766 69.602Q-36.672 69.860-36.672 70.192Q-36.672 70.284-36.754 70.305L-39.010 70.305L-39.010 70.366Q-39.010 70.954-38.726 71.337Q-38.443 71.720-37.875 71.720Q-37.554 71.720-37.286 71.527Q-37.017 71.334-36.929 71.019Q-36.922 70.978-36.846 70.964L-36.754 70.964Q-36.672 70.988-36.672 71.060Q-36.672 71.067-36.679 71.094Q-36.792 71.491-37.163 71.730Q-37.534 71.969-37.957 71.969Q-38.395 71.969-38.795 71.761Q-39.195 71.552-39.434 71.185Q-39.673 70.818-39.673 70.366M-39.003 70.096L-37.188 70.096Q-37.188 69.819-37.286 69.567Q-37.383 69.314-37.581 69.158Q-37.780 69.003-38.063 69.003Q-38.340 69.003-38.554 69.161Q-38.767 69.320-38.885 69.575Q-39.003 69.830-39.003 70.096M-36.026 71.173Q-36.026 70.841-35.802 70.614Q-35.578 70.387-35.235 70.259Q-34.891 70.130-34.519 70.078Q-34.146 70.025-33.842 70.025L-33.842 69.772Q-33.842 69.567-33.950 69.387Q-34.057 69.208-34.239 69.105Q-34.420 69.003-34.628 69.003Q-35.035 69.003-35.271 69.095Q-35.182 69.132-35.136 69.216Q-35.090 69.300-35.090 69.402Q-35.090 69.498-35.136 69.577Q-35.182 69.655-35.262 69.700Q-35.343 69.744-35.431 69.744Q-35.582 69.744-35.683 69.647Q-35.784 69.549-35.784 69.402Q-35.784 68.780-34.628 68.780Q-34.416 68.780-34.167 68.844Q-33.917 68.907-33.716 69.026Q-33.514 69.146-33.388 69.331Q-33.261 69.515-33.261 69.758L-33.261 71.334Q-33.261 71.450-33.200 71.546Q-33.138 71.641-33.025 71.641Q-32.916 71.641-32.851 71.547Q-32.786 71.453-32.786 71.334L-32.786 70.886L-32.519 70.886L-32.519 71.334Q-32.519 71.604-32.747 71.769Q-32.974 71.935-33.254 71.935Q-33.463 71.935-33.599 71.781Q-33.736 71.628-33.760 71.412Q-33.907 71.679-34.189 71.824Q-34.471 71.969-34.796 71.969Q-35.073 71.969-35.356 71.894Q-35.640 71.819-35.833 71.640Q-36.026 71.460-36.026 71.173M-35.411 71.173Q-35.411 71.347-35.310 71.477Q-35.209 71.607-35.054 71.677Q-34.898 71.747-34.734 71.747Q-34.515 71.747-34.307 71.650Q-34.098 71.552-33.970 71.371Q-33.842 71.190-33.842 70.964L-33.842 70.236Q-34.167 70.236-34.533 70.327Q-34.898 70.418-35.155 70.630Q-35.411 70.841-35.411 71.173M-30.352 71.901L-32.089 71.901L-32.089 71.621Q-31.860 71.621-31.711 71.587Q-31.562 71.552-31.562 71.412L-31.562 69.563Q-31.562 69.293-31.670 69.232Q-31.778 69.170-32.089 69.170L-32.089 68.890L-31.060 68.815L-31.060 69.522Q-30.930 69.214-30.687 69.015Q-30.445 68.815-30.127 68.815Q-29.908 68.815-29.737 68.939Q-29.566 69.064-29.566 69.276Q-29.566 69.413-29.665 69.512Q-29.764 69.611-29.898 69.611Q-30.034 69.611-30.134 69.512Q-30.233 69.413-30.233 69.276Q-30.233 69.136-30.134 69.037Q-30.424 69.037-30.624 69.233Q-30.824 69.430-30.916 69.724Q-31.009 70.018-31.009 70.298L-31.009 71.412Q-31.009 71.621-30.352 71.621\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cg fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" style=\"stroke-width:1.2\">\u003Cpath fill=\"none\" d=\"M-40.352 74.746 133.21-44.755\"\u002F>\u003Cg transform=\"translate(186.03 -114.906)\">\u003Cpath d=\"M-46.950 71.969Q-47.381 71.969-47.757 71.757Q-48.133 71.546-48.353 71.185Q-48.574 70.824-48.574 70.390Q-48.574 69.946-48.336 69.585Q-48.098 69.225-47.712 69.020Q-47.326 68.815-46.885 68.815Q-46.567 68.815-46.284 68.970Q-46 69.126-45.815 69.402L-45.569 68.815L-45.333 68.815L-45.333 72.769Q-45.333 72.906-45.183 72.942Q-45.033 72.978-44.807 72.978L-44.807 73.258L-46.437 73.258L-46.437 72.978Q-46.212 72.978-46.063 72.943Q-45.914 72.909-45.914 72.769L-45.914 71.508Q-46.113 71.727-46.384 71.848Q-46.656 71.969-46.950 71.969M-46.899 71.747Q-46.567 71.747-46.295 71.542Q-46.024 71.337-45.884 71.012L-45.884 69.878Q-45.942 69.655-46.073 69.473Q-46.205 69.290-46.395 69.179Q-46.584 69.068-46.810 69.068Q-47.138 69.068-47.389 69.264Q-47.640 69.461-47.774 69.768Q-47.907 70.076-47.907 70.397Q-47.907 70.698-47.791 71.014Q-47.675 71.330-47.446 71.539Q-47.217 71.747-46.899 71.747M-43.799 71.067L-43.799 69.563Q-43.799 69.293-43.906 69.232Q-44.014 69.170-44.325 69.170L-44.325 68.890L-43.218 68.815L-43.218 71.047L-43.218 71.067Q-43.218 71.347-43.166 71.491Q-43.115 71.634-42.973 71.691Q-42.831 71.747-42.544 71.747Q-42.291 71.747-42.086 71.607Q-41.881 71.467-41.765 71.241Q-41.649 71.016-41.649 70.766L-41.649 69.563Q-41.649 69.293-41.756 69.232Q-41.864 69.170-42.175 69.170L-42.175 68.890L-41.068 68.815L-41.068 71.228Q-41.068 71.419-41.015 71.501Q-40.962 71.583-40.861 71.602Q-40.760 71.621-40.545 71.621L-40.545 71.901L-41.621 71.969L-41.621 71.405Q-41.731 71.587-41.876 71.710Q-42.021 71.833-42.208 71.901Q-42.394 71.969-42.596 71.969Q-43.799 71.969-43.799 71.067M-39.899 71.173Q-39.899 70.841-39.675 70.614Q-39.451 70.387-39.107 70.259Q-38.764 70.130-38.391 70.078Q-38.019 70.025-37.715 70.025L-37.715 69.772Q-37.715 69.567-37.822 69.387Q-37.930 69.208-38.111 69.105Q-38.292 69.003-38.501 69.003Q-38.908 69.003-39.143 69.095Q-39.055 69.132-39.008 69.216Q-38.962 69.300-38.962 69.402Q-38.962 69.498-39.008 69.577Q-39.055 69.655-39.135 69.700Q-39.215 69.744-39.304 69.744Q-39.454 69.744-39.555 69.647Q-39.656 69.549-39.656 69.402Q-39.656 68.780-38.501 68.780Q-38.289 68.780-38.039 68.844Q-37.790 68.907-37.588 69.026Q-37.387 69.146-37.260 69.331Q-37.134 69.515-37.134 69.758L-37.134 71.334Q-37.134 71.450-37.072 71.546Q-37.011 71.641-36.898 71.641Q-36.788 71.641-36.723 71.547Q-36.659 71.453-36.659 71.334L-36.659 70.886L-36.392 70.886L-36.392 71.334Q-36.392 71.604-36.619 71.769Q-36.846 71.935-37.127 71.935Q-37.335 71.935-37.472 71.781Q-37.609 71.628-37.633 71.412Q-37.780 71.679-38.062 71.824Q-38.344 71.969-38.668 71.969Q-38.945 71.969-39.229 71.894Q-39.513 71.819-39.706 71.640Q-39.899 71.460-39.899 71.173M-39.284 71.173Q-39.284 71.347-39.183 71.477Q-39.082 71.607-38.926 71.677Q-38.771 71.747-38.607 71.747Q-38.388 71.747-38.180 71.650Q-37.971 71.552-37.843 71.371Q-37.715 71.190-37.715 70.964L-37.715 70.236Q-38.039 70.236-38.405 70.327Q-38.771 70.418-39.027 70.630Q-39.284 70.841-39.284 71.173M-35.975 70.390Q-35.975 70.052-35.835 69.761Q-35.695 69.471-35.450 69.257Q-35.206 69.044-34.902 68.929Q-34.597 68.815-34.273 68.815Q-34.003 68.815-33.740 68.914Q-33.476 69.013-33.285 69.191L-33.285 67.793Q-33.285 67.523-33.393 67.461Q-33.500 67.400-33.811 67.400L-33.811 67.119L-32.735 67.044L-32.735 71.228Q-32.735 71.416-32.680 71.499Q-32.625 71.583-32.524 71.602Q-32.424 71.621-32.208 71.621L-32.208 71.901L-33.316 71.969L-33.316 71.552Q-33.733 71.969-34.358 71.969Q-34.789 71.969-35.161 71.757Q-35.534 71.546-35.754 71.185Q-35.975 70.824-35.975 70.390M-34.300 71.747Q-34.092 71.747-33.905 71.675Q-33.719 71.604-33.565 71.467Q-33.411 71.330-33.316 71.152L-33.316 69.543Q-33.401 69.396-33.546 69.276Q-33.692 69.156-33.861 69.097Q-34.030 69.037-34.211 69.037Q-34.772 69.037-35.040 69.426Q-35.308 69.816-35.308 70.397Q-35.308 70.968-35.074 71.358Q-34.840 71.747-34.300 71.747M-29.809 71.901L-31.545 71.901L-31.545 71.621Q-31.316 71.621-31.168 71.587Q-31.019 71.552-31.019 71.412L-31.019 69.563Q-31.019 69.293-31.127 69.232Q-31.234 69.170-31.545 69.170L-31.545 68.890L-30.516 68.815L-30.516 69.522Q-30.387 69.214-30.144 69.015Q-29.901 68.815-29.583 68.815Q-29.365 68.815-29.194 68.939Q-29.023 69.064-29.023 69.276Q-29.023 69.413-29.122 69.512Q-29.221 69.611-29.354 69.611Q-29.491 69.611-29.590 69.512Q-29.689 69.413-29.689 69.276Q-29.689 69.136-29.590 69.037Q-29.881 69.037-30.081 69.233Q-30.281 69.430-30.373 69.724Q-30.465 70.018-30.465 70.298L-30.465 71.412Q-30.465 71.621-29.809 71.621L-29.809 71.901M-28.380 71.173Q-28.380 70.841-28.156 70.614Q-27.932 70.387-27.589 70.259Q-27.245 70.130-26.873 70.078Q-26.500 70.025-26.196 70.025L-26.196 69.772Q-26.196 69.567-26.304 69.387Q-26.411 69.208-26.593 69.105Q-26.774 69.003-26.982 69.003Q-27.389 69.003-27.625 69.095Q-27.536 69.132-27.490 69.216Q-27.444 69.300-27.444 69.402Q-27.444 69.498-27.490 69.577Q-27.536 69.655-27.616 69.700Q-27.697 69.744-27.785 69.744Q-27.936 69.744-28.037 69.647Q-28.138 69.549-28.138 69.402Q-28.138 68.780-26.982 68.780Q-26.770 68.780-26.521 68.844Q-26.271 68.907-26.070 69.026Q-25.868 69.146-25.742 69.331Q-25.615 69.515-25.615 69.758L-25.615 71.334Q-25.615 71.450-25.554 71.546Q-25.492 71.641-25.379 71.641Q-25.270 71.641-25.205 71.547Q-25.140 71.453-25.140 71.334L-25.140 70.886L-24.873 70.886L-24.873 71.334Q-24.873 71.604-25.101 71.769Q-25.328 71.935-25.608 71.935Q-25.817 71.935-25.953 71.781Q-26.090 71.628-26.114 71.412Q-26.261 71.679-26.543 71.824Q-26.825 71.969-27.150 71.969Q-27.427 71.969-27.710 71.894Q-27.994 71.819-28.187 71.640Q-28.380 71.460-28.380 71.173M-27.765 71.173Q-27.765 71.347-27.664 71.477Q-27.563 71.607-27.408 71.677Q-27.252 71.747-27.088 71.747Q-26.869 71.747-26.661 71.650Q-26.452 71.552-26.324 71.371Q-26.196 71.190-26.196 70.964L-26.196 70.236Q-26.521 70.236-26.887 70.327Q-27.252 70.418-27.509 70.630Q-27.765 70.841-27.765 71.173M-23.930 71.060L-23.930 69.163L-24.569 69.163L-24.569 68.941Q-24.251 68.941-24.034 68.731Q-23.817 68.521-23.716 68.211Q-23.616 67.902-23.616 67.594L-23.349 67.594L-23.349 68.883L-22.272 68.883L-22.272 69.163L-23.349 69.163L-23.349 71.047Q-23.349 71.323-23.245 71.522Q-23.140 71.720-22.881 71.720Q-22.723 71.720-22.617 71.616Q-22.512 71.511-22.462 71.358Q-22.412 71.204-22.412 71.047L-22.412 70.633L-22.146 70.633L-22.146 71.060Q-22.146 71.286-22.245 71.496Q-22.344 71.706-22.529 71.838Q-22.713 71.969-22.942 71.969Q-23.380 71.969-23.655 71.732Q-23.930 71.494-23.930 71.060M-19.719 71.901L-21.271 71.901L-21.271 71.621Q-21.045 71.621-20.897 71.587Q-20.748 71.552-20.748 71.412L-20.748 69.563Q-20.748 69.375-20.796 69.291Q-20.844 69.208-20.941 69.189Q-21.038 69.170-21.250 69.170L-21.250 68.890L-20.194 68.815L-20.194 71.412Q-20.194 71.552-20.063 71.587Q-19.931 71.621-19.719 71.621L-19.719 71.901M-20.991 67.594Q-20.991 67.423-20.867 67.304Q-20.744 67.184-20.574 67.184Q-20.406 67.184-20.283 67.304Q-20.160 67.423-20.160 67.594Q-20.160 67.769-20.283 67.892Q-20.406 68.015-20.574 68.015Q-20.744 68.015-20.867 67.892Q-20.991 67.769-20.991 67.594M-19.073 70.390Q-19.073 70.062-18.938 69.761Q-18.803 69.461-18.567 69.240Q-18.331 69.020-18.027 68.900Q-17.723 68.780-17.398 68.780Q-16.892 68.780-16.544 68.883Q-16.195 68.985-16.195 69.361Q-16.195 69.508-16.293 69.609Q-16.390 69.710-16.537 69.710Q-16.691 69.710-16.790 69.611Q-16.889 69.512-16.889 69.361Q-16.889 69.173-16.749 69.081Q-16.950 69.030-17.391 69.030Q-17.747 69.030-17.976 69.226Q-18.205 69.423-18.306 69.732Q-18.407 70.042-18.407 70.390Q-18.407 70.739-18.280 71.045Q-18.154 71.351-17.899 71.535Q-17.644 71.720-17.289 71.720Q-17.067 71.720-16.882 71.636Q-16.698 71.552-16.563 71.397Q-16.428 71.241-16.369 71.033Q-16.356 70.978-16.301 70.978L-16.188 70.978Q-16.158 70.978-16.135 71.002Q-16.113 71.026-16.113 71.060L-16.113 71.081Q-16.199 71.368-16.387 71.566Q-16.575 71.764-16.839 71.867Q-17.104 71.969-17.398 71.969Q-17.829 71.969-18.217 71.763Q-18.605 71.556-18.839 71.193Q-19.073 70.831-19.073 70.390\" fill=\"var(--tk-accent)\" stroke=\"var(--tk-accent)\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"none\" d=\"M14.847 71.9V36.62\" style=\"stroke-dasharray:3.0,3.0\"\u002F>\u003Cg stroke=\"none\" font-family=\"cmr7\" font-size=\"7\">\u003Cg transform=\"translate(49.081 8.394)\">\u003Cpath d=\"M-46.892 71.901L-48.526 71.901L-48.526 71.621Q-48.297 71.621-48.148 71.587Q-47.999 71.552-47.999 71.412L-47.999 69.563Q-47.999 69.293-48.107 69.232Q-48.215 69.170-48.526 69.170L-48.526 68.890L-47.466 68.815L-47.466 69.464Q-47.295 69.156-46.991 68.985Q-46.687 68.815-46.342 68.815Q-45.836 68.815-45.552 69.038Q-45.268 69.262-45.268 69.758L-45.268 71.412Q-45.268 71.549-45.120 71.585Q-44.971 71.621-44.745 71.621L-44.745 71.901L-46.376 71.901L-46.376 71.621Q-46.147 71.621-45.998 71.587Q-45.849 71.552-45.849 71.412L-45.849 69.772Q-45.849 69.437-45.969 69.237Q-46.089 69.037-46.403 69.037Q-46.673 69.037-46.907 69.173Q-47.141 69.310-47.280 69.544Q-47.418 69.778-47.418 70.052L-47.418 71.412Q-47.418 71.549-47.268 71.585Q-47.117 71.621-46.892 71.621\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(49.081 8.394)\">\u003Cpath d=\"M-39.781 71.901L-41.415 71.901L-41.415 71.621Q-41.186 71.621-41.037 71.587Q-40.888 71.552-40.888 71.412L-40.888 69.563Q-40.888 69.293-40.996 69.232Q-41.104 69.170-41.415 69.170L-41.415 68.890L-40.355 68.815L-40.355 69.464Q-40.184 69.156-39.880 68.985Q-39.576 68.815-39.231 68.815Q-38.725 68.815-38.441 69.038Q-38.157 69.262-38.157 69.758L-38.157 71.412Q-38.157 71.549-38.009 71.585Q-37.860 71.621-37.634 71.621L-37.634 71.901L-39.265 71.901L-39.265 71.621Q-39.036 71.621-38.887 71.587Q-38.738 71.552-38.738 71.412L-38.738 69.772Q-38.738 69.437-38.858 69.237Q-38.978 69.037-39.292 69.037Q-39.562 69.037-39.796 69.173Q-40.030 69.310-40.169 69.544Q-40.307 69.778-40.307 70.052L-40.307 71.412Q-40.307 71.549-40.157 71.585Q-40.006 71.621-39.781 71.621L-39.781 71.901M-37.088 70.366Q-37.088 70.045-36.963 69.756Q-36.838 69.467-36.612 69.244Q-36.387 69.020-36.091 68.900Q-35.796 68.780-35.478 68.780Q-35.150 68.780-34.888 68.880Q-34.627 68.979-34.451 69.161Q-34.275 69.344-34.181 69.602Q-34.087 69.860-34.087 70.192Q-34.087 70.284-34.169 70.305L-36.424 70.305L-36.424 70.366Q-36.424 70.954-36.141 71.337Q-35.857 71.720-35.290 71.720Q-34.968 71.720-34.700 71.527Q-34.432 71.334-34.343 71.019Q-34.336 70.978-34.261 70.964L-34.169 70.964Q-34.087 70.988-34.087 71.060Q-34.087 71.067-34.093 71.094Q-34.206 71.491-34.577 71.730Q-34.948 71.969-35.372 71.969Q-35.809 71.969-36.209 71.761Q-36.609 71.552-36.848 71.185Q-37.088 70.818-37.088 70.366M-36.418 70.096L-34.603 70.096Q-34.603 69.819-34.700 69.567Q-34.798 69.314-34.996 69.158Q-35.194 69.003-35.478 69.003Q-35.755 69.003-35.968 69.161Q-36.182 69.320-36.300 69.575Q-36.418 69.830-36.418 70.096M-33.441 71.173Q-33.441 70.841-33.217 70.614Q-32.993 70.387-32.649 70.259Q-32.306 70.130-31.933 70.078Q-31.561 70.025-31.256 70.025L-31.256 69.772Q-31.256 69.567-31.364 69.387Q-31.472 69.208-31.653 69.105Q-31.834 69.003-32.043 69.003Q-32.449 69.003-32.685 69.095Q-32.596 69.132-32.550 69.216Q-32.504 69.300-32.504 69.402Q-32.504 69.498-32.550 69.577Q-32.596 69.655-32.677 69.700Q-32.757 69.744-32.846 69.744Q-32.996 69.744-33.097 69.647Q-33.198 69.549-33.198 69.402Q-33.198 68.780-32.043 68.780Q-31.831 68.780-31.581 68.844Q-31.332 68.907-31.130 69.026Q-30.928 69.146-30.802 69.331Q-30.675 69.515-30.675 69.758L-30.675 71.334Q-30.675 71.450-30.614 71.546Q-30.552 71.641-30.440 71.641Q-30.330 71.641-30.265 71.547Q-30.200 71.453-30.200 71.334L-30.200 70.886L-29.934 70.886L-29.934 71.334Q-29.934 71.604-30.161 71.769Q-30.388 71.935-30.669 71.935Q-30.877 71.935-31.014 71.781Q-31.151 71.628-31.174 71.412Q-31.321 71.679-31.603 71.824Q-31.885 71.969-32.210 71.969Q-32.487 71.969-32.771 71.894Q-33.054 71.819-33.247 71.640Q-33.441 71.460-33.441 71.173M-32.825 71.173Q-32.825 71.347-32.725 71.477Q-32.624 71.607-32.468 71.677Q-32.313 71.747-32.149 71.747Q-31.930 71.747-31.721 71.650Q-31.513 71.552-31.385 71.371Q-31.256 71.190-31.256 70.964L-31.256 70.236Q-31.581 70.236-31.947 70.327Q-32.313 70.418-32.569 70.630Q-32.825 70.841-32.825 71.173M-27.767 71.901L-29.503 71.901L-29.503 71.621Q-29.274 71.621-29.125 71.587Q-28.977 71.552-28.977 71.412L-28.977 69.563Q-28.977 69.293-29.084 69.232Q-29.192 69.170-29.503 69.170L-29.503 68.890L-28.474 68.815L-28.474 69.522Q-28.344 69.214-28.102 69.015Q-27.859 68.815-27.541 68.815Q-27.322 68.815-27.152 68.939Q-26.981 69.064-26.981 69.276Q-26.981 69.413-27.080 69.512Q-27.179 69.611-27.312 69.611Q-27.449 69.611-27.548 69.512Q-27.647 69.413-27.647 69.276Q-27.647 69.136-27.548 69.037Q-27.839 69.037-28.038 69.233Q-28.238 69.430-28.331 69.724Q-28.423 70.018-28.423 70.298L-28.423 71.412Q-28.423 71.621-27.767 71.621\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003Cg transform=\"translate(49.081 8.394)\">\u003Cpath d=\"M-23.685 70.390Q-23.685 70.052-23.544 69.761Q-23.404 69.471-23.160 69.257Q-22.916 69.044-22.611 68.929Q-22.307 68.815-21.982 68.815Q-21.712 68.815-21.449 68.914Q-21.186 69.013-20.995 69.191L-20.995 67.793Q-20.995 67.523-21.102 67.461Q-21.210 67.400-21.521 67.400L-21.521 67.119L-20.444 67.044L-20.444 71.228Q-20.444 71.416-20.390 71.499Q-20.335 71.583-20.234 71.602Q-20.133 71.621-19.918 71.621L-19.918 71.901L-21.025 71.969L-21.025 71.552Q-21.442 71.969-22.068 71.969Q-22.499 71.969-22.871 71.757Q-23.244 71.546-23.464 71.185Q-23.685 70.824-23.685 70.390M-22.010 71.747Q-21.801 71.747-21.615 71.675Q-21.429 71.604-21.275 71.467Q-21.121 71.330-21.025 71.152L-21.025 69.543Q-21.111 69.396-21.256 69.276Q-21.401 69.156-21.571 69.097Q-21.740 69.037-21.921 69.037Q-22.481 69.037-22.750 69.426Q-23.018 69.816-23.018 70.397Q-23.018 70.968-22.784 71.358Q-22.550 71.747-22.010 71.747\" fill=\"currentColor\" stroke=\"currentColor\" class=\"tikz-text\" style=\"stroke-width:0.210\"\u002F>\u003C\u002Fg>\u003C\u002Fg>\u003Cpath fill=\"var(--tk-accent)\" stroke=\"none\" d=\"M16.447 36.62a1.6 1.6 0 1 0-3.2 0 1.6 1.6 0 0 0 3.2 0m-1.6 0\"\u002F>\u003C\u002Fg>\u003C\u002Fsvg>\u003Cfigcaption class=\"tikz-cap\">Per-layer cost vs. sequence length \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> (log–log). The projection\u002FFFN term is linear (black); attention is quadratic (blue). They cross near \u003Cspan class=\"katex\">\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.4831em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"base\">\u003Cspan class=\"strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>, after which attention dominates.\u003C\u002Ffigcaption>",1785117769638]