Courtade–Kumar proof module `CKLaneC.RSC2.BD_0097` (transplant)
DefinitionCK_CKLaneC_RSC2_BD_0097Verbatim transplant of the Lean module CKLaneC.RSC2.BD_0097 of the machine-checked proof of the general Courtade–Kumar theorem (the most informative Boolean function conjecture), so that the complete proof can be verified on this platform.
It is the original source with only two mechanical changes. Imports of project modules are redirected to their transplanted bundles Definitions.Def_CK_*. Declarations that already exist in earlier platform definition bundles of this mission are removed, and those bundles are imported instead, so every constant keeps a single platform identity.
The module contains both definitions and the lemmas proved alongside them in the source. They are kept together so the transplant stays faithful and every proof is re-checked by the server.
Source: Z. Chen, A. Gohari, A. Javanmard, H. Lin, V. Mirrokni, C. Nair, D. P. Woodruff, A Proof of the Most Informative Boolean Function Conjecture, arXiv:2609.24931 (2026). Lean development: https://github.com/dpwoodru/general-courtade-kumar-lean (Apache-2.0), module CKLaneC.RSC2.BD_0097 from release v1.0 (sources_v3.tar.zst).
import Definitions.Def_CK_CKLaneC_RSC2_BD_0097_part00
/-! RA-stat cover batch BD_0097 (generated by tools/emit_cover2.py; compact format). -/
namespace CKLaneC.RSC2.BD_0097
open CKLaneC.TM3 CKLaneC.RSCell
theorem s2_4 : stageC2 w4 q4 = true := by decide +kernel
theorem s3_4 : stageC3 w4 q4 = true := by decide +kernel
theorem sE_4 : stageE w4 q4 = true := by decide +kernel
theorem sF_4 : stageF w4 = true := by decide +kernel
theorem ok_4 : (domOK c4 && cellCheck c4 q4) = true :=
staged_check c4 q4 w4 (by decide +kernel) sB_4 s0_4 s1_4 s2_4 s3_4 sE_4 sF_4
noncomputable def c5 : Cell := { bc := 8791026472627208192, bh := 144115188075855872, tc := 15564440312192434176, th := 576460752303423488, sc := 3819052484010180608, sh := 504403158265495552 }
noncomputable def q5 : Cert := { V0 := [[[7146271563252896444]], [[(-357631458360262304), 210560821847100702], [69033258910010557]], [[8876892000253711, (-5426615087005696), (-2301774446344749)], [(-2412737458230204), 1047494328445964], [227387173409965]], [[(-432132190913580), (-219673297647042), 267961878282434, 4245094442513], [36908141494076, 100196772357875, (-51724425491814)], [6353197202438, (-9753550808987)], [3319721818859]], [[26669465541776, 14627489268430, (-11327357900243), (-3425563807955), 386293576159], [(-2613575170757), (-9697658284969), 3613066508998, 661233310827], [(-569413054256), 1871585148310, (-344609624366)], [14064824876, (-62451192813)], [7544601660]]], r0 := 417047183387700, V1 := [[[8142280428908927910]], [[(-378508514006566306), 0], [73063137026208570]], [[7551888136397167, 0, 0], [(-1842000750770066), 0], [171983066043095]], [[(-358552635718424), 0, 0, 0], [(-7699603765333), 0, 0], [14685055413619, 0], [3008544918299]], [[22665371521667, 0, 0, 0, 0], [(-993103669420), 0, 0, 0], [(-715866284119), 0, 0], [46682101923, 0], [910845366]]], r1 := 343396463577348, V2 := [[[7946141933895144115]], [[(-348811669378768700), 192576048747562737], [(-194910521480628297)]], [[8247876967501198, (-4074741979802419), (-2219274010825166)], [(-5438719739550681), 6830756386925496], [(-638985185739591)]], [[(-396503317443573), (-247065390209162), 228991416617248, 9242268484312], [239771481317714, (-314068002720533), (-81959097156862)], [32615181585724, 61365251510610], [(-5514117603819)]], [[24599245660176, 14126985587712, (-7479260547765), (-3534132862732), 247052940894], [(-13745463754573), (-2110932212908), 15409917896317, (-663511544583)], [1753466151384, (-9763764966584), 374358778580], [798070540437, (-230617745625)], [(-30070124731)]]], r2 := 536154268335152, V3 := [[[14135879392508994745]], [[(-545866598921886701), 154866218122807161], [(-83762070721160707)]], [[3644660012249869, 13998789614044883, (-4709168512830282)], [(-10042894279620445), 5912732202945260], [(-242288838373211)]], [[25049359704284, (-954754542392792), (-183849971430201), 127803582832861], [158583279543687, 463860590931577, (-257162032038723)], [(-14828083714532), 68023230922921], [(-309328161486)]], [[(-3178480194158), 263042799755, 53681402838554, (-3936122725205), (-3092046976814)], [652833807898, (-45786811068234), (-4149683047470), 8716353994048], [2597784441536, 2564774124432, (-4817569655215)], [126796813180, 163437818197], [3514236148]]], r3 := 20222224625378504, Vm := [[[10888046314426753657]], [[(-392131273745182969), 0], [(-58642501414621512)]], [[3553889332234396, 0, 0], [(-6025866126425446), 0], [1653294047318964]], [[(-217094384999664), 0, 0, 0], [26186492321326, 0, 0], [73631843164755, 0], [10512891888100]], [[16142994650922, 0, 0, 0, 0], [(-3246318543067), 0, 0, 0], [811648307076, 0, 0], [1753805891643, 0], [(-51462401924)]]], rm := 933562964101270 }
noncomputable def w5 : Wit := { Z0 := { p := [[[8039852244541579583]], [[(-505757637573056454), 297772305353391836], [97625913839842223]], [[21944019041316790, (-18731764354557647), 0], [(-7037315222055745), 3615774586660823], [671457575374797]], [[(-1396572818768696), 812741445974695, 0, 0], [453779801948219, (-260641304520584), 0], [(-63104609916812), 24868799087955], [9296130661791]], [[98879039775051, (-51724919213656), 0, 0, 0], [(-35679573468922), 16806659331415, 0, 0], [5940468645071, (-2337207774697), 0], [(-902813793634), 344301135621], [83178372470]]], r := 77868388146018, ok := true }, Z1 := { p := [[[9528713771308538765]], [[(-599416459345844686), 0], [115704786773146339]], [[26007726271190269, 0, 0], [(-8340521744658661), 0], [795801570814574]], [[(-1655197414836973), 0, 0, 0], [537813098605297, 0, 0], [(-74790648790295), 0], [11017636339900]], [[117189973066727, 0, 0, 0, 0], [(-42286901889092), 0, 0, 0], [7040555431195, 0, 0], [(-1070001533196), 0], [98581774779]]], r := 82945257380236, ok := true }, Z2 := { p := [[[9221803657989848625]], [[(-539352923692155748), 297772305353391836], [(-301382003091145234)]], [[24011585897465773, (-18731764354557647), 0], [4172190409217789, 3615774586660823], [2527236265668806]], [[(-1530589792168840), 812741445974695, 0, 0], [(-221201955418317), (-260641304520584), 0], [(-72851752304485), 24868799087955], [(-52663845835719)]], [[108794129090130, (-51724919213656), 0, 0, 0], [7603120409189, 16806659331415, 0, 0], [1642624263353, (-2337207774697), 0], [1129125203214, 344301135621], [655597578561]]], r := 89300381578853, ok := true }, Z3 := { p := [[[27172523578083671902]], [[(-3304392640932892621), 937479582932572458], [(-507052035473435258)]], [[376230627689507681, (-116218400156259273), 0], [47898117292293287, 4955753225435520], [6872632050020371]], [[(-46618282263344186), 13178416137870331, 0, 0], [(-6086799587786667), (-368094373606307), 0], [(-745312033785368), (-12238800423356)], [(-105525520032698)]], [[5882027059865690, (-1632663561873369), 0, 0, 0], [759750665679495, 36771395657088, 0, 0], [90011584274368, 2525658137135, 0], [11448526362248, 153914146283], [1648720354745]]], r := 2347959756654029, ok := true }, iE := { p := [[[25214963486896406225]], [[(-716699437207451602), 0], [(-107181065562263685)]], [[44108092931178303, 0, 0], [236307731351525, 0], [3862923538850966]], [[(-2859028765869724), 0, 0, 0], [303086819906657, 0, 0], [(-129169793819851), 0], [(-34171652329878)]], [[211521905388367, 0, 0, 0, 0], [(-29645452556877), 0, 0, 0], [9341593158907, 0, 0], [291433992796, 0], [821058953318]]], r := 194653543375712, ok := true }, iHu := { p := [[[39692263229956597694]], [[(-3551911183229701551), 0], [(-440869537965279126)]], [[435485695296186512, 0, 0], [49878467022922392, 0], [6709186789194183]], [[(-54109143312282399), 0, 0, 0], [(-5870150005869534), 0, 0], [(-728613466770697), 0], [(-103470045891940)]], [[6854096880101971, 0, 0, 0, 0], [741865407549610, 0, 0, 0], [90006498547187, 0, 0], [11429338886329, 0], [1626830166684]]], r := 2500224859832140, ok := true }, T := { p := [[[15564440312192434176]], [[0, 576460752303423488], [0]]], r := 0, ok := true }, E := { p := [[[13495255192329538982]], [[383583414917092418, 0], [57364185052269804]], [[(-12704200532612946), 0, 0], [3134516739959425, 0], [(-1823630817079448)]], [[498081090628325, 0, 0, 0], [(-231063030554280), 0, 0], [(-28679954612123), 0], [1749081003667]], [[(-33334713334655), 0, 0, 0, 0], [7945535541565, 0, 0, 0], [(-414638246804), 0, 0], [122410638661, 0], [(-74882374546)]]], r := 87278241832604, ok := true }, de := { p := [[[(-29436209227173967919)]], [[1949841887834478003, 0], [242017845562593289]], [[(-114668298672428007), 0, 0], [3498954462679104, 0], [(-1766604604702764)]], [[10232429850585133, 0, 0, 0], [50585866110174, 0, 0], [6278807737329, 0], [19566933080341]], [[(-1012116717612885), 0, 0, 0, 0], [731341284207, 0, 0, 0], [550801319626, 0, 0], [11267201967, 0], [(-240227419780)]]], r := 616218061360142, ok := true }, dde := { p := [[[(-149630957799906733502)]], [[17599301222005250143, 0], [2184456591958497099]], [[(-2355711438013866393), 0, 0], [(-296277058256283572), 0], [(-36292599802450223)]], [[310679537262192103, 0, 0, 0], [38449850802094648, 0, 0], [4772463916887634, 0], [594096006892555]], [[(-41039683529751822), 0, 0, 0, 0], [(-5096352753633138), 0, 0, 0], [(-633689850366516), 0, 0], [(-78515512534780), 0], [(-9740830391720)]]], r := 9161693067256682, ok := true }, nJu := { p := [[[(-58872418454347935837)]], [[3899683775668956007, 0], [484035691125186579]], [[(-229336597344856013), 0, 0], [6997908925358209, 0], [(-3533209209405527)]], [[20464859701170267, 0, 0, 0], [101171732220349, 0, 0], [12557615474658, 0], [39133866160683]], [[(-2024233435225769), 0, 0, 0, 0], [1462682568414, 0, 0, 0], [1101602639253, 0, 0], [22534403934, 0], [(-480454839559)]]], r := 1232436122720272, ok := true }, Jd1 := { p := [[[(-299261915599813467004)]], [[35198602444010500286, 0], [4368913183916994199]], [[(-4711422876027732785), 0, 0], [(-592554116512567144), 0], [(-72585199604900446)]], [[621359074524384206, 0, 0, 0], [76899701604189297, 0, 0], [9544927833775268, 0], [1188192013785111]], [[(-82079367059503643), 0, 0, 0, 0], [(-10192705507266276), 0, 0, 0], [(-1267379700733032), 0, 0], [(-157031025069560), 0], [(-19481660783440)]]], r := 18323386134513358, ok := true }, term0 := { p := [[[2492232978118581154395]], [[(-585235383033487166984), 0], [(-62089119878083081780)]], [[112708616171772257197, 0, 0], [15560518446628453094, 0], [1385813102932412752]], [[(-19532513034094002596), 0, 0, 0], [(-3019079769083773502), 0, 0], [(-351681653292983190), 0], [(-28742201641576174)]], [[3194007336967626286, 0, 0, 0, 0], [526749755940741889, 0, 0, 0], [68741983485013186, 0, 0], [7356731162431217, 0], [569902233531768]]], r := 839881421962025327, ok := true }, r0 := { p := [[[310694525573790795446]], [[(-41845516832018995463), 17154438440850413509], [(-1431784429840123115)]], [[5221376117629289677, (-1901715538477093180), 20966099611117694], [26246989826116487, (-162280821908079000)], [46225945264922493]], [[(-634394567214946817), 228442635127639433, 14472925254917127, (-4100777603180274)], [10735346966639769, 12965595438644859, (-3690876626758960)], [(-6137133454753704), 2728335952705794], [(-435405530615299)]], [[77955432534750242, (-27975117849030585), (-1266050924173223), 155956843913684, 116036846628180], [(-2336201432178445), (-830775381901087), 157947140370602, 95637084393174], [765721245681022, (-318776134965852), 45001210319252], [24402643682424, (-36142105096582)], [9953946877734]]], r := 243756217584726048, ok := true }, r1 := { p := [[[396546822520665831610]], [[(-50984987245504661217), 0], [(-2323180918696415953)]], [[6335479777195134989, 0, 0], [92366639698526715, 0], [61029759933672320]], [[(-772297635081313868), 0, 0, 0], [6790103664937238, 0, 0], [(-7871980469064068), 0], [(-627574254602651)]], [[95303924922462749, 0, 0, 0, 0], [(-2075306000882268), 0, 0, 0], [960378767444794, 0, 0], [38270886371199, 0], [13497221681007]]], r := 221135719162024268, ok := true }, r2 := { p := [[[339134566985458165923]], [[(-46325685183934800109), 16676326761153984541], [(-11464728061142967143)]], [[5809166243909513672, (-1839904359710210392), 2946370642551896], [1593686967712411238, (-636377549230526)], [244211356159462177]], [[(-710870142980945336), 223597648959223992, 13418956747684183, (-2875096162675252)], [(-194814374839130124), (-6936640283383879), 1877864758784854], [(-32874048860250755), 2020926811105808], [(-5258472753916473)]], [[87835137430901684, (-27590098328047405), (-1029058220367145), (-3179680313079), 91389879723139], [24364325602061313, 695848405011846, 506348947028892, (-273259994570153)], [4235388000986087, (-544482721327264), 172927221602802], [743870236323119, (-50355304301781)], [103302832623933]]], r := 372090297941302440, ok := true }, r3 := { p := [[[2883891950063516010053]], [[(-682827241126750690847), 97254825622911105127], [(-90490594959013712136)]], [[130797472311347396901, (-21693682023521047359), (-239560877325367306)], [22924693752966132841, (-1510551802176193575)], [2220916721066727823]], [[(-22649356467391093568), 4336839633965371210, (-13023290756642811), 9474703221787317], [(-4479960925756875669), 397453331595159549, (-11343439286756801)], [(-570761526818231519), 26386430567297258], [(-48491184349056242)]], [[3702484931220658431, (-758971984888115736), 2231418558336616, (-98922847088653), (-321831893547507)], [783558319973181778, (-73537752091739144), (-1173589950623552), 689180350642679], [111950845018064882, (-6000859982239626), (-203629773957698)], [12526865942758694, (-403747387279405)], [991631766316785]]], r := 323736411354068583230, ok := true }, eta := { p := [[[(-858468926857515943825)]], [[122722736768102004389, 0], [15725384781839345851]], [[(-16662782501219243354), 0, 0], [(-2219594858795917142), 0], [(-351189703951742161)]], [[2172776992980854640, 0, 0, 0], [276754094570664698, 0, 0], [50488151834887631, 0], [6534872223960813]], [[(-281767690919368163), 0, 0, 0, 0], [(-34912598045774575), 0, 0, 0], [(-6590199034764440), 0, 0], [(-901577748540310), 0], [(-127293192149781)]]], r := 539746754406758719, ok := true } }
theorem sB_5 : stageB c5 w5 = true := by decide +kernel
theorem s0_5 : stageC0 w5 q5 = true := by decide +kernel
theorem s1_5 : stageC1 w5 q5 = true := by decide +kernel
theorem s2_5 : stageC2 w5 q5 = true := by decide +kernel
theorem s3_5 : stageC3 w5 q5 = true := by decide +kernel
theorem sE_5 : stageE w5 q5 = true := by decide +kernel
theorem sF_5 : stageF w5 = true := by decide +kernel
theorem ok_5 : (domOK c5 && cellCheck c5 q5) = true :=
staged_check c5 q5 w5 (by decide +kernel) sB_5 s0_5 s1_5 s2_5 s3_5 sE_5 sF_5
theorem region : RegionPosI 8646911284551352320 8935141660703064064 13835058055282163712 16140901064495857664 2305843009213693952 4323455642275676160 :=
(RegionPosI.split_t 14987979559889010688 (RegionPosI.split_s 3314649325744685056 (RegionPosI.split_s 2810246167479189504 (RegionPosI.of_check c0 q0 ok_0 8646911284551352320 8935141660703064064 13835058055282163712 14987979559889010688 2305843009213693952 2810246167479189504 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 8646911284551352320 8935141660703064064 13835058055282163712 14987979559889010688 2810246167479189504 3314649325744685056 (by decide +kernel))) (RegionPosI.of_check c2 q2 ok_2 8646911284551352320 8935141660703064064 13835058055282163712 14987979559889010688 3314649325744685056 4323455642275676160 (by decide +kernel))) (RegionPosI.split_s 3314649325744685056 (RegionPosI.split_s 2810246167479189504 (RegionPosI.of_check c3 q3 ok_3 8646911284551352320 8935141660703064064 14987979559889010688 16140901064495857664 2305843009213693952 2810246167479189504 (by decide +kernel)) (RegionPosI.of_check c4 q4 ok_4 8646911284551352320 8935141660703064064 14987979559889010688 16140901064495857664 2810246167479189504 3314649325744685056 (by decide +kernel))) (RegionPosI.of_check c5 q5 ok_5 8646911284551352320 8935141660703064064 14987979559889010688 16140901064495857664 3314649325744685056 4323455642275676160 (by decide +kernel))))
end CKLaneC.RSC2.BD_0097