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Exact global Y/Z certificate: logs 1

Definition
mme_released_global_yz_logs_1

by raresbuhai · Sep 22, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

matrix-multiplicationmore-asymmetrynumerical-certificate

One component of the exact six-orientation Y/Z certificate: word enumeration and cached integer counts, finite entropy expressions, or outward-rounded logarithm intervals. All numerical data are connected to the published profile by the accompanying full proofs. Tables are split by orientation to fit publication and compilation limits.

Definition code
import Definitions.Def_mme_released_global_yz_expression_primitives
open BigOperators MME MME.ReleasedGlobalYZ
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 16000000
namespace MME.ReleasedGlobalYZ

private def mkLog (q : ℚ) (k : ℕ) (lo hi : ℤ) : Entry :=
  ((q,q),(k,(lo : ℚ)/1000000000000,(hi : ℚ)/1000000000000))

private def logTable : Fin 472 → Entry :=
![mkLog (2884311719/125000000000) 6 (-3769027438136) (-3769027438015),
  mkLog (113875467179/1000000000000) 4 (-2172649820891) (-2172649820810),
  mkLog (289598989021/1000000000000) 2 (-1239258109447) (-1239258109406),
  mkLog (88189275717/250000000000) 2 (-1041975552773) (-1041975552732),
  mkLog (95040352963/500000000000) 3 (-1660306529009) (-1660306528948),
  mkLog (7230066443/250000000000) 6 (-3543212691891) (-3543212691770),
  mkLog (829856839/500000000000) 10 (-6401110174724) (-6401110174523),
  mkLog (16571039/500000000000) 15 (-10314706844402) (-10314706844101),
  mkLog (59863/500000000000) 23 (-15938060038510) (-15938060038049),
  mkLog (11387489797936941344020649536507331/400000000000000000000000000000000000) 6 (-3558949180483) (-3558949180362),
  mkLog (11387603637863058655979350463492669/400000000000000000000000000000000000) 6 (-3558939183604) (-3558939183483),
  mkLog (346510797996724900538839747941225361403226109/200000000000000000000000000000000000000000000000) 10 (-6358158664437) (-6358158664236),
  mkLog (4983163899936995406673057789805405038596773891/100000000000000000000000000000000000000000000000) 5 (-2999105175461) (-2999105175360),
  mkLog (346510798071959362991839747941225361403226109/200000000000000000000000000000000000000000000000) 10 (-6358158664220) (-6358158664019),
  mkLog (183005585451768223037603999004266061/4000000000000000000000000000000000000) 5 (-3084532966183) (-3084532966082),
  mkLog (183005585454550207982007999004266061/4000000000000000000000000000000000000) 5 (-3084532966168) (-3084532966067),
  mkLog (1353557968616958871144361354014189552699601/781250000000000000000000000000000000000000000) 10 (-6358158543318) (-6358158543117),
  mkLog (183005585451881242246911999004266061/4000000000000000000000000000000000000) 5 (-3084532966182) (-3084532966081),
  mkLog (183005585447350826071463999004266061/4000000000000000000000000000000000000) 5 (-3084532966207) (-3084532966106),
  mkLog (19465448511803272414546273653121605369175399/390625000000000000000000000000000000000000000) 5 (-2999106997782) (-2999106997681),
  mkLog (1353557968635089878762330104014189552699601/781250000000000000000000000000000000000000000) 10 (-6358158543304) (-6358158543103),
  mkLog (462885531459764057721229867360839/200000000000000000000000000000000000) 9 (-6068592854370) (-6068592854189),
  mkLog (462885531454024420562829867360839/200000000000000000000000000000000000) 9 (-6068592854383) (-6068592854202),
  mkLog (2740540561838847944179587994992999435155687437/1000000000000000000000000000000000000000000000000) 9 (-5899600092789) (-5899600092608),
  mkLog (40196881806521779638400373372043471064844312563/500000000000000000000000000000000000000000000000) 4 (-2520818672848) (-2520818672767),
  mkLog (2740540561843577083367587994992999435155687437/1000000000000000000000000000000000000000000000000) 9 (-5899600092787) (-5899600092606),
  mkLog (1370270537567249828631512910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5899599905491) (-5899599905310),
  mkLog (1370270537548171596547512910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5899599905505) (-5899599905324),
  mkLog (2740540561853156618242587994992999435155687437/1000000000000000000000000000000000000000000000000) 9 (-5899600092783) (-5899600092602),
  mkLog (40196881804540613810845373372043471064844312563/500000000000000000000000000000000000000000000000) 4 (-2520818672898) (-2520818672817),
  mkLog (20098435534294985149332367812636275140950560023/250000000000000000000000000000000000000000000000) 4 (-2520818939982) (-2520818939901),
  mkLog (20098435533487474731863617812636275140950560023/250000000000000000000000000000000000000000000000) 4 (-2520818940022) (-2520818939941),
  mkLog (2314454756127514856951405036669187/1000000000000000000000000000000000000) 9 (-6068581145786) (-6068581145605),
  mkLog (1370270537569634607642012910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5899599905490) (-5899599905309),
  mkLog (1370270537569614398225512910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5899599905490) (-5899599905309),
  mkLog (2314454756160416737102405036669187/1000000000000000000000000000000000000) 9 (-6068581145772) (-6068581145591),
  mkLog (96385846781107003100898036983123/1000000000000000000000000000000000000) 14 (-9247151184891) (-9247151184610),
  mkLog (15757776845022194906002054175207071/4000000000000000000000000000000000000) 8 (-5536715628837) (-5536715628676),
  mkLog (15757776846214742189934054175207071/4000000000000000000000000000000000000) 8 (-5536715628761) (-5536715628600),
  mkLog (9697123452411066599031021922494665412439322747617156461/100000000000000000000000000000000000000000000000000000000000) 14 (-9241096174880) (-9241096174599),
  mkLog (204894304888369379841077714898692183574666026652382843539/50000000000000000000000000000000000000000000000000000000000) 8 (-5497284024223) (-5497284024062),
  mkLog (9697123458678841736531021922494665412439322747617156461/100000000000000000000000000000000000000000000000000000000000) 14 (-9241096174234) (-9241096173953),
  mkLog (15757776846325892134602054175207071/4000000000000000000000000000000000000) 8 (-5536715628754) (-5536715628593),
  mkLog (15757776845584624660570054175207071/4000000000000000000000000000000000000) 8 (-5536715628801) (-5536715628640),
  mkLog (204894300499172690198485671930661731922704455702382843539/50000000000000000000000000000000000000000000000000000000000) 8 (-5497284045645) (-5497284045484),
  mkLog (3539823772348772050366778122387848269090190194897617156461/25000000000000000000000000000000000000000000000000000000000) 3 (-1954798880815) (-1954798880754),
  mkLog (204894300779804945638885671930661731922704455702382843539/50000000000000000000000000000000000000000000000000000000000) 8 (-5497284044275) (-5497284044114),
  mkLog (7878888814722063036025863729249199/2000000000000000000000000000000000000) 8 (-5536715579057) (-5536715578896),
  mkLog (7878888814665994175397863729249199/2000000000000000000000000000000000000) 8 (-5536715579064) (-5536715578903),
  mkLog (204894304935034901627627714898692183574666026652382843539/50000000000000000000000000000000000000000000000000000000000) 8 (-5497284023996) (-5497284023835),
  mkLog (7878888793979372891883863729249199/2000000000000000000000000000000000000) 8 (-5536715581689) (-5536715581528),
  mkLog (7878888814695016382299863729249199/2000000000000000000000000000000000000) 8 (-5536715579060) (-5536715578899),
  mkLog (48192780121582752594709541861767/500000000000000000000000000000000000) 14 (-9247154157717) (-9247154157436),
  mkLog (170635380638036279106087820094329/1000000000000000000000000000000000000) 13 (-8675981555103) (-8675981554842),
  mkLog (188966747670074028957913334205767534783815861/1000000000000000000000000000000000000000000000000) 13 (-8573939496768) (-8573939496507),
  mkLog (188966747679609709126913334205767534783815861/1000000000000000000000000000000000000000000000000) 13 (-8573939496718) (-8573939496457),
  mkLog (170635380543261033026087820094329/1000000000000000000000000000000000000) 13 (-8675981555658) (-8675981555397),
  mkLog (3340748764835460226158588031738348465216184139/500000000000000000000000000000000000000000000000) 8 (-5008413135551) (-5008413135390),
  mkLog (3340748764627209923078088031738348465216184139/500000000000000000000000000000000000000000000000) 8 (-5008413135613) (-5008413135452),
  mkLog (188966764369889249026798507070852653433008721/1000000000000000000000000000000000000000000000000) 13 (-8573939408394) (-8573939408133),
  mkLog (3340749424041574902248740568537110846566991279/500000000000000000000000000000000000000000000000) 8 (-5008412938228) (-5008412938067),
  mkLog (188966764355731117675798507070852653433008721/1000000000000000000000000000000000000000000000000) 13 (-8573939408469) (-8573939408208),
  mkLog (188966764478370305427798507070852653433008721/1000000000000000000000000000000000000000000000000) 13 (-8573939407820) (-8573939407559),
  mkLog (3340749423809088435217740568537110846566991279/500000000000000000000000000000000000000000000000) 8 (-5008412938298) (-5008412938137),
  mkLog (21329262994328289810353912100189/125000000000000000000000000000000000) 13 (-8675989037069) (-8675989036808),
  mkLog (82531374380040706803211337449165761249239/10000000000000000000000000000000000000000000000) 17 (-11704917134567) (-11704917134226),
  mkLog (1174216216565664930006672531983834238750761/5000000000000000000000000000000000000000000000) 13 (-8356592316259) (-8356592315998),
  mkLog (2892517430448526708508674070971/10000000000000000000000000000000000) 12 (-8148213165946) (-8148213165705),
  mkLog (2892517431000183265918674070971/10000000000000000000000000000000000) 12 (-8148213165755) (-8148213165514),
  mkLog (82531374935252265043211337449165761249239/10000000000000000000000000000000000000000000000) 17 (-11704917127840) (-11704917127499),
  mkLog (2892517431205866316718674070971/10000000000000000000000000000000000) 12 (-8148213165684) (-8148213165443),
  mkLog (2892517429674482978898674070971/10000000000000000000000000000000000) 12 (-8148213166213) (-8148213165972),
  mkLog (82532900134187933026862422780458050386333/10000000000000000000000000000000000000000000000) 17 (-11704898647779) (-11704898647438),
  mkLog (1174253037507684919520905565844541949613667/5000000000000000000000000000000000000000000000) 13 (-8356560958862) (-8356560958600),
  mkLog (82532900074760126026862422780458050386333/10000000000000000000000000000000000000000000000) 17 (-11704898648499) (-11704898648158),
  mkLog (16571039/2000000000000) 17 (-11701001205542) (-11701001205201),
  mkLog (4113743/1000000000000) 18 (-12401177238482) (-12401177238121),
  mkLog (4113743/250000000000) 16 (-11014882877342) (-11014882877021),
  mkLog (1946290724796102381/500000000000000000000000) 18 (-12456438008888) (-12456438008527),
  mkLog (88537874556530772171/1000000000000000000000000) 14 (-9332080136550) (-9332080136269),
  mkLog (19019555311622785209/250000000000000000000000) 14 (-9483748520183) (-9483748519902),
  mkLog (38039110650578194803/500000000000000000000000) 14 (-9483748519464) (-9483748519183),
  mkLog (1946290762564819713/500000000000000000000000) 18 (-12456437989482) (-12456437989121),
  mkLog (38039110610821650243/500000000000000000000000) 14 (-9483748520509) (-9483748520228),
  mkLog (38039110611815563857/500000000000000000000000) 14 (-9483748520483) (-9483748520202),
  mkLog (243283067455623093/62500000000000000000000) 18 (-12456451462853) (-12456451462492),
  mkLog (88535826326190708549/1000000000000000000000000) 14 (-9332103270763) (-9332103270482),
  mkLog (1946264535172373481/500000000000000000000000) 18 (-12456451465151) (-12456451464790),
  mkLog (496956807/1000000000000) 11 (-7607007443200) (-7607007442979),
  mkLog (28253128824031523321/500000000000000000000000) 15 (-9781159171263) (-9781159170962),
  mkLog (52453252903588672499/1000000000000000000000000) 15 (-9855588206062) (-9855588205761),
  mkLog (26226626449434647691/500000000000000000000000) 15 (-9855588206152) (-9855588205851),
  mkLog (28253128805154014853/500000000000000000000000) 15 (-9781159171931) (-9781159171630),
  mkLog (1018431436447872140239/1000000000000000000000000) 10 (-6889491642830) (-6889491642629),
  mkLog (127303929525897988409/125000000000000000000000) 10 (-6889491643067) (-6889491642866),
  mkLog (52453249524514656727/1000000000000000000000000) 15 (-9855588270483) (-9855588270182),
  mkLog (5092156482190556051/5000000000000000000000) 10 (-6889491780306) (-6889491780105),
  mkLog (819582023599320709/15625000000000000000000) 15 (-9855588270753) (-9855588270452),
  mkLog (13113312410624771163/250000000000000000000000) 15 (-9855588268234) (-9855588267933),
  mkLog (509215645392148712017/500000000000000000000000) 10 (-6889491785858) (-6889491785657),
  mkLog (5650656603104137989/100000000000000000000000) 15 (-9781153713777) (-9781153713475),
  mkLog (4719377117/1000000000000) 8 (-5356078454911) (-5356078454750),
  mkLog (699820852700599609/31250000000000000000000) 16 (-10706705556732) (-10706705556411),
  mkLog (4889809726785506749/12500000000000000000000) 12 (-7846330531360) (-7846330531119),
  mkLog (12224524321187975229/31250000000000000000000) 12 (-7846330531014) (-7846330530773),
  mkLog (139347350407043179/6250000000000000000000) 16 (-10711122282070) (-10711122281749),
  mkLog (11878035702912271063/31250000000000000000000) 12 (-7875083699895) (-7875083699654),
  mkLog (3056131078184889629/7812500000000000000000) 12 (-7846330531705) (-7846330531464),
  mkLog (23756071786003294211/62500000000000000000000) 12 (-7875083683891) (-7875083683650),
  mkLog (29315501920862894621/3906250000000000000000) 8 (-4892216661657) (-4892216661495),
  mkLog (11878035839623014237/31250000000000000000000) 12 (-7875083688385) (-7875083688144),
  mkLog (24449047744539665231/62500000000000000000000) 12 (-7846330567737) (-7846330567496),
  mkLog (24449047753756119827/62500000000000000000000) 12 (-7846330567360) (-7846330567119),
  mkLog (23756071388159670817/62500000000000000000000) 12 (-7875083700638) (-7875083700397),
  mkLog (195592382066914777/500000000000000000000) 12 (-7846330567171) (-7846330566930),
  mkLog (24449047747611816763/62500000000000000000000) 12 (-7846330567611) (-7846330567370),
  mkLog (349911186323785033/15625000000000000000000) 16 (-10706703384826) (-10706703384505),
  mkLog (768037883/62500000000) 7 (-4399082777041) (-4399082776900),
  mkLog (823357732665758153/15625000000000000000000) 15 (-9850991978407) (-9850991978106),
  mkLog (6586861862508350021/125000000000000000000000) 15 (-9850991978227) (-9850991977926),
  mkLog (11646169099816661109/250000000000000000000000) 15 (-9974238903695) (-9974238903394),
  mkLog (32388146326720090259/31250000000000000000000) 10 (-6871982153522) (-6871982153321),
  mkLog (5823084550499472953/125000000000000000000000) 15 (-9974238903594) (-9974238903293),
  mkLog (11646167506096754753/250000000000000000000000) 15 (-9974239040540) (-9974239040239),
  mkLog (259105169463397614591/250000000000000000000000) 10 (-6871982157962) (-6871982157761),
  mkLog (129552610176241065931/125000000000000000000000) 10 (-6871981961558) (-6871981961357),
  mkLog (32388152547902692073/31250000000000000000000) 10 (-6871981961440) (-6871981961239),
  mkLog (13173611149040614499/250000000000000000000000) 15 (-9851000523757) (-9851000523456),
  mkLog (232923350145580791/5000000000000000000000) 15 (-9974239040439) (-9974239040138),
  mkLog (13173611163228032063/250000000000000000000000) 15 (-9851000522681) (-9851000522380),
  mkLog (1182284797/250000000000) 8 (-5354012082973) (-5354012082812),
  mkLog (69269073244973407/20000000000000000000000) 19 (-12573244298645) (-12573244298264),
  mkLog (3126279220587959159/40000000000000000000000) 14 (-9456791183222) (-9456791182941),
  mkLog (138538158177836083/40000000000000000000000) 19 (-12573244214279) (-12573244213898),
  mkLog (332753344535958447/4000000000000000000000) 14 (-9394403410803) (-9394403410522),
  mkLog (3327533460869675049/40000000000000000000000) 14 (-9394403406142) (-9394403405861),
  mkLog (138538145383520119/40000000000000000000000) 19 (-12573244306631) (-12573244306250),
  mkLog (3327533445580869809/40000000000000000000000) 14 (-9394403410737) (-9394403410456),
  mkLog (3327533445741804601/40000000000000000000000) 14 (-9394403410688) (-9394403410407),
  mkLog (1563141693222700313/20000000000000000000000) 14 (-9456789850694) (-9456789850413),
  mkLog (13853814536340327/4000000000000000000000) 19 (-12573244306777) (-12573244306395),
  mkLog (20116849/40000000000) 11 (-7595077010578) (-7595077010357),
  mkLog (3317013/800000000000) 18 (-12393302327670) (-12393302327309),
  mkLog (3317013/200000000000) 16 (-11007007966530) (-11007007966209),
  mkLog (119927/1000000000000) 23 (-15936382612839) (-15936382612378),
  mkLog (922974953/40000000000) 6 (-3769032635534) (-3769032635413),
  mkLog (11385831291436941344020649536507331/400000000000000000000000000000000000) 6 (-3559094833943) (-3559094833822),
  mkLog (11385945131363058655979350463492669/400000000000000000000000000000000000) 6 (-3559084835608) (-3559084835487),
  mkLog (56929441057/500000000000) 4 (-2172795473623) (-2172795473542),
  mkLog (345818107264275166468839747941225361403226109/200000000000000000000000000000000000000000000000) 10 (-6360159710351) (-6360159710150),
  mkLog (4975348201885525508775557789805405038596773891/100000000000000000000000000000000000000000000000) 5 (-3000674827549) (-3000674827448),
  mkLog (345818107281070182576839747941225361403226109/200000000000000000000000000000000000000000000000) 10 (-6360159710303) (-6360159710102),
  mkLog (182672832107232264590603999004266061/4000000000000000000000000000000000000) 5 (-3086352890031) (-3086352889930),
  mkLog (182672832108463240477107999004266061/4000000000000000000000000000000000000) 5 (-3086352890024) (-3086352889923),
  mkLog (1350852145464936993820142604014189552699601/781250000000000000000000000000000000000000000) 10 (-6360159588973) (-6360159588772),
  mkLog (182672832107323155266011999004266061/4000000000000000000000000000000000000) 5 (-3086352890030) (-3086352889929),
  mkLog (182672832102776645611363999004266061/4000000000000000000000000000000000000) 5 (-3086352890055) (-3086352889954),
  mkLog (19434918400607516549057992403121605369175399/390625000000000000000000000000000000000000000) 5 (-3000676654826) (-3000676654725),
  mkLog (1350852145483460908645142604014189552699601/781250000000000000000000000000000000000000000) 10 (-6360159588960) (-6360159588758),
  mkLog (72274016949/250000000000) 2 (-1240996231609) (-1240996231568),
  mkLog (452346552481642353362829867360839/200000000000000000000000000000000000) 9 (-6091624050530) (-6091624050349),
  mkLog (452346552474011060529229867360839/200000000000000000000000000000000000) 9 (-6091624050547) (-6091624050366),
  mkLog (2693955885439581299743587994992999435155687437/1000000000000000000000000000000000000000000000000) 9 (-5916744576334) (-5916744576153),
  mkLog (39678671465294258194256373372043471064844312563/500000000000000000000000000000000000000000000000) 4 (-2533794297824) (-2533794297743),
  mkLog (1346978202555056319125512910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5916744383432) (-5916744383251),
  mkLog (1346978202535978087041512910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5916744383446) (-5916744383265),
  mkLog (2693955885453889973806587994992999435155687437/1000000000000000000000000000000000000000000000000) 9 (-5916744576329) (-5916744576148),
  mkLog (39678671465613818581663373372043471064844312563/500000000000000000000000000000000000000000000000) 4 (-2533794297816) (-2533794297735),
  mkLog (19839330313942503017470367812636275140950560023/250000000000000000000000000000000000000000000000) 4 (-2533794570954) (-2533794570873),
  mkLog (19839330313104253195279617812636275140950560023/250000000000000000000000000000000000000000000000) 4 (-2533794570996) (-2533794570915),
  mkLog (2261760311531352398955405036669187/1000000000000000000000000000000000000) 9 (-6091611870066) (-6091611869885),
  mkLog (1346978202557441098136012910477144109049439977/500000000000000000000000000000000000000000000000) 9 (-5916744383430) (-5916744383249),
  mkLog (2261760311507504608850405036669187/1000000000000000000000000000000000000) 9 (-6091611870076) (-6091611869895),
  mkLog (2175174773/6250000000) 2 (-1055472447054) (-1055472447013),
  mkLog (73991579494687815612898036983123/1000000000000000000000000000000000000) 14 (-9511559261988) (-9511559261707),
  mkLog (14193037732450832746322054175207071/4000000000000000000000000000000000000) 9 (-5641298096354) (-5641298096173),
  mkLog (14193037733102681360622054175207071/4000000000000000000000000000000000000) 9 (-5641298096308) (-5641298096127),
  mkLog (7467565845898375735031021922494665412439322747617156461/100000000000000000000000000000000000000000000000000000000000) 14 (-9502356376379) (-9502356376098),
  mkLog (185889447763709746140277714898692183574666026652382843539/50000000000000000000000000000000000000000000000000000000000) 9 (-5594626154356) (-5594626154174),
  mkLog (7467565852166150872531021922494665412439322747617156461/100000000000000000000000000000000000000000000000000000000000) 14 (-9502356375540) (-9502356375259),
  mkLog (14193037733754529974922054175207071/4000000000000000000000000000000000000) 9 (-5641298096262) (-5641298096081),
  mkLog (14193037733553961170522054175207071/4000000000000000000000000000000000000) 9 (-5641298096276) (-5641298096095),
  mkLog (185889443070370054829685671930661731922704455702382843539/50000000000000000000000000000000000000000000000000000000000) 9 (-5594626179604) (-5594626179422),
  mkLog (3352204560055249524792378122387848269090190194897617156461/25000000000000000000000000000000000000000000000000000000000) 3 (-2009257617872) (-2009257617811),
  mkLog (185889443436408122859685671930661731922704455702382843539/50000000000000000000000000000000000000000000000000000000000) 9 (-5594626177635) (-5594626177453),
  mkLog (7096519286896793748633863729249199/2000000000000000000000000000000000000) 9 (-5641298037075) (-5641298036894),
  mkLog (7096519286545798340933863729249199/2000000000000000000000000000000000000) 9 (-5641298037125) (-5641298036944),
  mkLog (185889447824507164974027714898692183574666026652382843539/50000000000000000000000000000000000000000000000000000000000) 9 (-5594626154029) (-5594626153847),
  mkLog (7096519265711713783883863729249199/2000000000000000000000000000000000000) 9 (-5641298040061) (-5641298039880),
  mkLog (7096519286771438245883863729249199/2000000000000000000000000000000000000) 9 (-5641298037093) (-5641298036912),
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  mkLog (468153250468999823383/62500000000000000000000) 8 (-4894126135223) (-4894126135062),
  mkLog (25759760280592292539/62500000000000000000000) 12 (-7794108240530) (-7794108240289),
  mkLog (2548861430715825657/6250000000000000000000) 12 (-7804689981150) (-7804689980909),
  mkLog (79651919685388103/195312500000000000000) 12 (-7804689981457) (-7804689981216),
  mkLog (1367793648266483941/62500000000000000000000) 16 (-10729722869974) (-10729722869653),
  mkLog (12879880291885277123/31250000000000000000000) 12 (-7794108228761) (-7794108228520),
  mkLog (25488614306374850209/62500000000000000000000) 12 (-7804689981180) (-7804689980939),
  mkLog (5097722860648244953/12500000000000000000000) 12 (-7804689981303) (-7804689981062),
  mkLog (1416994505511137691/62500000000000000000000) 16 (-10694383752735) (-10694383752414),
  mkLog (783406361/62500000000) 7 (-4379270294862) (-4379270294721),
  mkLog (333973156375961753/6250000000000000000000) 15 (-9837031402249) (-9837031401948),
  mkLog (83493289049097011/1562500000000000000000) 15 (-9837031402787) (-9837031402486),
  mkLog (149011014885024747/3125000000000000000000) 15 (-9950924612688) (-9950924612387),
  mkLog (409513727006368593/390625000000000000000) 10 (-6860532875459) (-6860532875258),
  mkLog (596044101859636409/12500000000000000000000) 15 (-9950924541687) (-9950924541386),
  mkLog (6552219656344348203/6250000000000000000000) 10 (-6860532871760) (-6860532871559),
  mkLog (596044059360525279/12500000000000000000000) 15 (-9950924612989) (-9950924612688),
  mkLog (3276109063577250131/3125000000000000000000) 10 (-6860533105145) (-6860533104944),
  mkLog (13104436246228183619/12500000000000000000000) 10 (-6860533105761) (-6860533105560),
  mkLog (667953326122844307/12500000000000000000000) 15 (-9837020902402) (-9837020902101),
  mkLog (133590665176682539/2500000000000000000000) 15 (-9837020902760) (-9837020902459),
  mkLog (59857903/12500000000) 8 (-5341510453301) (-5341510453140),
  mkLog (3683087793755734401/1000000000000000000000000) 19 (-12511759083411) (-12511759083029),
  mkLog (4924562298936622731/62500000000000000000000) 14 (-9448686438504) (-9448686438223),
  mkLog (92077194831172821/25000000000000000000000) 19 (-12511759083549) (-12511759083167),
  mkLog (84125804068821856239/1000000000000000000000000) 14 (-9383197212162) (-9383197211881),
  mkLog (8412580407441889341/100000000000000000000000) 14 (-9383197212095) (-9383197211814),
  mkLog (92077189742957211/25000000000000000000000) 19 (-12511759138809) (-12511759138428),
  mkLog (3365032162264405551/40000000000000000000000) 14 (-9383197212307) (-9383197212026),
  mkLog (84125804073910071849/1000000000000000000000000) 14 (-9383197212101) (-9383197211820),
  mkLog (78792997192587320301/1000000000000000000000000) 14 (-9448686433305) (-9448686433024),
  mkLog (3683087573944820049/1000000000000000000000000) 19 (-12511759143092) (-12511759142710),
  mkLog (508821561/1000000000000) 11 (-7583413170768) (-7583413170547),
  mkLog (16719623/4000000000000) 18 (-12385221859710) (-12385221859349),
  mkLog (16719623/1000000000000) 16 (-10998927498570) (-10998927498249),
  mkLog (11385020251/500000000000) 6 (-3782309620225) (-3782309620104),
  mkLog (56796688561209870048317497118221257/2000000000000000000000000000000000000) 6 (-3561424435554) (-3561424435433),
  mkLog (56796705947790129951682502881778743/2000000000000000000000000000000000000) 6 (-3561424129434) (-3561424129313),
  mkLog (113593394509/1000000000000) 4 (-2175129921354) (-2175129921273),
  mkLog (100643402879166608840721197878979004270105229/62500000000000000000000000000000000000000000000) 10 (-6431338231053) (-6431338230852),
  mkLog (1561516201553315691313047604117212683229894771/31250000000000000000000000000000000000000000000) 5 (-2996362102911) (-2996362102810),
  mkLog (18247292578332667928479917530374449/400000000000000000000000000000000000) 5 (-3087447830008) (-3087447829907),
  mkLog (4025736571518046915474273226775244924998011/2500000000000000000000000000000000000000000000) 10 (-6431338117694) (-6431338117493),
  mkLog (62460647045774311972376005563696475075001989/1250000000000000000000000000000000000000000000) 5 (-2996362119183) (-2996362119082),
  mkLog (288851140019/1000000000000) 2 (-1241843810032) (-1241843809991),
  mkLog (2209053175825457847915515443082593/1000000000000000000000000000000000000) 9 (-6115191282573) (-6115191282392),
  mkLog (522014491324526727883108456213713278418893769/200000000000000000000000000000000000000000000000) 9 (-5948377296966) (-5948377296785),
  mkLog (7850535244155516611361873902512843071581106231/100000000000000000000000000000000000000000000000) 4 (-2544588472590) (-2544588472509),
  mkLog (81564755863394976083337835589266914095249249/31250000000000000000000000000000000000000000000) 9 (-5948377400026) (-5948377399845),
  mkLog (1226646542782288829825230317224390648404750751/15625000000000000000000000000000000000000000000) 4 (-2544588137626) (-2544588137545),
  mkLog (4418037035100690362972598379155519/2000000000000000000000000000000000000) 9 (-6115206971895) (-6115206971714),
  mkLog (343738184323/1000000000000) 2 (-1067875003491) (-1067875003450),
  mkLog (26694918239500344458263211654037/500000000000000000000000000000000000) 15 (-9837890158373) (-9837890158072),
  mkLog (370686200134946936678922446648833/125000000000000000000000000000000000) 9 (-5820713133416) (-5820713133235),
  mkLog (29802174179315584372912146933521594720608952298476555109/500000000000000000000000000000000000000000000000000000000000) 15 (-9727782027668) (-9727782027366),
  mkLog (725008865064812358570203015397443935067455772701523444891/250000000000000000000000000000000000000000000000000000000000) 9 (-5843032314480) (-5843032314299),
  mkLog (725008899565172218161350473375587491256458044451523444891/250000000000000000000000000000000000000000000000000000000000) 9 (-5843032266894) (-5843032266713),
  mkLog (16154642983312963499184698531693313853955477230548476555109/125000000000000000000000000000000000000000000000000000000000) 3 (-2046106237755) (-2046106237694),
  mkLog (11861961962939561203099987927561667/4000000000000000000000000000000000000) 9 (-5820712833413) (-5820712833232),
  mkLog (13346720821256712986163504292167/250000000000000000000000000000000000) 15 (-9837945473688) (-9837945473387),
  mkLog (10306650029/62500000000) 3 (-1802377235986) (-1802377235925),
  mkLog (31928419878815950221882046769667/500000000000000000000000000000000000) 14 (-9658866859083) (-9658866858802),
  mkLog (39612564780797539617806655469130096365653187/500000000000000000000000000000000000000000000000) 14 (-9443217017167) (-9443217016886),
  mkLog (1152183668770097811961966783409309903634346813/250000000000000000000000000000000000000000000000) 8 (-5379801933682) (-5379801933521),
  mkLog (39612565401962648958241575547932756792898769/500000000000000000000000000000000000000000000000) 14 (-9443217001486) (-9443217001205),
  mkLog (1152183679715034709680706519979743493207101231/250000000000000000000000000000000000000000000000) 8 (-5379801924182) (-5379801924021),
  mkLog (63856717070797258681349768836201/1000000000000000000000000000000000000) 14 (-9658868780365) (-9658868780084),
  mkLog (19324166943/1000000000000) 6 (-3946398793235) (-3946398793114),
  mkLog (41480407535726776476937919770443559183/500000000000000000000000000000000000000000000000) 34 (-23212652727525) (-23212652726844),
  mkLog (18930393392438470569604568930564729556440817/250000000000000000000000000000000000000000000000) 14 (-9488447450552) (-9488447450271),
  mkLog (126666624779324116260816588867073/1000000000000000000000000000000000000) 13 (-8973951924733) (-8973951924472),
  mkLog (20592347259748188607231271588128696893/250000000000000000000000000000000000000000000000) 34 (-23219807240621) (-23219807239940),
  mkLog (9397691831567678973212575400949661871303107/125000000000000000000000000000000000000000000000) 14 (-9495604907135) (-9495604906854),
  mkLog (328784969/500000000000) 11 (-7326959430099) (-7326959429878)]

private def refs0 : List (Bool × Fin 472) :=
[(false,0),
  (false,1),
  (false,2),
  (false,3),
  (false,4),
  (false,5),
  (false,6),
  (false,7),
  (false,8),
  (false,0),
  (true,0),
  (false,9),
  (false,9),
  (false,10),
  (false,10),
  (true,1),
  (false,11),
  (false,12),
  (false,13),
  (false,14),
  (false,15),
  (false,16),
  (false,17),
  (false,18),
  (false,19),
  (false,20),
  (true,2),
  (false,21),
  (false,22),
  (false,23),
  (false,24),
  (false,25),
  (false,26),
  (false,27),
  (false,28),
  (false,29),
  (false,25),
  (false,30),
  (false,31),
  (false,32),
  (false,33),
  (false,34),
  (false,35),
  (true,3),
  (false,36),
  (false,37),
  (false,38),
  (false,39),
  (false,40),
  (false,41),
  (false,42),
  (false,43),
  (false,44),
  (false,45),
  (false,46),
  (false,47),
  (false,48),
  (false,39),
  (false,49),
  (false,39),
  (false,50),
  (false,51),
  (false,52),
  (true,4),
  (false,53),
  (false,54),
  (false,55),
  (false,56),
  (false,57),
  (false,58),
  (false,59),
  (false,60),
  (false,61),
  (false,55),
  (false,55),
  (false,62),
  (false,63),
  (false,59),
  (false,64),
  (false,64),
  (true,5),
  (false,65),
  (false,66),
  (false,67),
  (false,68),
  (false,69),
  (false,70),
  (false,71),
  (false,72),
  (false,73),
  (false,74),
  (true,6),
  (false,75),
  (false,75),
  (false,75),
  (false,75),
  (true,7),
  (false,8),
  (true,8),
  (true,8),
  (false,8),
  (true,76),
  (true,76),
  (true,76),
  (true,76),
  (false,77),
  (true,78),
  (true,79),
  (true,80),
  (true,81),
  (true,82),
  (true,83),
  (true,84),
  (true,85),
  (true,86),
  (true,87),
  (false,88),
  (true,89),
  (true,90),
  (true,91),
  (true,92),
  (true,93),
  (true,94),
  (true,95),
  (true,96),
  (true,97),
  (true,91),
  (true,91),
  (true,98),
  (true,99),
  (true,95),
  (true,100),
  (true,100),
  (false,101),
  (true,102),
  (true,103),
  (true,104),
  (true,105),
  (true,106),
  (true,105),
  (true,103),
  (true,107),
  (true,108),
  (true,109),
  (true,110),
  (true,111),
  (true,112),
  (true,105),
  (true,113),
  (true,105),
  (true,114),
  (true,115),
  (true,116),
  (false,117),
  (true,118),
  (true,119),
  (true,120),
  (true,121),
  (true,122),
  (true,123),
  (true,123),
  (true,120),
  (true,124),
  (true,122),
  (true,125),
  (true,126),
  (true,127),
  (true,123),
  (true,128),
  (true,129),
  (false,130),
  (true,131),
  (true,132),
  (true,133),
  (true,134),
  (true,135),
  (true,136),
  (true,137),
  (true,138),
  (true,139),
  (true,140),
  (false,141),
  (true,142),
  (true,142),
  (true,142),
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  (false,143),
  (true,144),
  (false,144),
  (true,145),
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  (true,146),
  (true,146),
  (true,147),
  (true,147),
  (false,148),
  (true,149),
  (true,150),
  (true,151),
  (true,152),
  (true,153),
  (true,154),
  (true,155),
  (true,156),
  (true,157),
  (true,158),
  (false,159),
  (true,160),
  (true,161),
  (true,162),
  (true,163),
  (true,162),
  (true,164),
  (true,165),
  (true,166),
  (true,167),
  (true,162),
  (true,168),
  (true,169),
  (true,170),
  (true,171),
  (true,164),
  (true,172),
  (false,173),
  (true,174),
  (true,175),
  (true,176),
  (true,177),
  (true,178),
  (true,179),
  (true,180),
  (true,181),
  (true,182),
  (true,183),
  (true,184),
  (true,185),
  (true,186),
  (true,177),
  (true,187),
  (true,177),
  (true,188),
  (true,189),
  (true,190),
  (false,191),
  (true,192),
  (true,193),
  (true,194),
  (true,195),
  (true,196),
  (true,197),
  (true,198),
  (true,199),
  (true,198),
  (true,194),
  (true,194),
  (true,200),
  (true,201),
  (true,198),
  (true,202),
  (true,202),
  (false,203),
  (true,204),
  (true,205),
  (true,206),
  (true,207),
  (true,208),
  (true,209),
  (true,210),
  (true,211),
  (true,212),
  (true,213),
  (false,214),
  (true,215),
  (true,215),
  (true,215),
  (true,215),
  (false,216)]

private def refs1 : List (Bool × Fin 472) :=
[(false,217),
  (false,218),
  (false,219),
  (false,220),
  (false,221),
  (false,222),
  (false,223),
  (false,224),
  (false,225),
  (false,217),
  (true,217),
  (false,226),
  (false,226),
  (false,227),
  (false,227),
  (true,218),
  (false,228),
  (false,229),
  (false,230),
  (false,231),
  (false,232),
  (false,233),
  (false,234),
  (false,235),
  (false,236),
  (false,237),
  (true,219),
  (false,238),
  (false,239),
  (false,240),
  (false,241),
  (false,242),
  (false,243),
  (false,243),
  (false,240),
  (false,244),
  (false,245),
  (false,246),
  (false,247),
  (false,248),
  (false,243),
  (false,249),
  (false,250),
  (true,220),
  (false,251),
  (false,252),
  (false,253),
  (false,254),
  (false,255),
  (false,254),
  (false,256),
  (false,257),
  (false,258),
  (false,259),
  (false,260),
  (false,261),
  (false,262),
  (false,263),
  (false,264),
  (false,254),
  (false,265),
  (false,266),
  (false,267),
  (true,221),
  (false,268),
  (false,269),
  (false,270),
  (false,271),
  (false,272),
  (false,273),
  (false,274),
  (false,275),
  (false,276),
  (false,277),
  (false,278),
  (false,279),
  (false,280),
  (false,279),
  (false,281),
  (false,282),
  (true,222),
  (false,283),
  (false,284),
  (false,285),
  (false,286),
  (false,287),
  (false,288),
  (false,289),
  (false,290),
  (false,291),
  (false,292),
  (true,223),
  (false,293),
  (false,293),
  (false,293),
  (false,293),
  (true,224),
  (false,225),
  (true,225),
  (true,225),
  (false,225),
  (true,294),
  (true,294),
  (true,294),
  (true,294),
  (false,295),
  (true,296),
  (true,297),
  (true,298),
  (true,299),
  (true,300),
  (true,301),
  (true,302),
  (true,303),
  (true,304),
  (true,305),
  (false,306),
  (true,307),
  (true,308),
  (true,309),
  (true,310),
  (true,311),
  (true,312),
  (true,313),
  (true,314),
  (true,315),
  (true,316),
  (true,308),
  (true,313),
  (true,317),
  (true,313),
  (true,318),
  (true,319),
  (false,320),
  (true,321),
  (true,322),
  (true,323),
  (true,324),
  (true,325),
  (true,324),
  (true,326),
  (true,327),
  (true,328),
  (true,329),
  (true,330),
  (true,331),
  (true,332),
  (true,333),
  (true,334),
  (true,324),
  (true,335),
  (true,336),
  (true,337),
  (false,338),
  (true,339),
  (true,339),
  (true,340),
  (true,341),
  (true,342),
  (true,343),
  (true,343),
  (true,340),
  (true,344),
  (true,340),
  (true,345),
  (true,346),
  (true,347),
  (true,343),
  (true,348),
  (true,349),
  (false,350),
  (true,351),
  (true,352),
  (true,353),
  (true,354),
  (true,355),
  (true,356),
  (true,357),
  (true,358),
  (true,359),
  (true,360),
  (false,361),
  (true,215),
  (true,215),
  (true,215),
  (true,215),
  (false,216),
  (true,8),
  (false,8),
  (true,362),
  (true,362),
  (true,362),
  (true,362),
  (false,363),
  (true,364),
  (true,365),
  (true,366),
  (true,367),
  (true,368),
  (true,369),
  (true,370),
  (true,371),
  (true,372),
  (true,373),
  (false,374),
  (true,375),
  (true,376),
  (true,377),
  (true,378),
  (true,379),
  (true,380),
  (true,381),
  (true,382),
  (true,383),
  (true,384),
  (true,385),
  (true,386),
  (true,387),
  (true,386),
  (true,388),
  (true,389),
  (false,390),
  (true,391),
  (true,392),
  (true,393),
  (true,394),
  (true,395),
  (true,394),
  (true,392),
  (true,396),
  (true,397),
  (true,398),
  (true,399),
  (true,400),
  (true,401),
  (true,402),
  (true,403),
  (true,394),
  (true,404),
  (true,405),
  (true,406),
  (false,407),
  (true,408),
  (true,409),
  (true,410),
  (true,411),
  (true,410),
  (true,412),
  (true,412),
  (true,410),
  (true,413),
  (true,414),
  (true,415),
  (true,416),
  (true,417),
  (true,412),
  (true,412),
  (true,418),
  (false,419),
  (true,420),
  (true,421),
  (true,422),
  (true,423),
  (true,424),
  (true,425),
  (true,426),
  (true,427),
  (true,428),
  (true,429),
  (false,430),
  (true,431),
  (true,431),
  (true,431),
  (true,431),
  (false,432),
  (true,144),
  (false,144),
  (true,433),
  (false,433),
  (true,434),
  (true,434),
  (true,435),
  (true,435),
  (false,436),
  (true,437),
  (true,438),
  (true,437),
  (true,439),
  (true,439),
  (true,440),
  (true,439),
  (true,439),
  (true,441),
  (true,440),
  (false,442),
  (true,443),
  (true,443),
  (true,444),
  (true,445),
  (true,444),
  (true,446),
  (true,446),
  (true,444),
  (true,445),
  (true,444),
  (true,447),
  (true,447),
  (true,448),
  (true,446),
  (true,446),
  (true,448),
  (false,449),
  (true,450),
  (true,451),
  (true,451),
  (true,452),
  (true,453),
  (true,452),
  (true,451),
  (true,451),
  (true,454),
  (true,455),
  (true,454),
  (true,456),
  (true,456),
  (true,452),
  (true,453),
  (true,452),
  (true,456),
  (true,456),
  (true,457),
  (false,458),
  (true,459),
  (true,460),
  (true,460),
  (true,459),
  (true,461),
  (true,461),
  (true,462),
  (true,463),
  (true,462),
  (true,460),
  (true,460),
  (true,462),
  (true,463),
  (true,462),
  (true,464),
  (true,464),
  (false,465),
  (true,466),
  (true,467),
  (true,468),
  (true,468),
  (true,466),
  (true,468),
  (true,468),
  (true,469),
  (true,470),
  (true,469),
  (false,471)]

def entriesOwner1 (i : Fin 2) : List Entry :=
  ((![(refs0),(refs1)] i).map (fun p ↦
    let e := logTable p.2
    ((if p.1 then e.1.1 else -e.1.1,e.1.2),e.2)))

end MME.ReleasedGlobalYZ
Source
Exact released global candidate from primitive seed f8187420c24231b83d9d1fb7b327fee76cd50ada0af0525e77b3d3b0d8f4d4e6.

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Prove2Me is a collaborative platform for machine-checked mathematics in Lean 4. Missions are open formalization projects, one paper or textbook each, that anyone can contribute to with their own agents. Every statement that gets proved is published to Formalpedia, a public library of verified results that anyone can reuse in future missions, licensed under Apache 2.0.

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