RH height 14–100 — theta arithmetic interface
DefinitionTaoFivePrimes_RH14To100ThetaInterfacenumerical-verificationriemann-zetatao-five-primes
The theta arithmetic interface for the existing height-14–100 finite certificate. This module defines the proposed data structures and exact integer validators, without asserting numerical correctness or a Riemann-hypothesis conclusion. It extracts the ordinary definitions from sometik179’s publicly submitted certificate, with the theta/Mellin attribution to Gabewhigham retained.
Port note. This is a port, to the Mathlib 777aaa6 / Lean v4.29.0-rc3 environment of the Riemann Hypothesis mission tree, of the definition TaoFivePrimes_RH14To100ThetaInterface (id 87fa5460-d8d5-4605-96a5-b606fe3bc5af, env 0df444a, published by @raresbuhai). The Lean source is unchanged.
Definition code
/- Ordinary finite arithmetic definitions extracted from sometik179's
height-14–100 certificate, Prove2Me c9908072-d99a-4431-aad8-a72c6352619a.
Theta/Mellin attribution to Gabewhigham is retained. No certificate assertion
or RH theorem is supplied in this definition interface. -/
import Definitions.Def_TaoFivePrimes_RH14To100ArithmeticCore
import Definitions.Def_TaoFivePrimes_RH14To100ThetaDataA
import Definitions.Def_TaoFivePrimes_RH14To100ThetaDataB
import Definitions.Def_TaoFivePrimes_RH14To100ThetaDataC
import Mathlib.Data.Int.Basic
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Data.Nat.Bitwise
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.List.GetD
import Mathlib.Data.List.OfFn
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Abs
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option exponentiation.threshold 20000
set_option Elab.async false
set_option linter.unusedSimpArgs false
set_option linter.unnecessarySeqFocus false
section Height100Module0
open Finset
namespace CertifiedPackedConvolution
end CertifiedPackedConvolution
end Height100Module0
section Height100Module1
set_option autoImplicit false
open Finset
open scoped BigOperators
namespace CertifiedMomentConvolution
end CertifiedMomentConvolution
end Height100Module1
section Height100Module2
open Finset
namespace CertifiedTaylorQuadrature
end CertifiedTaylorQuadrature
end Height100Module2
section Height100Module3
set_option autoImplicit false
open Finset
open scoped BigOperators
namespace CertifiedMomentConvolution
open CertifiedTaylorQuadrature
end CertifiedMomentConvolution
end Height100Module3
section Height100Module4
open Finset
namespace CertifiedExponentialJets
open CertifiedTaylorQuadrature CertifiedMomentConvolution
end CertifiedExponentialJets
end Height100Module4
section Height100Module5
open Finset
namespace CertifiedIntegerExponentialJets
open CertifiedMomentConvolution CertifiedExponentialJets
end CertifiedIntegerExponentialJets
end Height100Module5
section Height100Module6
set_option autoImplicit false
open Finset
open scoped BigOperators
namespace CertifiedSignedODEConvolution
open CertifiedIntegerExponentialJets
end CertifiedSignedODEConvolution
end Height100Module6
section Height100Module7
set_option autoImplicit false
namespace CertifiedListODEVectors
open CertifiedSignedODEConvolution
open Finset
open scoped BigOperators
def absDerivativeList (g : List ℤ) : List ℕ :=
(g.tail.zipIdx).map (fun (x,k) => (k+1)*x.natAbs)
def radiusDerivativeList (r : List ℕ) : List ℕ :=
(r.tail.zipIdx).map (fun (x,k) => (k+1)*x)
def radiusFactorList (f : List ℤ) (s : List ℕ) : List ℕ :=
List.zipWith (fun x y => x.natAbs+y) f s
end CertifiedListODEVectors
end Height100Module7
section Height100Module8
set_option autoImplicit false
open Finset
namespace CertifiedPackedHorner
open CertifiedPackedConvolution
end CertifiedPackedHorner
namespace CertifiedPackedHorner
end CertifiedPackedHorner
end Height100Module8
section Height100Module9
namespace ZetaSix
end ZetaSix
end Height100Module9
section Height100Module10
namespace TaoZetaBounds
end TaoZetaBounds
end Height100Module10
section Height100Module11
namespace TaoZetaBounds
end TaoZetaBounds
end Height100Module11
section Height100Module12
open Finset
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module12
section Height100Module13
open Finset
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module13
section Height100Module14
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module14
section Height100Module15
open Finset
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module15
section Height100Module16
open Finset
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module16
section Height100Module17
set_option autoImplicit false
set_option exponentiation.threshold 1024
set_option maxRecDepth 10000
namespace TaoZetaWide256
end TaoZetaWide256
end Height100Module17
section Height100Module18
open Finset
open scoped BigOperators
set_option autoImplicit false
set_option exponentiation.threshold 1024
namespace TaoZetaGlobal
end TaoZetaGlobal
end Height100Module18
section Height100Module19
set_option autoImplicit false
namespace TaoZetaCertificate
end TaoZetaCertificate
end Height100Module19
section Height100Module20
set_option autoImplicit false
namespace TaoZetaCertificate
end TaoZetaCertificate
end Height100Module20
section Height100Module21
set_option autoImplicit false
namespace TaoZetaCertificate
end TaoZetaCertificate
end Height100Module21
section Height100Module22
open Finset
namespace CertifiedComplexTaylor
open CertifiedTaylorQuadrature
end CertifiedComplexTaylor
end Height100Module22
section Height100Module23
set_option autoImplicit false
namespace TaoZetaWide
end TaoZetaWide
end Height100Module23
section Height100Module24
namespace CertifiedLocalXi
end CertifiedLocalXi
end Height100Module24
section Height100Module25
open Finset
namespace CertifiedGlobalMoments
open CertifiedZetaQuadrature
end CertifiedGlobalMoments
end Height100Module25
section Height100Module26
open Finset
namespace CertifiedEvenPolynomial
end CertifiedEvenPolynomial
end Height100Module26
section Height100Module27
namespace CertifiedLocalXi
end CertifiedLocalXi
end Height100Module27
section Height100Module28
namespace CertifiedLocalXi
end CertifiedLocalXi
end Height100Module28
section Height100Module29
open Finset
namespace CertifiedLocalXi
end CertifiedLocalXi
end Height100Module29
section Height100Module30
open Finset
namespace CertifiedLocalXi
end CertifiedLocalXi
end Height100Module30
section Height100Module31
open Finset
namespace CertifiedPolynomialTranslation
open CertifiedTaylorQuadrature
end CertifiedPolynomialTranslation
end Height100Module31
section Height100Module32
open Finset
namespace CertifiedPolynomialTranslation
open CertifiedTaylorQuadrature CertifiedGlobalMoments
end CertifiedPolynomialTranslation
end Height100Module32
section Height100Module33
set_option maxRecDepth 10000
set_option exponentiation.threshold 1024
namespace CertifiedDenseGlobalPolynomial
open Finset CertifiedPolynomialTranslation
end CertifiedDenseGlobalPolynomial
end Height100Module33
section Height100Module34
set_option autoImplicit false
open Finset
open scoped BigOperators
namespace CertifiedFixedPoint
structure Box where
lo : ℕ
hi : ℕ
deriving DecidableEq, Repr
def mulDivBox (S d : ℕ) (a b : Box) : Box :=
⟨a.lo*b.lo/(S*d),a.hi*b.hi/(S*d)+1⟩
def repeatedSquare (S : ℕ) : ℕ → Box → Box
| 0, a => a
| n+1, a => repeatedSquare S n (mulDivBox S 1 a a)
end CertifiedFixedPoint
end Height100Module34
section Height100Module35
set_option autoImplicit false
set_option maxHeartbeats 0
set_option exponentiation.threshold 1024
namespace CertifiedFixedPoint
def scale310 : ℕ := 10^310
end CertifiedFixedPoint
end Height100Module35
section Height100Module36
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
set_option Elab.async false
namespace CertifiedThetaPoints
open CertifiedFixedPoint
/-- Candidate literals are generated by ordinary computation, then verified by
an explicit kernel equality to the executable interval algorithm. -/
@[noinline] def _root_.CertifiedThetaPoints.pointExpCache : List CertifiedFixedPoint.Box :=
[{
lo :=
10237143166023579169688505321657689580745565901200831129596736021287697168088173224424651281461283976321111731811507959020450621264061803446739409751452091587359289984752075369215569551264120305183502194305664766262292381170445029927074092436647729719514377220852805010990673450530425771289877348096329239178975,
hi :=
10237143166023579169688505321657689580745565901200831129596736021287697168088173224424651281461283976321111731811507959020450621264061803446739409751452091587359289984752075369215569551264120305183502194305664766262292381170445029927074092436647729719514377220852805010990673450530425771289877348096329239179177 },
{
lo :=
10728433924348774444113000950108137669286240070507301265720032611972644950499744180094313653536755326566736380600553039677721496946934808088503508123980768498989077882275722689596682393787471681284293900026933585800355169016974330823946808142426639595908892275311227606368570571966724763118930039739756918484484,
hi :=
10728433924348774444113000950108137669286240070507301265720032611972644950499744180094313653536755326566736380600553039677721496946934808088503508123980768498989077882275722689596682393787471681284293900026933585800355169016974330823946808142426639595908892275311227606368570571966724763118930039739756918484686 },
{
lo :=
11243302218447507174517329054449565537714045938180256129119447489271559248778461755934182711214300053112963591429621092682804883140017292657835547502565009690268626986762788628675513484240747136837639609413408613560513310365632973765196708553997451974988438949084530407415752338148169977660255642005476800797675,
hi :=
11243302218447507174517329054449565537714045938180256129119447489271559248778461755934182711214300053112963591429621092682804883140017292657835547502565009690268626986762788628675513484240747136837639609413408613560513310365632973765196708553997451974988438949084530407415752338148169977660255642005476800797877 },
{
lo :=
11782879557886632426631433081958559090232306216515978089646341248807954831349379078649859547455394860469645209984085880707599425128154662683144218277543611738242613789290959017155157574841587148332051230851915843018407551160619534732469621555906823961835455544677588373849186166470921729526315226938961122289729,
hi :=
11782879557886632426631433081958559090232306216515978089646341248807954831349379078649859547455394860469645209984085880707599425128154662683144218277543611738242613789290959017155157574841587148332051230851915843018407551160619534732469621555906823961835455544677588373849186166470921729526315226938961122289931 },
{
lo :=
12348351754510910046840161108760027424078237285532324479745246811225626522655900308116910910725958725275599636699637897495058188131628678869308375491651355437648948194212519195061595418484399052153126919927629169694858465335688674644663871348115013387512720875893273250361705062601522938839087005354382832808793,
hi :=
12348351754510910046840161108760027424078237285532324479745246811225626522655900308116910910725958725275599636699637897495058188131628678869308375491651355437648948194212519195061595418484399052153126919927629169694858465335688674644663871348115013387512720875893273250361705062601522938839087005354382832808995 },
{
lo :=
12940961528463733098261106268100709645926577196080268062415496705066132082609495796248626145679442108084416527264921202382673470654057497510070110282826483028779303560797778912791145724088329890993553744195098957312177698797452718975120747615649943134291637926209554503196161268800548000539459132249890719733440,
hi :=
12940961528463733098261106268100709645926577196080268062415496705066132082609495796248626145679442108084416527264921202382673470654057497510070110282826483028779303560797778912791145724088329890993553744195098957312177698797452718975120747615649943134291637926209554503196161268800548000539459132249890719733642 },
{
lo :=
13562011239273402330584882593857570013204578364337200307679170464530825294145825607870960356296235768281354590908923615994309745851939182128228151655857813830221543700489620323509332359456642912193460211068489133442875909816793116070539982617121812720408137971552322439513977788095421006639810397844729551220768,
hi :=
13562011239273402330584882593857570013204578364337200307679170464530825294145825607870960356296235768281354590908923615994309745851939182128228151655857813830221543700489620323509332359456642912193460211068489133442875909816793116070539982617121812720408137971552322439513977788095421006639810397844729551220970 },
{
lo :=
14212865748006967555595399377075767858324403710629537647701231053033114578094157270986392798494023931780012710323076734116594877530336734739146867719986489134893396455315189789688873948204748888203836380625485926389080077058949125508387163829265445952585536993704127050610457897232765405685122061189739921190664,
hi :=
14212865748006967555595399377075767858324403710629537647701231053033114578094157270986392798494023931780012710323076734116594877530336734739146867719986489134893396455315189789688873948204748888203836380625485926389080077058949125508387163829265445952585536993704127050610457897232765405685122061189739921190867 },
{
lo :=
14894955416781699796055764474013653746366884178910026227298101777322265604116469545445137694258726457670403753109386456353092688420637176088955587339898732748229160749979766787079524985174383710416461636711938189427551260876751519708313450719736472090247025391719199263897652037741140261117255629536470321615728,
hi :=
14894955416781699796055764474013653746366884178910026227298101777322265604116469545445137694258726457670403753109386456353092688420637176088955587339898732748229160749979766787079524985174383710416461636711938189427551260876751519708313450719736472090247025391719199263897652037741140261117255629536470321615933 },
{
lo :=
15609779252226124543404296589529359617213440719531707423988232390737363352583454195334484255580156674086558732933544972503169406932257924498271878668722409276067165492132483233103782373916081271782746872122297328133617032253147922082563807491927186001133955818081197809404789681621049744287756920993700339769920,
hi :=
15609779252226124543404296589529359617213440719531707423988232390737363352583454195334484255580156674086558732933544972503169406932257924498271878668722409276067165492132483233103782373916081271782746872122297328133617032253147922082563807491927186001133955818081197809404789681621049744287756920993700339770126 },
{
lo :=
16358908199798899801726944886054803066336858485647291169015306766787567026961244486926550791708161290183144923651069814844331049862137135534966094082383516265695133043830917107576442580130867302478108797529506087059336599177776055564000299786261542372103865540887064771440795212711938857097516606015752901998940,
hi :=
16358908199798899801726944886054803066336858485647291169015306766787567026961244486926550791708161290183144923651069814844331049862137135534966094082383516265695133043830917107576442580130867302478108797529506087059336599177776055564000299786261542372103865540887064771440795212711938857097516606015752901999144 },
{
lo :=
17143988596205358051369170173112717453784531664493378370272656156223721692898329678220432968053697559859356770778283020830785579810282433800830177918761860331976775216243932634216110467682303795054378491054355136486408341537550254120299186412189194200815105894707445557335375553527352817814008691724617825491093,
hi :=
17143988596205358051369170173112717453784531664493378370272656156223721692898329678220432968053697559859356770778283020830785579810282433800830177918761860331976775216243932634216110467682303795054378491054355136486408341537550254120299186412189194200815105894707445557335375553527352817814008691724617825491295 },
{
lo :=
17966745787498977440179624291990663920674300962032715938586594978712163892246956433029363493472708532887900726707600005955315129202002325490540183839313174653371934239178144719371835461417177520201340857874465918666123782490326206378063891988699387850788545747295077541212224199631498673821830085385325453497937,
hi :=
17966745787498977440179624291990663920674300962032715938586594978712163892246956433029363493472708532887900726707600005955315129202002325490540183839313174653371934239178144719371835461417177520201340857874465918666123782490326206378063891988699387850788545747295077541212224199631498673821830085385325453498140 },
{
lo :=
18828987920819167975074551877605054582064687859329394166371377113521693485083502050607257600589666169236372629665865247540973916966619136624586137463310368779881396805486053651002729611479526021037788610107932673015456104117517207188181967534884454309235128193118156286014082756499604895470905515489684196685077,
hi :=
18828987920819167975074551877605054582064687859329394166371377113521693485083502050607257600589666169236372629665865247540973916966619136624586137463310368779881396805486053651002729611479526021037788610107932673015456104117517207188181967534884454309235128193118156286014082756499604895470905515489684196685280 },
{
lo :=
19732609918098353457263977417630639167722963005157263384678039590861788811069838948652151371345670742343332765810224167790792105546022625715348386757747025618584088858106539386596843262133865716188637502424234874694855178614363857997753222630827128872939450196709656786509194204808347324618957931859589885789437,
hi :=
19732609918098353457263977417630639167722963005157263384678039590861788811069838948652151371345670742343332765810224167790792105546022625715348386757747025618584088858106539386596843262133865716188637502424234874694855178614363857997753222630827128872939450196709656786509194204808347324618957931859589885789641 },
{
lo :=
20679597640471238000138982954032159493019471177830363294939835440110210072503740417740381900425537572656900416980743662534324441155055384527548415246798144983041233808994467713412090934702287640065939689846780665308728479428337390054165459965775983416861404668018294020941157859129684336152398331796420668673927,
hi :=
20679597640471238000138982954032159493019471177830363294939835440110210072503740417740381900425537572656900416980743662534324441155055384527548415246798144983041233808994467713412090934702287640065939689846780665308728479428337390054165459965775983416861404668018294020941157859129684336152398331796420668674134 }]
def cachedPointExp (i : Fin 16) : Box := pointExpCache.getD i.val ⟨0,0⟩
end CertifiedThetaPoints
end Height100Module36
section Height100Module37
set_option autoImplicit false
set_option maxHeartbeats 0
open Finset
open scoped BigOperators
namespace CertifiedHighPrecisionPi
end CertifiedHighPrecisionPi
end Height100Module37
section Height100Module38
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option exponentiation.threshold 1024
set_option Elab.async false
namespace CertifiedHighPrecisionPi
def piFloor310 : ℕ := 31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066
end CertifiedHighPrecisionPi
end Height100Module38
section Height100Module39
set_option autoImplicit false
set_option maxHeartbeats 0
namespace CertifiedFixedPoint
def scaleBox (m : ℕ) (a : Box) : Box := ⟨m*a.lo,m*a.hi⟩
end CertifiedFixedPoint
end Height100Module39
section Height100Module40
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
set_option Elab.async false
set_option exponentiation.threshold 1024
namespace CertifiedThetaPoints
open CertifiedFixedPoint CertifiedHighPrecisionPi
def piBox : Box := ⟨piFloor310,piFloor310+1⟩
def centerExpBox (i : Fin 16) : Box := repeatedSquare scale310 3 (cachedPointExp i)
def lambdaBox (i : Fin 16) (n : Fin 8) : Box :=
scaleBox ((n.val+1)^2) (mulDivBox scale310 1 piBox (centerExpBox i))
def active (i : Fin 16) (n : Fin 8) : Prop := (lambdaBox i n).lo < 800*scale310
end CertifiedThetaPoints
end Height100Module40
section Height100Module41
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
set_option Elab.async false
namespace CertifiedThetaPoints
open CertifiedFixedPoint
@[noinline] def _root_.CertifiedThetaPoints.initialCache : List (List CertifiedFixedPoint.Box) :=
[[{
lo :=
473844146330744279496607164301957160408351761179772120752036477775456373469618303852708631280963231359827706433150248949889145344286892806255419995930680932287669717627427689697853440742714224127083881534930978194151262469203660705546299664735025458460111624553896106411580494387817820545596113395119801669424,
hi :=
473844146330744279496607164301957160408351761179772120752036477775456373469618303852708631280963231359827706433150248949889145344286892806255419995930680932287669717627427689697853440742714224127083881534930978194151262469203660705546299664735025458460111624553896106411580494387817820545596113395119801679610 },
{
lo :=
5474940844810197884385452769572109293835113296188271273393108645172077236375759162496214770901536208154781164656224049295858795040835125818837444583868175210192950698864271452021261076761434339989019959093983684754413263025613372429761959793469903644174701751829502968049878343973989801743002052878116894,
hi :=
5474940844810197884385452769572109293835113296188271273393108645172077236375759162496214770901536208154781164656224049295858795040835125818837444583868175210192950698864271452021261076761434339989019959093983684754413263025613372429761959793469903644174701751829502968049878343973989801743002052878116898 },
{
lo :=
32331010834547957006994088750712714107734812710021891797899987812553642629342774718163723653149069397455685926575365593385162053764956329453461177654329985406625445948028013273806435340911484364495701029121413254575367583269016910030716111654720467676277760935191706725680062973338788987597355712,
hi :=
32331010834547957006994088750712714107734812710021891797899987812553642629342774718163723653149069397455685926575365593385162053764956329453461177654329985406625445948028013273806435340911484364495701029121413254575367583269016910030716111654720467676277760935191706725680062973338788987597355716 },
{
lo :=
97578710791874776971617276641791470733640341257005097675638869633546926575531784026769053921257996353709396103195345426570681118792506233684577574660438852876686614174386459277393114352083799586314173939743909856356345501655739092507742088833315400024791283158381492340984711877855440,
hi :=
97578710791874776971617276641791470733640341257005097675638869633546926575531784026769053921257996353709396103195345426570681118792506233684577574660438852876686614174386459277393114352083799586314173939743909856356345501655739092507742088833315400024791283158381492340984711877855444 },
{
lo :=
150517435252905675138237165858692517734806531899353369870735729979513305461539057883789398125558041599436303853325178932643893296317089905572574936184772162698193340216673988368245346148232440236473452667148917728026792166552909804592445701816670831369269835906196575998,
hi :=
150517435252905675138237165858692517734806531899353369870735729979513305461539057883789398125558041599436303853325178932643893296317089905572574936184772162698193340216673988368245346148232440236473452667148917728026792166552909804592445701816670831369269835906196576002 },
{
lo :=
118662770516904690159119526944153249275760855844465517739985325666074204950629949734779332145942027481051278354516512569151967570014334049166815678136042138527029242769550729850451181028252511894388142701128169157664170233398628406699078246945344526180,
hi :=
118662770516904690159119526944153249275760855844465517739985325666074204950629949734779332145942027481051278354516512569151967570014334049166815678136042138527029242769550729850451181028252511894388142701128169157664170233398628406699078246945344526184 },
{
lo :=
47812130825182893238677048032749160804193706754855880398160210808499094139258988186808286606362205090378320865453881015719747610462011613605899472189998032088109845840065271295131070369476155246794041522304718916181137983142607966,
hi :=
47812130825182893238677048032749160804193706754855880398160210808499094139258988186808286606362205090378320865453881015719747610462011613605899472189998032088109845840065271295131070369476155246794041522304718916181137983142607970 },
{
lo :=
9845950661754742481183052800862700554668729686639782619127085145803862424232019082130235810456418183093338252133009439548596770415459354148021989997481728678140754551193661697237321497676282872762246667986,
hi :=
9845950661754742481183052800862700554668729686639782619127085145803862424232019082130235810456418183093338252133009439548596770415459354148021989997481728678140754551193661697237321497676282872762246667990 }],
[{
lo :=
92799916089251988467107979292804641505354363240492828246897422734702471171778300715177949247343214742261819928261353657051678349866126910641498313876917725572952479254488309932612059679103549751584218021022410473927799932562809705455109516077869146352675475293371563867861593238875073767641363978675377050456,
hi :=
92799916089251988467107979292804641505354363240492828246897422734702471171778300715177949247343214742261819928261353657051678349866126910641498313876917725572952479254488309932612059679103549751584218021022410473927799932562809705455109516077869146352675475293371563867861593238875073767641363978675377052484 },
{
lo :=
6079702979204730657980097638237384071187007184008869330669446433761815759520470464826982967003235996186205888948233666755253549882517501225255720116768985337252078754256153625555304514987612136222560679709708517276355352871409348523562296414767190164367781197218325871681625722083918745190057823684582,
hi :=
6079702979204730657980097638237384071187007184008869330669446433761815759520470464826982967003235996186205888948233666755253549882517501225255720116768985337252078754256153625555304514987612136222560679709708517276355352871409348523562296414767190164367781197218325871681625722083918745190057823684586 },
{
lo :=
6473020676544801686121201508927275505598741752653973763537423448756054488883162977677354907615186630049716909593973928497412096467111553283553064283622899220384763244365611630789749968500735702392996619545397107041414235268916673662878365624923844484097507032891762750086252387680260331738,
hi :=
6473020676544801686121201508927275505598741752653973763537423448756054488883162977677354907615186630049716909593973928497412096467111553283553064283622899220384763244365611630789749968500735702392996619545397107041414235268916673662878365624923844484097507032891762750086252387680260331742 },
{
lo :=
112000891271122895427810510204264761764012153754633744601092352602413307108373837351518634368527573933907506577235315153338620324470210009114246808374008214263565909322941989975258400802599069736059054035307547650106155038843373868918418700049189694154198265498082743114188,
hi :=
112000891271122895427810510204264761764012153754633744601092352602413307108373837351518634368527573933907506577235315153338620324470210009114246808374008214263565909322941989975258400802599069736059054035307547650106155038843373868918418700049189694154198265498082743114192 },
{
lo :=
31493854429487644567695811847364435138179948400797890746943353818616606560464329619594907282921376197548479222341595392592752546959260753828586154183692323705324071129940501814297897858601970900868211198525547652784775981788659679731397651518784828650,
hi :=
31493854429487644567695811847364435138179948400797890746943353818616606560464329619594907282921376197548479222341595392592752546959260753828586154183692323705324071129940501814297897858601970900868211198525547652784775981788659679731397651518784828656 },
{
lo :=
143919620629201627254019628646937652108162272695533294143182962312025952664107728622847786470122183780738818077046697464353404144044541042957027400836332918169881762919684854204484096746676395683819139603606240435686656263260,
hi :=
143919620629201627254019628646937652108162272695533294143182962312025952664107728622847786470122183780738818077046697464353404144044541042957027400836332918169881762919684854204484096746676395683819139603606240435686656263264 },
{
lo :=
10688187108615664884276289261940982208686689271238747952526774172084948145542303594778890872277907297593687497962039592043393161530608182786630323792384657090095583090648286647866087941252551336,
hi :=
10688187108615664884276289261940982208686689271238747952526774172084948145542303594778890872277907297593687497962039592043393161530608182786630323792384657090095583090648286647866087941252551340 },
{
lo :=
12899650481215532817715707232504950553939230730363514418047448974610460439341724692440661076225250296075821774242482264759089276538677864182391845437364166308,
hi :=
12899650481215532817715707232504950553939230730363514418047448974610460439341724692440661076225250296075821774242482264759089276538677864182391845437364166312 }],
[{
lo :=
8293936210901419248224994079676730595276971485280564414751489186493253442276456790819781561268075336297304145882451154045628453858231456409664186051617399350108465140778978157677072195054933433463590001447526715829419610718661794112618573763295950166021082961736813354079740509513413262688399750448167915142,
hi :=
8293936210901419248224994079676730595276971485280564414751489186493253442276456790819781561268075336297304145882451154045628453858231456409664186051617399350108465140778978157677072195054933433463590001447526715829419610718661794112618573763295950166021082961736813354079740509513413262688399750448167915330 },
{
lo :=
292812403106194443275963622888293027320337851989270361311089998377864008265407800125895833006622276407531449844052893598707220974311006698883842706447202455281511368880116463163327603528060046638299014543176052816678317007106607465769075811849376865483126745381592971249533361748583855842510833698,
hi :=
292812403106194443275963622888293027320337851989270361311089998377864008265407800125895833006622276407531449844052893598707220974311006698883842706447202455281511368880116463163327603528060046638299014543176052816678317007106607465769075811849376865483126745381592971249533361748583855842510833702 },
{
lo :=
1112510449431841398449433560934728690475399862149262267677773153762328100116629259266056377952220157220901013148387591334321914630760217234205014511066202558965470056473377647775385549425364151517237262675432233192341336043792375624732553333766194312839873711091958294164384785114,
hi :=
1112510449431841398449433560934728690475399862149262267677773153762328100116629259266056377952220157220901013148387591334321914630760217234205014511066202558965470056473377647775385549425364151517237262675432233192341336043792375624732553333766194312839873711091958294164384785118 },
{
lo :=
454888105376322798752114513089115414686643279953272413972919297893406134343501919904503201730722599048515383715726839671237766391631875293953298042936288571372937424321284244916215558454833463976337234841195126447798583091435569054012653163913273507994968,
hi :=
454888105376322798752114513089115414686643279953272413972919297893406134343501919904503201730722599048515383715726839671237766391631875293953298042936288571372937424321284244916215558454833463976337234841195126447798583091435569054012653163913273507994972 },
{
lo :=
20016627850529840044791515630814881824572904441383947183667310672672689445194733710176786926971064136103194831134687906548881072345465808177327359804902584785933183684522366929074842914135515328355193100460244092199795357562,
hi :=
20016627850529840044791515630814881824572904441383947183667310672672689445194733710176786926971064136103194831134687906548881072345465808177327359804902584785933183684522366929074842914135515328355193100460244092199795357566 },
{
lo :=
94790126059866658931152141187115578725672691018227864761666691837405218933264607988033666123761772287023893226621351548604096573876822193131848606881008043251201708188064637217926821996,
hi :=
94790126059866658931152141187115578725672691018227864761666691837405218933264607988033666123761772287023893226621351548604096573876822193131848606881008043251201708188064637217926822000 },
{
lo :=
48308231498088755468428275195728109791445640609145316827135952877714517975068669983529422298753559995076242365171585488899542759545739832684,
hi :=
48308231498088755468428275195728109791445640609145316827135952877714517975068669983529422298753559995076242365171585488899542759545739832690 },
{ lo := 2649506741004712598618360657479538096447732437461193502203741675372160908904703311177516,
hi := 2649506741004712598618360657479538096447732437461193502203741675372160908904703311177520 }],
[{
lo :=
236733512442725346977344004325913230814407584971953805498049193036284833151151201017918538857163557519199947616509718758175554891799128724270199631327521544624312263593800842545432523539730873569039739911300663710381171215732312792909131647212795282233244769651755018598516683774472851139964303810734622904,
hi :=
236733512442725346977344004325913230814407584971953805498049193036284833151151201017918538857163557519199947616509718758175554891799128724270199631327521544624312263593800842545432523539730873569039739911300663710381171215732312792909131647212795282233244769651755018598516683774472851139964303810734622914 },
{
lo :=
146703457600989938422897813601743231992341724832243056856784886124121490052637349624213337922203689367207178224210677524590586511715320374295559565856836035269294766194099352916979301120417752104436662891236444596194248990650578079127496835397448644351934505777851459730874600945164364617998,
hi :=
146703457600989938422897813601743231992341724832243056856784886124121490052637349624213337922203689367207178224210677524590586511715320374295559565856836035269294766194099352916979301120417752104436662891236444596194248990650578079127496835397448644351934505777851459730874600945164364618004 },
{
lo :=
6608070932320771367464525601886782580657000398923392492343291678151969129005242630506655982342440790304127249369140536391273332903051921934491337136481689627549593318729933837899302792850026445197029093024321848565894650882092098400278065375916690180783815285219648,
hi :=
6608070932320771367464525601886782580657000398923392492343291678151969129005242630506655982342440790304127249369140536391273332903051921934491337136481689627549593318729933837899302792850026445197029093024321848565894650882092098400278065375916690180783815285219654 },
{
lo :=
21635293003622168437842376274261278905749946765532951697352360526621167269656082156768501413319727599741188389144833294740484869499136576882514413797417682711511353223240672128101324742180231117480580353465367227202611343360210024,
hi :=
21635293003622168437842376274261278905749946765532951697352360526621167269656082156768501413319727599741188389144833294740484869499136576882514413797417682711511353223240672128101324742180231117480580353465367227202611343360210028 },
{
lo :=
5148783192923695065309737780338715244055328993303134194195955403479387304589367295479349508686720258083553035682318290707548376873939163679484297839694295206165705499344428674068705878,
hi :=
5148783192923695065309737780338715244055328993303134194195955403479387304589367295479349508686720258083553035682318290707548376873939163679484297839694295206165705499344428674068705884 },
{
lo :=
89063583874209087073550511759319736315669669786762979736359996858058265537211718114834864454694760927649241666878362927666970864,
hi :=
89063583874209087073550511759319736315669669786762979736359996858058265537211718114834864454694760927649241666878362927666970868 },
{ lo := 111982321785333492837774035806833611497241015158404039998550776,
hi := 111982321785333492837774035806833611497241015158404039998550782 },
{ lo := 0, hi := 4 }],
[{
lo :=
1283805100184978883256627694952696972851105716431523832605309795640545781786427734740550958425180803662062448964840559162674544234600496672389614606277141194322872226103070151663943693076442334188404393306897345055457179601339809784806100793404299376029959076077225252637117696457429448854360834775948664,
hi :=
1283805100184978883256627694952696972851105716431523832605309795640545781786427734740550958425180803662062448964840559162674544234600496672389614606277141194322872226103070151663943693076442334188404393306897345055457179601339809784806100793404299376029959076077225252637117696457429448854360834775948670 },
{
lo :=
95775062940298351783235864616504885421113571901497694959270253509651674114545557257571101283183915556369769793654189281462899168437677104416898655857007205336677987664220978786765919202218896170871522795009423804573110832298444024970242023981148952626274257089740699487211066418254,
hi :=
95775062940298351783235864616504885421113571901497694959270253509651674114545557257571101283183915556369769793654189281462899168437677104416898655857007205336677987664220978786765919202218896170871522795009423804573110832298444024970242023981148952626274257089740699487211066418258 },
{
lo :=
12662166745619881262084175653272131114459218276034215656350477622749148102784775681749863902367199959322781400513312551287272162332372286093055272557546143806212459954185249663708986831292021355532465509592746828693701163960578805127178314265144,
hi :=
12662166745619881262084175653272131114459218276034215656350477622749148102784775681749863902367199959322781400513312551287272162332372286093055272557546143806212459954185249663708986831292021355532465509592746828693701163960578805127178314265148 },
{
lo :=
2966646799872176259361731236534590368388501236842350204791805141619629986301718492933843532497136358975291041478009995680370400070905640213302741903982477993585079584169749936576101811281297588,
hi :=
2966646799872176259361731236534590368388501236842350204791805141619629986301718492933843532497136358975291041478009995680370400070905640213302741903982477993585079584169749936576101811281297592 },
{
lo :=
1231759418482032906811663806029772033247060444715641844842303702159547707444871356428624109300132842681211285419342212326246908,
hi :=
1231759418482032906811663806029772033247060444715641844842303702159547707444871356428624109300132842681211285419342212326246914 },
{ lo := 906333792314389529178501953148190744264741354, hi := 906333792314389529178501953148190744264741360 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
621314924662569093404257583822715381069729402013206755064720758695923846113868236673467223525696765376360954833288715047848674845880145494912440217617913289986360070503380826535887450033411392849164591807639941678258122511485149211051763339499770329663702766424369868411364219115315835242031519267132,
hi :=
621314924662569093404257583822715381069729402013206755064720758695923846113868236673467223525696765376360954833288715047848674845880145494912440217617913289986360070503380826535887450033411392849164591807639941678258122511485149211051763339499770329663702766424369868411364219115315835242031519267138 },
{
lo :=
3966047215805442876766071327474634040496958764312995360709198880643526015372435167613084363940173997656944563349239630627077232258960355170565619582068396824695681829300049373597205798501090469180462908690688416184379565305806243851548874692990217790090035718595346828,
hi :=
3966047215805442876766071327474634040496958764312995360709198880643526015372435167613084363940173997656944563349239630627077232258960355170565619582068396824695681829300049373597205798501090469180462908690688416184379565305806243851548874692990217790090035718595346834 },
{
lo :=
8711669090151855591117163945069473193017134120673803640780504083399324594780964884723926691239228224600448697138479921858513356836894374814635879681347221586242935345799817410752862207202317569545315682623215376866,
hi :=
8711669090151855591117163945069473193017134120673803640780504083399324594780964884723926691239228224600448697138479921858513356836894374814635879681347221586242935345799817410752862207202317569545315682623215376872 },
{
lo :=
6584794971395587440062163863740243153736250733419750145122497255235058829159926224983258788261671828664663322576580597176818091632417777098,
hi :=
6584794971395587440062163863740243153736250733419750145122497255235058829159926224983258788261671828664663322576580597176818091632417777104 },
{ lo := 1712697010454821707808246554944148578423192, hi := 1712697010454821707808246554944148578423196 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
8937533581061687019710310086629507284505050652603071201661535773796175837596284451828301105940750208874700299885825458180586566538164622862579078989724154021968871879408535349856840337598880445426400592797251100546128009831618627206166106015122367544406977070729504591553336729404358988170978560,
hi :=
8937533581061687019710310086629507284505050652603071201661535773796175837596284451828301105940750208874700299885825458180586566538164622862579078989724154021968871879408535349856840337598880445426400592797251100546128009831618627206166106015122367544406977070729504591553336729404358988170978566 },
{
lo :=
128184690651254090294294978050681425680573001351885172414848750677751975332754091281082547981730047235410609223050238211191762029618260319857364132425070538252160184122356694133939238056778805912807794128974732662335116759308551826915582855579290816,
hi :=
128184690651254090294294978050681425680573001351885172414848750677751975332754091281082547981730047235410609223050238211191762029618260319857364132425070538252160184122356694133939238056778805912807794128974732662335116759308551826915582855579290822 },
{
lo :=
108525954629013635413319649218702580281304514652112966165874789221423114470221749480215937003613813221752692074919431541953424325487763544024756142654476755399228817941984,
hi :=
108525954629013635413319649218702580281304514652112966165874789221423114470221749480215937003613813221752692074919431541953424325487763544024756142654476755399228817941990 },
{ lo := 5423879742319435253282943419390691589051912446345184428965664,
hi := 5423879742319435253282943419390691589051912446345184428965670 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
771768979930335292696372196109939833546303460772395089278111144178930940016097515607195070641879667693058735650927909266578367242986920474933842104375371115991092286676230260845904263407788864591351930676907384494884718651474120185681622933794413154271697215938171030183731403700770805438,
hi :=
771768979930335292696372196109939833546303460772395089278111144178930940016097515607195070641879667693058735650927909266578367242986920474933842104375371115991092286676230260845904263407788864591351930676907384494884718651474120185681622933794413154271697215938171030183731403700770805444 },
{
lo :=
5379840071031757665397807506206100961142060614064844276377616488188946458172109677923287769285859723872006673881920595831397019508806979492506610059299349791478035455044455152878023729953134642399092270623278228246037392,
hi :=
5379840071031757665397807506206100961142060614064844276377616488188946458172109677923287769285859723872006673881920595831397019508806979492506610059299349791478035455044455152878023729953134642399092270623278228246037398 },
{ lo := 13684831144030687671293932066344301116104373436096268486563387363049108791742491041314038121285546596756728,
hi :=
13684831144030687671293932066344301116104373436096268486563387363049108791742491041314038121285546596756734 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
39020717789273287260923495346233669636878407666091826374136247829696339559715865446802702149485629895000655199185168618178776354022662175244798621435105965705722473522301586955006538871589113779609755821477118316939964793053053624979363952921124055663836003066652570240931400342,
hi :=
39020717789273287260923495346233669636878407666091826374136247829696339559715865446802702149485629895000655199185168618178776354022662175244798621435105965705722473522301586955006538871589113779609755821477118316939964793053053624979363952921124055663836003066652570240931400348 },
{
lo :=
26537241899923529348113689296706643411044628475680374137405949503742148836164108179589088288319906014452585713616801648896699007624066009916366513250284519768671386371467761602236,
hi :=
26537241899923529348113689296706643411044628475680374137405949503742148836164108179589088288319906014452585713616801648896699007624066009916366513250284519768671386371467761602242 },
{ lo := 13956933160784, hi := 13956933160790 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
39075016679393794286891776648948094344523117008248944921713735939358810102200730116960353009420626340180135499697087543359255527106545780676887131441378381465489886521832909639032000291138041900488947629233042239155276049129001992488996939228910059852225184787736,
hi :=
39075016679393794286891776648948094344523117008248944921713735939358810102200730116960353009420626340180135499697087543359255527106545780676887131441378381465489886521832909639032000291138041900488947629233042239155276049129001992488996939228910059852225184787744 },
{
lo :=
20143091821975798561858068891134911636945457553346750026948880539171308121488639515783052922773694823427267367101258216,
hi :=
20143091821975798561858068891134911636945457553346750026948880539171308121488639515783052922773694823427267367101258222 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }],
[{
lo :=
5615411976885460364272111889567306060239464833680785118644837706457878813862895452219003660922110889972647248515438683168275351015001677414100497120024760801357817137856581873312917223943682200231259909607987212421853880529996185538898033164,
hi :=
5615411976885460364272111889567306060239464833680785118644837706457878813862895452219003660922110889972647248515438683168275351015001677414100497120024760801357817137856581873312917223943682200231259909607987212421853880529996185538898033172 },
{ lo := 6485009504655476790348720899336, hi := 6485009504655476790348720899342 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
89162265197335648319885559170830536040991506948950374834872369909528166755739782765273253124255403582521014288216059754892166976431453380942408041850421618893935026011249477872080652185642772727814865909632276,
hi :=
89162265197335648319885559170830536040991506948950374834872369909528166755739782765273253124255403582521014288216059754892166976431453380942408041850421618893935026011249477872080652185642772727814865909632284 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{
lo :=
4614156336366775121652137744869256842766691347875401541209735453274705736654124436530799665280623600284459332170037719811945042572639566169492653706037972751195534,
hi :=
4614156336366775121652137744869256842766691347875401541209735453274705736654124436530799665280623600284459332170037719811945042572639566169492653706037972751195542 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{ lo := 199390966102334164289432724351092125421682055424604844219735938128271923345143342430244005903000,
hi := 199390966102334164289432724351092125421682055424604844219735938128271923345143342430244005903010 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{ lo := 0, hi := 8 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }],
[{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 },
{ lo := 0, hi := 2 }, { lo := 0, hi := 2 }, { lo := 0, hi := 2 }]]
def cachedInitial (i : Fin 16) (n : Fin 8) : Box :=
(initialCache.getD i.val []).getD n.val ⟨0,0⟩
end CertifiedThetaPoints
end Height100Module41
section Height100Module42
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
namespace CertifiedThetaCandidates
open CertifiedThetaPoints CertifiedFixedPoint
end CertifiedThetaCandidates
end Height100Module42
section Height100Module43
namespace CertifiedStreamingODE
open CertifiedSignedODEConvolution
def checkSteps (bits D : Nat) : Nat → Nat → List Int → List Nat → Nat → Nat → Nat → Nat → Bool
| _,0,_,_,_,_,_,_ => true
| i,n+1,fs,ss,pp,pm,pe,pr =>
decide (((i+1:Int)*fs.headD 0*D+(pp%2^bits:Int)-(pm%2^bits:Int)).natAbs+
pe%2^bits+pr%2^bits ≤ (i+1)*ss.headD 0*D) &&
checkSteps bits D (i+1) n fs.tail ss.tail
(pp>>>bits) (pm>>>bits) (pe>>>bits) (pr>>>bits)
end CertifiedStreamingODE
end Height100Module43
section Height100Module44
set_option autoImplicit false
set_option maxHeartbeats 0
namespace CertifiedJetRecords
open CertifiedThetaCandidates CertifiedThetaPoints CertifiedFixedPoint
open CertifiedListODEVectors CertifiedPackedConvolution CertifiedStreamingODE
structure Entry where
lo : ℕ
hi : ℕ
g : ℤ
r : ℕ
f : ℤ
s : ℕ
deriving DecidableEq, Repr
def zeroEntry : Entry := ⟨0,0,0,0,0,0⟩
def offset (D p j : ℕ) : ℕ :=
if j=0 then D*(6*p+3)/64 else if j=1 then D*3/64 else 0
def entryCondition (D p limit j : ℕ) (e : Entry) : Prop :=
e.lo≤ e.hi ∧ e.g=(offset D p j:ℤ)-(e.lo:ℤ) ∧ e.hi-e.lo+1≤ e.r ∧ e.s≤ limit
instance (D p limit j : ℕ) (e : Entry) : Decidable (entryCondition D p limit j e) :=
inferInstanceAs (Decidable (_ ∧ _ ∧ _ ∧ _))
def nextCondition (j : ℕ) (a b : Entry) : Prop :=
b.lo*(16*(j+1))≤ 3*a.lo ∧ 3*a.hi≤ b.hi*(16*(j+1))
instance (j : ℕ) (a b : Entry) : Decidable (nextCondition j a b) :=
inferInstanceAs (Decidable (_ ∧ _))
def checkInputs (D p limit : ℕ) : ℕ → List Entry → Bool
| _, [] => true
| j, e::es =>
decide (entryCondition D p limit j e) &&
(match es with | [] => true | f::_ => decide (nextCondition j e f)) &&
checkInputs D p limit (j+1) es
structure Record where
entries : List Entry
pp : ℕ
pm : ℕ
pe : ℕ
pr : ℕ
deriving Repr
def bits : ℕ := 2176
def precision : ℕ := 184
def Record.gs (d : Record) : List ℤ := d.entries.map Entry.g
def Record.rs (d : Record) : List ℕ := d.entries.map Entry.r
def Record.fs (d : Record) : List ℤ := d.entries.map Entry.f
def Record.ss (d : Record) : List ℕ := d.entries.map Entry.s
def Record.ad (d : Record) : List ℕ := absDerivativeList d.gs
def Record.rd (d : Record) : List ℕ := radiusDerivativeList d.rs
def Record.fp (d : Record) : List ℕ := positiveList d.fs
def Record.fm (d : Record) : List ℕ := negativeList d.fs
def Record.fr (d : Record) : List ℕ := radiusFactorList d.fs d.ss
def lowProduct (a b : List ℕ) : ℕ :=
(encode bits a*encode bits b) % (Nat.shiftLeft 1 (bits*(precision-1)))
def initialCondition (i : Fin 16) (n : Fin 8) (d : Record) : Prop :=
d.entries.length=184 ∧
(d.entries.headD zeroEntry).lo≤ (lambdaBox i n).lo ∧
(lambdaBox i n).hi≤ (d.entries.headD zeroEntry).hi ∧
(d.entries.headD zeroEntry).f=((cachedInitial i n).lo:ℤ) ∧
(cachedInitial i n).hi-(cachedInitial i n).lo≤ (d.entries.headD zeroEntry).s
instance (i : Fin 16) (n : Fin 8) (d : Record) : Decidable (initialCondition i n d) :=
inferInstanceAs (Decidable (_ ∧ _ ∧ _ ∧ _ ∧ _))
def productCondition (d : Record) : Prop :=
d.pp=lowProduct d.ad d.fp ∧ d.pm=lowProduct d.ad d.fm ∧
d.pe=lowProduct d.ad d.ss ∧ d.pr=lowProduct d.rd d.fr
instance (d : Record) : Decidable (productCondition d) :=
inferInstanceAs (Decidable (_ ∧ _ ∧ _ ∧ _))
def carryCondition (d : Record) : Prop :=
d.ad.sum*d.fp.sum<2^bits ∧ d.ad.sum*d.fm.sum<2^bits ∧
d.ad.sum*d.ss.sum<2^bits ∧ d.rd.sum*d.fr.sum<2^bits
instance (d : Record) : Decidable (carryCondition d) :=
inferInstanceAs (Decidable (_ ∧ _ ∧ _ ∧ _))
def checkRecord (i : Fin 16) (n : Fin 8) (d : Record) : Bool :=
decide (initialCondition i n d) &&
checkInputs scale310 i.val (10^75) 0 d.entries &&
d.gs.tail.all (fun g => decide (g≤ 0)) &&
decide (carryCondition d) && decide (productCondition d) &&
checkSteps bits scale310 0 (precision-1) d.fs.tail d.ss.tail d.pp d.pm d.pe d.pr
end CertifiedJetRecords
end Height100Module44
section Height100Module45
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0
set_option Elab.async false
set_option exponentiation.threshold 20000
namespace CertifiedJetRecords
open CertifiedThetaPoints
/-- This command supplies proposed literal data only. Its correctness is established
by records_checked below, using the ordinary kernel and the complete validator. -/
def emptyRecord : Record := ⟨[],0,0,0,0⟩
def compactEntries (p : ℕ) :
ℕ → ℕ → ℕ → List ℤ → List ℕ → List Entry
| j, lo, hi, f::fs, radius::radii =>
⟨lo,hi,(offset CertifiedFixedPoint.scale310 p j : ℤ)-(lo : ℤ),
hi-lo+1,f,radius⟩ ::
compactEntries p (j+1) (3*lo/(16*(j+1))) (3*hi/(16*(j+1))+1) fs radii
| _, _, _, _, _ => []
def compactRecord (i : Fin 16) (n : Fin 8) (fs : List ℤ) (radii : List ℕ) : Record :=
let lam := CertifiedThetaPoints.lambdaBox i n
let entries := compactEntries i.val 0 lam.lo lam.hi fs radii
let d : Record := ⟨entries,0,0,0,0⟩
⟨entries,lowProduct d.ad d.fp,lowProduct d.ad d.fm,
lowProduct d.ad d.ss,lowProduct d.rd d.fr⟩
@[noinline] def pointRecord.«0».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 0 ([],[])
compactRecord (0 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 1 ([],[])
compactRecord (0 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 2 ([],[])
compactRecord (0 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 3 ([],[])
compactRecord (0 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«4» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 4 ([],[])
compactRecord (0 : Fin 16) (4 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«5» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 5 ([],[])
compactRecord (0 : Fin 16) (5 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«6» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 6 ([],[])
compactRecord (0 : Fin 16) (6 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«0».«7» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 7 ([],[])
compactRecord (0 : Fin 16) (7 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 8 ([],[])
compactRecord (1 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 9 ([],[])
compactRecord (1 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 10 ([],[])
compactRecord (1 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 11 ([],[])
compactRecord (1 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«4» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 12 ([],[])
compactRecord (1 : Fin 16) (4 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«5» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 13 ([],[])
compactRecord (1 : Fin 16) (5 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«6» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 14 ([],[])
compactRecord (1 : Fin 16) (6 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«1».«7» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 15 ([],[])
compactRecord (1 : Fin 16) (7 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 16 ([],[])
compactRecord (2 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 17 ([],[])
compactRecord (2 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 18 ([],[])
compactRecord (2 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 19 ([],[])
compactRecord (2 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«4» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 20 ([],[])
compactRecord (2 : Fin 16) (4 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«5» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataA.getD 21 ([],[])
compactRecord (2 : Fin 16) (5 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«6» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 0 ([],[])
compactRecord (2 : Fin 16) (6 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«2».«7» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 1 ([],[])
compactRecord (2 : Fin 16) (7 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 2 ([],[])
compactRecord (3 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 3 ([],[])
compactRecord (3 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 4 ([],[])
compactRecord (3 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 5 ([],[])
compactRecord (3 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«4» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 6 ([],[])
compactRecord (3 : Fin 16) (4 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«5» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 7 ([],[])
compactRecord (3 : Fin 16) (5 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«6» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 8 ([],[])
compactRecord (3 : Fin 16) (6 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«3».«7» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 9 ([],[])
compactRecord (3 : Fin 16) (7 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«4».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 10 ([],[])
compactRecord (4 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«4».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 11 ([],[])
compactRecord (4 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«4».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 12 ([],[])
compactRecord (4 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«4».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 13 ([],[])
compactRecord (4 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«4».«4» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 14 ([],[])
compactRecord (4 : Fin 16) (4 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«4».«5» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 15 ([],[])
compactRecord (4 : Fin 16) (5 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«5».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 16 ([],[])
compactRecord (5 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«5».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 17 ([],[])
compactRecord (5 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«5».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 18 ([],[])
compactRecord (5 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«5».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 19 ([],[])
compactRecord (5 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«5».«4» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 20 ([],[])
compactRecord (5 : Fin 16) (4 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«6».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 21 ([],[])
compactRecord (6 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«6».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 22 ([],[])
compactRecord (6 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«6».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 23 ([],[])
compactRecord (6 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«6».«3» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataB.getD 24 ([],[])
compactRecord (6 : Fin 16) (3 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«7».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 0 ([],[])
compactRecord (7 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«7».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 1 ([],[])
compactRecord (7 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«7».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 2 ([],[])
compactRecord (7 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«8».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 3 ([],[])
compactRecord (8 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«8».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 4 ([],[])
compactRecord (8 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«8».«2» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 5 ([],[])
compactRecord (8 : Fin 16) (2 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«9».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 6 ([],[])
compactRecord (9 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«9».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 7 ([],[])
compactRecord (9 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«10».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 8 ([],[])
compactRecord (10 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«10».«1» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 9 ([],[])
compactRecord (10 : Fin 16) (1 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«11».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 10 ([],[])
compactRecord (11 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«12».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 11 ([],[])
compactRecord (12 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«13».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 12 ([],[])
compactRecord (13 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def pointRecord.«14».«0» : Record :=
let d := _root_.TaoFivePrimes_RH14To100ThetaDataC.getD 13 ([],[])
compactRecord (14 : Fin 16) (0 : Fin 8) d.1 d.2
@[noinline] def _root_.CertifiedJetRecords.recordBank : (@_root_.List (@_root_.List (@_root_.CertifiedJetRecords.Record))) :=
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(@_root_.List.nil
(@_root_.List
(@_root_.CertifiedJetRecords.Record)))))))))))))))))))
noncomputable def recordAt (i : Fin 16) (n : Fin 8) : Record :=
(recordBank.getD i.val []).getD n.val ⟨[],0,0,0,0⟩
end CertifiedJetRecords
end Height100Module45
section Height100Module46
end Height100Module46
section Height100Module47
namespace CertifiedJetRecords
end CertifiedJetRecords
end Height100Module47
section Height100Module48
set_option autoImplicit false
namespace CertifiedJetRecords
open CertifiedFixedPoint CertifiedThetaPoints CertifiedSignedODEConvolution
open CertifiedListODEVectors CertifiedStreamingODE CertifiedIntegerExponentialJets
end CertifiedJetRecords
end Height100Module48
section Height100Module49
set_option autoImplicit false
namespace CertifiedFixedPoint
end CertifiedFixedPoint
end Height100Module49
section Height100Module50
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module50
section Height100Module51
open Finset
namespace CertifiedZetaQuadrature
set_option exponentiation.threshold 512
open CertifiedTaylorQuadrature CertifiedMomentConvolution
end CertifiedZetaQuadrature
end Height100Module51
section Height100Module52
open Finset
namespace CertifiedZetaQuadrature
open CertifiedTaylorQuadrature CertifiedMomentConvolution CertifiedExponentialJets
end CertifiedZetaQuadrature
end Height100Module52
section Height100Module53
open Finset
namespace CertifiedJetRecords
open CertifiedFixedPoint CertifiedThetaPoints CertifiedIntegerExponentialJets
open CertifiedZetaQuadrature CertifiedMomentConvolution CertifiedTaylorQuadrature
end CertifiedJetRecords
end Height100Module53
section Height100Module54
open Finset
namespace CertifiedMomentConvolution
open CertifiedTaylorQuadrature
end CertifiedMomentConvolution
end Height100Module54
section Height100Module55
open Finset
namespace CertifiedMomentConvolution
open CertifiedTaylorQuadrature
set_option exponentiation.threshold 512
end CertifiedMomentConvolution
end Height100Module55
section Height100Module56
open Finset
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module56
section Height100Module57
open Finset
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module57
section Height100Module58
namespace CertifiedZetaQuadrature
end CertifiedZetaQuadrature
end Height100Module58
section Height100Module59
open Finset
namespace CertifiedGlobalQuadrature
open CertifiedZetaQuadrature CertifiedTaylorQuadrature
end CertifiedGlobalQuadrature
end Height100Module59
section Height100Module60
open Finset
namespace CertifiedZetaQuadrature
open CertifiedMomentConvolution CertifiedTaylorQuadrature
end CertifiedZetaQuadrature
end Height100Module60
section Height100Module61
open Finset
namespace CertifiedZetaQuadrature
open CertifiedTaylorQuadrature CertifiedMomentConvolution
set_option exponentiation.threshold 1024
end CertifiedZetaQuadrature
end Height100Module61
section Height100Module62
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option exponentiation.threshold 20000
open Finset
open scoped BigOperators
namespace CertifiedGlobalJetCenters
open CertifiedJetRecords CertifiedThetaPoints CertifiedFixedPoint
open CertifiedMomentConvolution CertifiedZetaQuadrature
end CertifiedGlobalJetCenters
end Height100Module62
section Height100Module63
set_option autoImplicit false
open Finset
open scoped BigOperators
namespace CertifiedPackedCorrelation
open CertifiedSignedODEConvolution CertifiedListODEVectors CertifiedPackedConvolution
end CertifiedPackedCorrelation
end Height100Module63
section Height100Module64
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
namespace CertifiedMomentWeights
open CertifiedMomentConvolution
end CertifiedMomentWeights
end Height100Module64
section Height100Module65
namespace CertifiedExponentialIntegerSequence
end CertifiedExponentialIntegerSequence
end Height100Module65
section Height100Module66
set_option autoImplicit false
set_option maxHeartbeats 0
open Finset
open scoped BigOperators
namespace CertifiedMomentArithmetic
open CertifiedFixedPoint CertifiedExponentialIntegerSequence
open CertifiedMomentConvolution
end CertifiedMomentArithmetic
end Height100Module66
section Height100Module67
set_option autoImplicit false
namespace CertifiedPackedExtraction
open CertifiedSignedODEConvolution
end CertifiedPackedExtraction
end Height100Module67
section Height100Module68
set_option autoImplicit false
set_option maxHeartbeats 0
namespace CertifiedMomentRecords
open CertifiedGlobalJetCenters CertifiedThetaCandidates CertifiedThetaPoints
open CertifiedJetRecords CertifiedFixedPoint CertifiedPackedConvolution
open CertifiedMomentArithmetic CertifiedListODEVectors CertifiedPackedExtraction
end CertifiedMomentRecords
end Height100Module68
section Height100Module69
namespace CertifiedExponentialSequenceCheck
open CertifiedExponentialIntegerSequence
end CertifiedExponentialSequenceCheck
end Height100Module69
section Height100Module70
namespace CertifiedPackedExponentialSequence
open CertifiedPackedConvolution CertifiedExponentialSequenceCheck
end CertifiedPackedExponentialSequence
end Height100Module70
section Height100Module71
namespace CertifiedChunkedExponentialSequence
open CertifiedPackedConvolution CertifiedPackedExponentialSequence
end CertifiedChunkedExponentialSequence
end Height100Module71
section Height100Module72
namespace CertifiedChunkedEncoding
open CertifiedPackedConvolution CertifiedPackedExponentialSequence
open CertifiedChunkedExponentialSequence
end CertifiedChunkedEncoding
end Height100Module72
section Height100Module73
set_option autoImplicit false
set_option maxHeartbeats 0
namespace CertifiedMomentSequenceCache
open CertifiedMomentRecords CertifiedMomentArithmetic CertifiedPackedConvolution
open CertifiedExponentialIntegerSequence CertifiedExponentialSequenceCheck
open CertifiedChunkedEncoding CertifiedListODEVectors CertifiedPackedExtraction
end CertifiedMomentSequenceCache
end Height100Module73
section Height100Module74
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
set_option exponentiation.threshold 20000
namespace CertifiedMomentRecords
open CertifiedListODEVectors CertifiedPackedExtraction CertifiedMomentArithmetic
end CertifiedMomentRecords
end Height100Module74
section Height100Module75
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
namespace CertifiedMomentRecords
end CertifiedMomentRecords
end Height100Module75
section Height100Module76
end Height100Module76
section Height100Module77
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
namespace CertifiedLocalCandidates
end CertifiedLocalCandidates
end Height100Module77
section Height100Module78
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
set_option exponentiation.threshold 20000
namespace CertifiedGlobalTranslation
open CertifiedMomentRecords CertifiedPackedHorner CertifiedSignedODEConvolution
open CertifiedPackedExtraction CertifiedListODEVectors
end CertifiedGlobalTranslation
end Height100Module78
section Height100Module79
open Finset
namespace CertifiedPolynomialTranslation
end CertifiedPolynomialTranslation
end Height100Module79
section Height100Module80
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
set_option exponentiation.threshold 20000
namespace CertifiedTranslationConvolution
open CertifiedGlobalTranslation CertifiedPackedConvolution CertifiedListODEVectors
open CertifiedExponentialIntegerSequence CertifiedPackedExtraction
end CertifiedTranslationConvolution
end Height100Module80
section Height100Module81
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
namespace CertifiedPackedTranslation
open CertifiedTranslationConvolution CertifiedGlobalTranslation
open CertifiedPackedConvolution CertifiedPackedExtraction CertifiedExponentialIntegerSequence
end CertifiedPackedTranslation
end Height100Module81
section Height100Module82
set_option autoImplicit false
set_option maxHeartbeats 0
namespace CertifiedLiteralTranslation
open CertifiedTranslationConvolution CertifiedGlobalTranslation
open CertifiedPackedConvolution CertifiedPackedExtraction CertifiedExponentialIntegerSequence
end CertifiedLiteralTranslation
end Height100Module82
section Height100Module83
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
namespace CertifiedLiteralTranslation
end CertifiedLiteralTranslation
end Height100Module83
section Height100Module84
namespace CertifiedExponentialSequenceBound
open CertifiedExponentialSequenceCheck CertifiedPackedExponentialSequence
open CertifiedPackedConvolution
set_option maxRecDepth 100000
set_option exponentiation.threshold 8192
end CertifiedExponentialSequenceBound
end Height100Module84
section Height100Module85
set_option autoImplicit false
open Finset
namespace CertifiedPackedHorner
open CertifiedTaylorQuadrature CertifiedPolynomialTranslation
end CertifiedPackedHorner
namespace CertifiedPackedHorner
open CertifiedTaylorQuadrature
end CertifiedPackedHorner
namespace CertifiedPackedHorner
open CertifiedTaylorQuadrature
end CertifiedPackedHorner
namespace CertifiedPackedHorner
open CertifiedTaylorQuadrature CertifiedPolynomialTranslation
end CertifiedPackedHorner
end Height100Module85
section Height100Module86
set_option autoImplicit false
open Finset
namespace CertifiedTranslationAlgebra
open CertifiedPolynomialTranslation CertifiedPackedHorner CertifiedListODEVectors
open CertifiedPackedCorrelation CertifiedPackedConvolution CertifiedSignedODEConvolution
end CertifiedTranslationAlgebra
namespace CertifiedTranslationAlgebra
open CertifiedPackedConvolution CertifiedSignedODEConvolution
end CertifiedTranslationAlgebra
end Height100Module86
section Height100Module87
set_option autoImplicit false
set_option maxHeartbeats 0
open Finset
namespace CertifiedMomentRecords
open CertifiedPackedCorrelation CertifiedMomentArithmetic CertifiedMomentConvolution
open CertifiedListODEVectors CertifiedPackedExtraction CertifiedSignedODEConvolution
open CertifiedGlobalJetCenters CertifiedFixedPoint CertifiedPackedConvolution
end CertifiedMomentRecords
end Height100Module87
section Height100Module88
set_option autoImplicit false
namespace CertifiedIntegerRounding
end CertifiedIntegerRounding
end Height100Module88
section Height100Module89
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
open Finset
open scoped BigOperators
namespace CertifiedGlobalMomentEnclosure
open CertifiedMomentRecords CertifiedMomentArithmetic CertifiedGlobalJetCenters
open CertifiedZetaQuadrature CertifiedIntegerRounding
end CertifiedGlobalMomentEnclosure
end Height100Module89
section Height100Module90
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option exponentiation.threshold 20000
open Finset
namespace CertifiedGlobalTranslation
open CertifiedPackedHorner CertifiedListODEVectors CertifiedPackedExtraction
open CertifiedSignedODEConvolution CertifiedTaylorQuadrature CertifiedPolynomialTranslation
end CertifiedGlobalTranslation
end Height100Module90
section Height100Module91
set_option autoImplicit false
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option exponentiation.threshold 20000
open Finset
namespace CertifiedPackedTranslation
open CertifiedTranslationConvolution CertifiedGlobalTranslation
open CertifiedPackedConvolution CertifiedListODEVectors CertifiedPackedExtraction
open CertifiedSignedODEConvolution CertifiedTranslationAlgebra CertifiedPackedExponentialSequence
end CertifiedPackedTranslation
end Height100Module91
section Height100Module92
namespace CertifiedPackedTranslation
open CertifiedTranslationConvolution CertifiedGlobalTranslation CertifiedPolynomialTranslation
end CertifiedPackedTranslation
end Height100Module92
section Height100Module93
set_option autoImplicit false
set_option exponentiation.threshold 8192
namespace CertifiedLiteralTranslation
open CertifiedTranslationConvolution CertifiedGlobalTranslation
open CertifiedPackedConvolution CertifiedPackedExtraction
end CertifiedLiteralTranslation
end Height100Module93
section Height100Module94
set_option autoImplicit false
set_option maxHeartbeats 0
namespace TaoZetaPoly
end TaoZetaPoly
end Height100Module94
section Height100Module95
namespace CertifiedLocalPolynomial
open Finset CertifiedLocalXi
end CertifiedLocalPolynomial
end Height100Module95
section Height100Module96
namespace CertifiedIntegerLocalPolynomial
open Finset
end CertifiedIntegerLocalPolynomial
end Height100Module96
section Height100Module97
open Finset
set_option autoImplicit false
namespace TaoZetaNumerics
end TaoZetaNumerics
end Height100Module97
section Height100Module98
open Finset
set_option autoImplicit false
set_option maxHeartbeats 0
namespace TaoZetaNumerics
end TaoZetaNumerics
end Height100Module98
section Height100Module99
namespace CertifiedLocalPolynomial
open Finset TaoZetaNumerics
end CertifiedLocalPolynomial
end Height100Module99
section Height100Module100
namespace CertifiedLocalPolynomial
open Finset CertifiedLocalXi
end CertifiedLocalPolynomial
end Height100Module100
section Height100Module101
open Finset
set_option autoImplicit false
set_option maxHeartbeats 0
namespace TaoZetaNumerics
end TaoZetaNumerics
end Height100Module101
section Height100Module102
namespace CertifiedLocalBoxes
open CertifiedLocalCandidates CertifiedLocalPolynomial TaoZetaNumerics
open Finset
end CertifiedLocalBoxes
end Height100Module102
section Height100Module103
namespace CertifiedFastLocalBoxes
open CertifiedLocalBoxes CertifiedIntegerLocalPolynomial TaoZetaNumerics Finset
end CertifiedFastLocalBoxes
end Height100Module103
section Height100Module104
namespace CertifiedStreamingBernstein
open CertifiedLocalBoxes CertifiedIntegerLocalPolynomial TaoZetaNumerics Finset
end CertifiedStreamingBernstein
end Height100Module104
section Height100Module105
namespace CertifiedStreamingLocalBoxes
open CertifiedLocalBoxes CertifiedFastLocalBoxes CertifiedStreamingBernstein
open TaoZetaNumerics
end CertifiedStreamingLocalBoxes
end Height100Module105
section Height100Module106
namespace CertifiedFastLocalBoxes
open CertifiedLocalBoxes
open CertifiedLocalPolynomial CertifiedIntegerLocalPolynomial TaoZetaNumerics Finset
end CertifiedFastLocalBoxes
end Height100Module106
section Height100Module107
namespace CertifiedLocalBoxes
open CertifiedLocalCandidates CertifiedLocalPolynomial CertifiedLocalXi
end CertifiedLocalBoxes
end Height100Module107
section Height100Module108
namespace CertifiedFastLocalBoxes
open CertifiedLocalBoxes CertifiedIntegerLocalPolynomial CertifiedLocalPolynomial CertifiedLocalXi
end CertifiedFastLocalBoxes
end Height100Module108
section Height100Module109
namespace CertifiedStreamingLocalBoxes
open CertifiedLocalBoxes CertifiedFastLocalBoxes CertifiedStreamingBernstein
end CertifiedStreamingLocalBoxes
end Height100Module109
section Height100Module110
set_option maxHeartbeats 0
set_option maxRecDepth 100000
set_option Elab.async false
namespace CertifiedStreamingLocalBoxes
open CertifiedLocalBoxes
end CertifiedStreamingLocalBoxes
end Height100Module110
section Height100Module111
namespace CertifiedStreamingLocalBoxes
open CertifiedFastLocalBoxes
open CertifiedLocalBoxes CertifiedLocalPolynomial CertifiedLocalXi
end CertifiedStreamingLocalBoxes
end Height100Module111
section Height100Module112
namespace CertifiedHeight100
open CertifiedPolynomialTranslation CertifiedGlobalMoments CertifiedLocalXi
end CertifiedHeight100
end Height100Module112
section Height100Module113
set_option autoImplicit false
namespace TaoFivePrimes
end TaoFivePrimes
end Height100Module113
def TaoFivePrimes_RH14To100ThetaInterface : Nat := 14
Source
sometik179, Prove2Me submission c9908072-d99a-4431-aad8-a72c6352619a (2026-10-03), https://prove2.me/submissions/c9908072-d99a-4431-aad8-a72c6352619a. Original theta/Mellin attribution: Gabewhigham. These definitions already occur in public pilot 9fe11bf7-b735-43df-b4a3-f64c598366d3 and the published finite arithmetic interface 9b37fd72-f28f-4143-ba7e-0c2e92b04787; only dependency partitioning is changed.; ported from 0df444a definition 87fa5460-d8d5-4605-96a5-b606fe3bc5af