| import Mathlib |
| import OAI.LinearAlgebra.MatrixFields.Certificates.SplitB5_1_2 |
|
|
| namespace OAI |
|
|
| namespace MatrixAllFields |
|
|
| open scoped BigOperators Topology Polynomial |
|
|
| section |
| noncomputable section |
| namespace MatrixMultiplication.NativeNumerics |
| open AllFieldParameters AllFieldHistory AllFieldCertificates AllFieldCertificates.Replay |
| open AllFieldInitialEntropyCertificate AllFieldNativeCapacity |
| open scoped BigOperators |
| def CB3_2_3I0Value (a : Fin 17) : ℝ := marginal (below (shape 3 2 3)) (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) ((stageBPriority (shape 3 2 3)) 0) a |
| def CB3_2_3I0Raw (a : Fin 17) : Ball := marginalBall (below (shape 3 2 3)) B3_2_3Law ((stageBPriority (shape 3 2 3)) 0) a |
| lemma CB3_2_3I0Raw_sound (a : Fin 17) : |
| (CB3_2_3I0Raw a).Encloses (CB3_2_3I0Value a) := by |
| exact marginalBall_sound (below (shape 3 2 3)) B3_2_3Law (fun u => (stageBLaw (shape 3 2 3) u : ℝ)) (fun u _ => B3_2_3Law_sound u) ((stageBPriority (shape 3 2 3)) 0) a |
| def CB3_2_3I0Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(660954401694675365284077503627 / 50000000000000000000000000000000), (1 / 20000000000000000000000000000000)⟩ ⟨(5718700990404566998542725209219 / 100000000000000000000000000000000), (2239400647 / 100000000000000000000000000000000)⟩ ⟨(-86521868615171017372683118901063 / 20000000000000000000000000000000), (84703294921 / 50000000000000000000000000000000)⟩ ⟨-7, 660954401694675365284077503627, 390625000000000000000000000000⟩, |
| .log ⟨(24339045598305324634715922496373 / 50000000000000000000000000000000), (53 / 100000000000000000000000000000000)⟩ ⟨(8761339994149058187289105091327 / 25000000000000000000000000000000), (483186881 / 1562500000000000000000000000000)⟩ ⟨(-71994112988219155445620039600637 / 100000000000000000000000000000000), (31763735579 / 50000000000000000000000000000000)⟩ ⟨-2, 24339045598305324634715922496373, 12500000000000000000000000000000⟩] |
| lemma CB3_2_3I0Certificates_valid : |
| CB3_2_3I0Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB3_2_3I0CertificateIndex (a : Fin 17) : ℕ := |
| match a.val with |
| | 0 => 1 |
| | 1 => 2 |
| | 2 => 2 |
| | 3 => 1 |
| | _ => 0 |
| def CB3_2_3I0P (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I0Certificates (CB3_2_3I0CertificateIndex a)).input |
| lemma CB3_2_3I0P_check : ∀ a : Fin 17, contains (CB3_2_3I0Raw a) (CB3_2_3I0P a) = true := by |
| decide +kernel |
| lemma CB3_2_3I0P_sound (a : Fin 17) : |
| (CB3_2_3I0P a).Encloses (CB3_2_3I0Value a) := |
| contains_sound (CB3_2_3I0Raw_sound a) (CB3_2_3I0P_check a) |
| def CB3_2_3I0Terms (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CB3_2_3I0Certificates (CB3_2_3I0CertificateIndex a)).output |
| lemma CB3_2_3I0Terms_sound (a : Fin 17) : |
| (CB3_2_3I0Terms a).Encloses (Foundation.entropyTerm (CB3_2_3I0Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB3_2_3I0Certificates_valid |
| (CB3_2_3I0CertificateIndex a) (CB3_2_3I0P_sound a) |
| def CB3_2_3I0Entropy : Ball := ⟨(40764060967000799747699145574527 / 50000000000000000000000000000000), (33163361031 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I0Entropy_sound : CB3_2_3I0Entropy.Encloses (Foundation.finiteEntropy CB3_2_3I0Value) := by |
| exact contains_sound (entropyFin_enclosed 17 CB3_2_3I0Value CB3_2_3I0Terms CB3_2_3I0Terms_sound) (by decide +kernel) |
| def CB3_2_3I0Mass : Ball := ⟨1, (29 / 25000000000000000000000000000000)⟩ |
| lemma CB3_2_3I0Mass_sound : CB3_2_3I0Mass.Encloses (∑ a, CB3_2_3I0Value a) := by |
| exact contains_sound (finSumBall_sound 17 CB3_2_3I0P CB3_2_3I0Value CB3_2_3I0P_sound) (by decide +kernel) |
| def CB3_2_3I0MassTermLogWitness : LogWitness := ⟨0, 1, 1⟩ |
| def CB3_2_3I0MassTermLog : Ball := ⟨0, (10587911899 / 50000000000000000000000000000000)⟩ |
| lemma CB3_2_3I0MassTermLog_sound : CB3_2_3I0MassTermLog.Encloses (Real.log ((∑ a, CB3_2_3I0Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CB3_2_3I0Mass_sound) (w := CB3_2_3I0MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB3_2_3I0MassTerm : Ball := ⟨0, (21175823799 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I0MassTerm_sound : CB3_2_3I0MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB3_2_3I0Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB3_2_3I0Mass_sound) CB3_2_3I0MassTermLog_sound) (by decide +kernel) |
| def CB3_2_3I0H : Ball := ⟨(40764060967000799747699145574527 / 50000000000000000000000000000000), (87502545861 / 100000000000000000000000000000000)⟩ |
| lemma CB3_2_3I0H_sound : CB3_2_3I0H.Encloses (homogeneousEntropy CB3_2_3I0Value) := by |
| exact contains_sound (homogeneous_enclosed CB3_2_3I0Value CB3_2_3I0MassTerm_sound CB3_2_3I0Entropy_sound) (by decide +kernel) |
| lemma CB3_2_3I0_sound : CB3_2_3I0H.Encloses (stageBCapacity (shape 3 2 3) 0) := by |
| exact CB3_2_3I0H_sound |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| end OAI |
|
|
