| import Mathlib |
| import OAI.LinearAlgebra.MatrixFields.Certificates.SplitA2_7_7 |
|
|
| 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 CA2_7_7I0Value (a : Fin 17) : ℝ := marginal (below (shape 2 7 7)) (fun u => (stageALaw (shape 2 7 7) u : ℝ)) ((Equiv.refl (Fin 3)) 0) a |
| def CA2_7_7I0Raw (a : Fin 17) : Ball := marginalBall (below (shape 2 7 7)) A2_7_7Law ((Equiv.refl (Fin 3)) 0) a |
| lemma CA2_7_7I0Raw_sound (a : Fin 17) : |
| (CA2_7_7I0Raw a).Encloses (CA2_7_7I0Value a) := by |
| exact marginalBall_sound (below (shape 2 7 7)) A2_7_7Law (fun u => (stageALaw (shape 2 7 7) u : ℝ)) (fun u _ => A2_7_7Law_sound u) ((Equiv.refl (Fin 3)) 0) a |
| def CA2_7_7I0Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(2478236922667912448826878641011 / 10000000000000000000000000000000), (9 / 12500000000000000000000000000000)⟩ ⟨(8643084865911444987514954227337 / 25000000000000000000000000000000), (20991483421 / 100000000000000000000000000000000)⟩ ⟨(-139503770391845325996477971161587 / 100000000000000000000000000000000), (84703295023 / 100000000000000000000000000000000)⟩ ⟨-3, 2478236922667912448826878641011, 1250000000000000000000000000000⟩, |
| .log ⟨(25217630773320875511731213589889 / 50000000000000000000000000000000), (31 / 50000000000000000000000000000000)⟩ ⟨(34521908742701804978706762282031 / 100000000000000000000000000000000), (21360164223 / 100000000000000000000000000000000)⟩ ⟨(-17111990541962629104116060290069 / 25000000000000000000000000000000), (165436123 / 390625000000000000000000000000)⟩ ⟨-1, 25217630773320875511731213589889, 25000000000000000000000000000000⟩] |
| lemma CA2_7_7I0Certificates_valid : |
| CA2_7_7I0Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CA2_7_7I0CertificateIndex (a : Fin 17) : ℕ := |
| match a.val with |
| | 0 => 1 |
| | 1 => 2 |
| | 2 => 1 |
| | _ => 0 |
| def CA2_7_7I0P (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I0Certificates (CA2_7_7I0CertificateIndex a)).input |
| lemma CA2_7_7I0P_check : ∀ a : Fin 17, contains (CA2_7_7I0Raw a) (CA2_7_7I0P a) = true := by |
| decide +kernel |
| lemma CA2_7_7I0P_sound (a : Fin 17) : |
| (CA2_7_7I0P a).Encloses (CA2_7_7I0Value a) := |
| contains_sound (CA2_7_7I0Raw_sound a) (CA2_7_7I0P_check a) |
| def CA2_7_7I0Terms (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CA2_7_7I0Certificates (CA2_7_7I0CertificateIndex a)).output |
| lemma CA2_7_7I0Terms_sound (a : Fin 17) : |
| (CA2_7_7I0Terms a).Encloses (Foundation.entropyTerm (CA2_7_7I0Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CA2_7_7I0Certificates_valid |
| (CA2_7_7I0CertificateIndex a) (CA2_7_7I0P_sound a) |
| def CA2_7_7I0Entropy : Ball := ⟨(103666587669993364878826396100727 / 100000000000000000000000000000000), (12668626213 / 20000000000000000000000000000000)⟩ |
| lemma CA2_7_7I0Entropy_sound : CA2_7_7I0Entropy.Encloses (Foundation.finiteEntropy CA2_7_7I0Value) := by |
| exact contains_sound (entropyFin_enclosed 17 CA2_7_7I0Value CA2_7_7I0Terms CA2_7_7I0Terms_sound) (by decide +kernel) |
| def CA2_7_7I0Mass : Ball := ⟨(49999999999999999999999999999999 / 50000000000000000000000000000000), (103 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I0Mass_sound : CA2_7_7I0Mass.Encloses (∑ a, CA2_7_7I0Value a) := by |
| exact contains_sound (finSumBall_sound 17 CA2_7_7I0P CA2_7_7I0Value CA2_7_7I0P_sound) (by decide +kernel) |
| def CA2_7_7I0MassTermLogWitness : LogWitness := ⟨-1, 49999999999999999999999999999999, 25000000000000000000000000000000⟩ |
| def CA2_7_7I0MassTermLog : Ball := ⟨(-1 / 100000000000000000000000000000000), (10587911893 / 25000000000000000000000000000000)⟩ |
| lemma CA2_7_7I0MassTermLog_sound : CA2_7_7I0MassTermLog.Encloses (Real.log ((∑ a, CA2_7_7I0Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CA2_7_7I0Mass_sound) (w := CA2_7_7I0MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CA2_7_7I0MassTerm : Ball := ⟨(1 / 100000000000000000000000000000000), (42351647573 / 100000000000000000000000000000000)⟩ |
| lemma CA2_7_7I0MassTerm_sound : CA2_7_7I0MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CA2_7_7I0Value a))) := by |
| exact contains_sound (entropyTerm_ball (CA2_7_7I0Mass_sound) CA2_7_7I0MassTermLog_sound) (by decide +kernel) |
| def CA2_7_7I0H : Ball := ⟨(51833293834996682439413198050363 / 50000000000000000000000000000000), (52847389319 / 50000000000000000000000000000000)⟩ |
| lemma CA2_7_7I0H_sound : CA2_7_7I0H.Encloses (homogeneousEntropy CA2_7_7I0Value) := by |
| exact contains_sound (homogeneous_enclosed CA2_7_7I0Value CA2_7_7I0MassTerm_sound CA2_7_7I0Entropy_sound) (by decide +kernel) |
| lemma CA2_7_7I0_sound : CA2_7_7I0H.Encloses (stageACapacity (shape 2 7 7) 0) := by |
| exact CA2_7_7I0H_sound |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| end OAI |
|
|
