| import Mathlib |
| import OAI.LinearAlgebra.MatrixFields.Certificates.Terminal2_4_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 CB2_4_2I0Value (a : Fin 17) : ℝ := marginal (below (shape 2 4 2)) (fun u => (stageBLaw (shape 2 4 2) u : ℝ)) ((stageBPriority (shape 2 4 2)) 0) a |
| def CB2_4_2I0Raw (a : Fin 17) : Ball := marginalBall (below (shape 2 4 2)) B2_4_2Law ((stageBPriority (shape 2 4 2)) 0) a |
| lemma CB2_4_2I0Raw_sound (a : Fin 17) : |
| (CB2_4_2I0Raw a).Encloses (CB2_4_2I0Value a) := by |
| exact marginalBall_sound (below (shape 2 4 2)) B2_4_2Law (fun u => (stageBLaw (shape 2 4 2) u : ℝ)) (fun u _ => B2_4_2Law_sound u) ((stageBPriority (shape 2 4 2)) 0) a |
| def CB2_4_2I0Certificates : List CompactCertificate.EntropyDatum := |
| [.zero, |
| .log ⟨(18444910185167131143404389881443 / 100000000000000000000000000000000), (17 / 25000000000000000000000000000000)⟩ ⟨(15589469541528843690691167499179 / 50000000000000000000000000000000), (15623446821 / 100000000000000000000000000000000)⟩ ⟨(-169038172428353149777145115754231 / 100000000000000000000000000000000), (847032951 / 1000000000000000000000000000000)⟩ ⟨-3, 18444910185167131143404389881443, 12500000000000000000000000000000⟩, |
| .log ⟨(31555089814832868856595610118557 / 50000000000000000000000000000000), (19 / 20000000000000000000000000000000)⟩ ⟨(29048864931223719890654738023041 / 100000000000000000000000000000000), (6682050217 / 25000000000000000000000000000000)⟩ ⟨(-46028810410117948265016649511163 / 100000000000000000000000000000000), (10587911879 / 25000000000000000000000000000000)⟩ ⟨-1, 31555089814832868856595610118557, 25000000000000000000000000000000⟩] |
| lemma CB2_4_2I0Certificates_valid : |
| CB2_4_2I0Certificates.all (fun c => c.check logTwoBall) = true := by decide +kernel |
| def CB2_4_2I0CertificateIndex (a : Fin 17) : ℕ := |
| match a.val with |
| | 0 => 1 |
| | 1 => 2 |
| | 2 => 1 |
| | _ => 0 |
| def CB2_4_2I0P (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CB2_4_2I0Certificates (CB2_4_2I0CertificateIndex a)).input |
| lemma CB2_4_2I0P_check : ∀ a : Fin 17, contains (CB2_4_2I0Raw a) (CB2_4_2I0P a) = true := by |
| decide +kernel |
| lemma CB2_4_2I0P_sound (a : Fin 17) : |
| (CB2_4_2I0P a).Encloses (CB2_4_2I0Value a) := |
| contains_sound (CB2_4_2I0Raw_sound a) (CB2_4_2I0P_check a) |
| def CB2_4_2I0Terms (a : Fin 17) : Ball := |
| (CompactCertificate.entropyLookup CB2_4_2I0Certificates (CB2_4_2I0CertificateIndex a)).output |
| lemma CB2_4_2I0Terms_sound (a : Fin 17) : |
| (CB2_4_2I0Terms a).Encloses (Foundation.entropyTerm (CB2_4_2I0Value a)) := |
| CompactCertificate.entropyLookup_sound logTwoBall_sound CB2_4_2I0Certificates_valid |
| (CB2_4_2I0CertificateIndex a) (CB2_4_2I0P_sound a) |
| def CB2_4_2I0Entropy : Ball := ⟨(91406743097339094653419408019757 / 100000000000000000000000000000000), (5797509451 / 10000000000000000000000000000000)⟩ |
| lemma CB2_4_2I0Entropy_sound : CB2_4_2I0Entropy.Encloses (Foundation.finiteEntropy CB2_4_2I0Value) := by |
| exact contains_sound (entropyFin_enclosed 17 CB2_4_2I0Value CB2_4_2I0Terms CB2_4_2I0Terms_sound) (by decide +kernel) |
| def CB2_4_2I0Mass : Ball := ⟨1, (231 / 100000000000000000000000000000000)⟩ |
| lemma CB2_4_2I0Mass_sound : CB2_4_2I0Mass.Encloses (∑ a, CB2_4_2I0Value a) := by |
| exact contains_sound (finSumBall_sound 17 CB2_4_2I0P CB2_4_2I0Value CB2_4_2I0P_sound) (by decide +kernel) |
| def CB2_4_2I0MassTermLogWitness : LogWitness := ⟨0, 1, 1⟩ |
| def CB2_4_2I0MassTermLog : Ball := ⟨0, (21175823913 / 100000000000000000000000000000000)⟩ |
| lemma CB2_4_2I0MassTermLog_sound : CB2_4_2I0MassTermLog.Encloses (Real.log ((∑ a, CB2_4_2I0Value a))) := by |
| exact checkLog_sound logTwoBall_sound (CB2_4_2I0Mass_sound) (w := CB2_4_2I0MassTermLogWitness) (by |
| simp only [checkLog, Bool.and_eq_true] |
| exact ⟨by decide +kernel, by decide +kernel⟩) |
| def CB2_4_2I0MassTerm : Ball := ⟨0, (10587911957 / 50000000000000000000000000000000)⟩ |
| lemma CB2_4_2I0MassTerm_sound : CB2_4_2I0MassTerm.Encloses (Foundation.entropyTerm ((∑ a, CB2_4_2I0Value a))) := by |
| exact contains_sound (entropyTerm_ball (CB2_4_2I0Mass_sound) CB2_4_2I0MassTermLog_sound) (by decide +kernel) |
| def CB2_4_2I0H : Ball := ⟨(91406743097339094653419408019757 / 100000000000000000000000000000000), (9893864803 / 12500000000000000000000000000000)⟩ |
| lemma CB2_4_2I0H_sound : CB2_4_2I0H.Encloses (homogeneousEntropy CB2_4_2I0Value) := by |
| exact contains_sound (homogeneous_enclosed CB2_4_2I0Value CB2_4_2I0MassTerm_sound CB2_4_2I0Entropy_sound) (by decide +kernel) |
| lemma CB2_4_2I0_sound : CB2_4_2I0H.Encloses (stageBCapacity (shape 2 4 2) 0) := by |
| exact CB2_4_2I0H_sound |
|
|
| end MatrixMultiplication.NativeNumerics |
|
|
| end |
| end |
|
|
| end MatrixAllFields |
|
|
| end OAI |
|
|
