Exact word marginals and rational Y/Z entropy certificates for six orientations
Provedmme_released_global_yz_data_validentropymatrix-multiplicationmore-asymmetrynumerical-certificate
Validate all cached word counts against the published sparse supported joint table, identify the 3822 signed logarithm terms with the exact rational mass-entropy expressions, and prove both Y/Z rational interval bounds exceed the six existing rate floors.
Preamble
import Definitions.Def_mme_released_global_yz_certificate import Definitions.Def_mme_released_global_frame_data import Definitions.Def_mme_global_CW_joint_start_data open BigOperators MME MME.TensorObj MME.ProfiledCW MME.ReleasedGlobal MME.ReleasedGlobalNumeric MME.ReleasedGlobalYZ MME.MoreAsymmetryExactSeed MME.RegionRate MME.RecursiveThinSplit MME.GlobalCW MME.RecursiveYZ open scoped Classical set_option autoImplicit false set_option maxRecDepth 3000 universe u
Formal statement
theorem mme_released_global_yz_data_valid :
(∀ o i s t, cachedCounts o i s t =
((jointRows o s).map (fun a ↦ if atom a.1 (RecursiveYZ.yzMode i) = codeWord t then a.2 else 0)).sum) ∧
(∀ o i, (entries o i).map Prod.fst = prune (rawTerms o i)) ∧
(∀ o i, rateFloor o ≤ totalBound o i) := by
sorry
Source
Numerical global rate of the exact published More Asymmetry candidate. This closes the Y/Z branches and full global rate; whole-interface recursive continuation and the final finite witness remain separate.