E0 / E1 · EXACT + MACHINE VERIFICATION · Finite proof statements plus deterministic recorded assertions.

E47 First-Principles Proof

Corrected Consolidated Validation

Nicholas Shane Kouns, DO · Independent computational validation: OpenAI GPT-5.6 Sol

MC-E47-FIRST-PRINCIPLES-CONSOLIDATED-20261001-001
37/37 executable assertions PASS
PASS WITH EXPLICIT SCOPE BOUNDARIES

Validated core

dim H=125=47+78; Casimir multiplicities 1,9,25,28,27,22,13; rank(P)=47; rank(Q)=78; rho(Gamma*|Q)=15/17. The CPTP block-dephasing map D_P(rho)=P rho P+Q rho Q is kept distinct from the Gamma contraction.

Corrections locked

The component inventory is 90+135+47=272. The illustrated layer list 3+14+15+8+3=43 is explicitly noncanonical. Newton convergence order is 2 while its fixed-point derivative is 0. Banach uniqueness is not asserted without a proved contraction domain. The faceting volume law is identified as an assumed scalar model.

Coupled dynamics

Direct Newton × E47: 0 ⊕ I47 ⊕ Gamma78. Newton–Mean × E47: 0 ⊕ tau ⊕ I47 ⊕ Gamma78. General transverse rate: max(|tau|,15/17). For the witness (4,9,0.5), tau=0.509893953950370, hence the E47 complement controls the asymptotic rate.

Provenance

Python validator · certificate index · SHA-256 ae49806a17715c9c512cfa8067e8f1bebca6d30699f1502d188c591ab48620e2.

Boundary: finite-dimensional mathematical/numerical validation. No quantum-hardware execution or physical realization is claimed.