E0 / E1 · EXACT + MACHINE VERIFICATION · Product-map theorem plus deterministic finite-dimensional reconstruction; no hardware or physical realization claim.

Newton–Mean × E47 Product-Kernel Invariant

MC-E47-NEWTON-MEAN-PRODUCT-20260930-001 · 24/24 PASS

Invariant

Fix(F_NM) = {z*} × E47

D F_NM ~ 0 ⊕ τ ⊕ I₄₇ ⊕ Γ*|₇₈

r_joint = max(|τ|,15/17), with rate-resonance surface |τ|=15/17.

Deterministic witness

For (a,b,κ)=(4,9,0.5), τ=0.509893953950370 while 15/17=0.882352941176471. The E47 complement is therefore the asymptotic bottleneck for this witness.

CheckResidual/value
rank P / Q47 / 78
scalar quadratic identity1.110e-16
product fixed map3.508e-16
product kernel1.635e-13
Kraus completeness1.332e-14
trace1.112e-16
E47-state invariance1.587e-15

Quantum simulation boundary

The finite-dimensional simulation validates the CPTP block-dephasing channel D_P(ρ)=PρP+QρQ. It is not a quantum-hardware execution and does not assert that the nonlinear Newton map is a physical quantum channel.

Certificate JSON · Proof · Python