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Corrected convergence criterion PASS. The validator now tests the theorem-bound identity $\|\Gamma^n-P\|_2\le(15/17)^n$ rather than the arbitrary cutoff $\|\Gamma^{220}-P\|_2<10^{-12}$.
At $n=220$: measured operator error 1.0998014527879737e-12, exactly matching (15/17)^220 to displayed precision. At n=600: 2.4288606920515912e-33. Rank(P)=47, Ωc=47/125, kernel fixed, complement spectral radius=15/17, runtime capture→1.
Corrected Python validator · commit e8424d9b0e8f0b7426557f38514a162c3d603b71
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135 original named checks and 27 supplemental reconstruction checks passed; 2,000 randomized Newton cases had zero stability disagreements. Python sources also compiled successfully.
E47 Python Validation — 162/162 PASS — 2026-10-02
GitHub source and continuous logs · Website · Drive archive
Supabase certificate: MC-E47-PYTHON-RERUN-20261002-001. Full sources, logs, environment, checksums and ZIP archived.
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MC-E47-FIRST-PRINCIPLES-CONSOLIDATED-20261001-001 · 37/37 executable assertions PASS WITH EXPLICIT SCOPE BOUNDARIES
Primary author/framework: Nicholas Shane Kouns, DO. Independent computational validation: OpenAI GPT-5.6 Sol.
Corrected: component inventory is 272; illustrated layer census 3+14+15+8+3=43 is explicitly noncanonical and four faces short of 47; the 15/17 contraction belongs to Γ*=I-K²/99144, not the CPTP block-dephasing channel; direct Newton×E47 has fixed manifold {√a}×E47, while Newton–Mean×E47 uses {z_*}×E47; Newton convergence order is 2 with zero first derivative; Banach uniqueness is not promoted without a proved contraction domain.
Validated reconstruction: Casimir multiplicities {0:1,2:9,6:25,12:28,20:27,30:22,42:13}; rank P=47; rank Q=78; ρ(Γ|Q)=15/17; CPTP P/Q dephasing; Newton quadratic identity; Newton–Mean witness τ=0.509893953950370; scalar faceting arithmetic; ENU house-frame rotation.
Corrected Python validator · Certificate index
Boundary: the scalar faceting law is assumed rather than coordinate-derived; the full hyperbolic certificate requires its generating data/code; the ENU frame is mathematically valid but does not itself establish a physical E47 state-to-vector map.
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MC-E47-NEWTON-MEAN-PRODUCT-20260930-001 · 24/24 PASS · E0/E1 + finite-dimensional quantum-channel simulation
Fixed manifold: $\{z_\}\times E_{47}$. Tangent split: $0\oplus\tau\oplus I_{47}\oplus\Gamma_|_{78}$. Joint transverse rate: $\max\{|\tau|,15/17\}$; rate-resonance surface: $|\tau|=15/17$.
Witness $(a,b,\kappa)=(4,9,0.5)$: $\tau=0.509893953950370$, so the E47 complement controls the asymptotic rate. Scalar quadratic residual 1.110e-16; product fixed-map residual 3.508e-16; product-kernel residual 1.635e-13.
Finite-dimensional quantum simulation validates $\mathcal D_P(\rho)=P\rho P+Q\rho Q$ as the CPTP block-dephasing completion. Certificate · Proof · Python
Boundary: no quantum-hardware execution; the nonlinear Newton map is not asserted to be a physical quantum channel.
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MC-E47-NEWTON-PRODUCT-20260930-001 · 17/17 PASS · E1
The coupled map (mathscr F_a(x,psi)=(B_a(x),Gamma_psi)) has fixed manifold ({sqrt a}times E_{47}). The tangent split is (mathbb R_{rm Newton}oplus E_{47}oplus E_{47}^{perp}) with multipliers (0oplus I_{47}oplus Gamma_|{78}). The Newton–Mean extension has joint asymptotic rate (r{rm joint}=max{|tau|,15/17}) and switching surface (|tau|=15/17).
Numerical reconstruction: rank(P)=47, rank(Q)=78, (rho(Gamma_*|_Q)=0.882352941176472). Joint fixed residual (1.635times10^{-13}); product-map residual (3.508times10^{-16}); Newton quadratic identity residual (1.110times10^{-16}). Spectral-norm-law errors through n=25 are ≤ (4.441times10^{-16}).
Quantum-channel simulation for (D_P(rho)=Prho P+Qrho Q): trace residual (1.112times10^{-16}), Hermiticity (4.257times10^{-16}), minimum eigenvalue (-2.965times10^{-16}), cross-block residual (1.288times10^{-15}), kernel-state invariance (1.587times10^{-15}).
Dedicated Notion record · GitHub PR · Drive proof + validation
Boundary: finite-dimensional numerical and density-matrix quantum-channel validation only. No laboratory or hardware realization is certified.
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MC-HLFB-RUN-B-REPRO-20260930-001 · PASS_WITH_CALIBRATION · E1
The historical HLFB-IND-20260730 record now has an immutable repository reproduction without superseding the July run. The executable checks the Poincaré metric sample, H² exponential growth, synthetic fractal exponent recovery, Kuramoto order parameter/locking, finite buoy residual, finite contraction bound for L<1, and Weyl spectral stability.
Public Pages · Python · certificate · Drive code archive · reconciliation monograph
Boundary: finite typed mathematical/numerical witness. The buoy residual is calibration, not a high-fidelity equivalence certificate.
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45/45 reported PASS · exit 0. Two first-run harness failures are preserved and repaired: Frobenius → spectral norm with $\|\Gamma^n-P_E\|_2=(15/17)^n$, and finite √5 tolerance → exact Pell identity $(m/u)^2=5-4/u^2$ plus monotonicity. The record also binds Lagrange denominators 1741824, -43545600, kernel ranks 47,1,10, and twist defect 8√3; the n=25,243 exclusions remain explicitly E1 finite searches through s≤1000.
Dedicated Notion record · GitHub formalism · machine JSON · public Pages
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E47 Neutrino Flavor Snapshot — τ = π · Pages · source
$P(\mu\to e)=0.04720552$, $P(\mu\to\mu)=0.00314068$, $P(\mu\to\tau)=0.94965381$ at $\tau=\pi$. Supplied inputs. E2.