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Exact finite layer: $\dim V=125$, $\dim\ker[(C-6I)(C-30I)]=47$, $P_{47}^2=P_{47}=P_{47}^\dagger$, and $KP_{47}=0$. A regenerated generic-basis witness gives projector, conjugation, and finite AQSFT product-kernel residuals at floating-point scale.
Cryptographic boundary: a public concrete spectral operator yields its selected projector and kernel in polynomial time; a fixed public E47/ISSR instance is not a hardness assumption. The finite proof therefore does not imply post-quantum secrecy.
Conditional hybrid route: ML-KEM/MLWE may establish a secret seed $\sigma$ that derives a unitary $U_\sigma$; E47 then acts only as a keyed transform/filter. Any confidentiality theorem is carried by the stated ML-KEM/KDF/AEAD reduction, with protocol and implementation obligations remaining open.
Canonical monograph: E47–AQSFT Spectral Cryptography — Multi-Silo Reconciliation Monograph.
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PROVENANCE RECONCILIATION · refreshed 2026-08-19
Current GitHub authority: generator 10667959 · controlled release da5501b. Historical finite-core witness: ad297e1. Certificate-era Google Drive proof: finite E47 spectral-kernel proof.
The attached validator remains a certificate witness rather than a byte-for-byte statement about the current controlled release. Its finite results retain their certified scope; the continuum audit remains conditional and does not inherit E0/E1 authority from the finite core.
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CERTIFICATE STATE · 2026-08-07
37 PASS · 10 FORMAL REVISIONS · 8 CONSTITUTIVE REQUIREMENTS · 0 FAIL
Deterministic seed: 470125 · Carrier: 125 × 125 · Invariant rank: 47
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The executable certificate establishes the finite-dimensional E47 spectral selector, polynomial projector, optimal Richardson extraction, exact contraction rate, and perturbation-stability bound. It simultaneously audits the continuum field-actuation extension and keeps every uninstantiated constitutive, numerical, and experimental claim outside the exact certificate.
Machine verdict: Finite-dimensional spectral and contraction core validated; continuum extension requires the listed formal revisions and model data.
37 PASS
E0 identities and E1 deterministic NumPy witnesses.
10 REQUIRED
Typing, sign, domain, finite-iteration, and evidence corrections.
8 REQUIRED
Source laws, field data, PDE solutions, and experimental closure.
$$ \mathcal H=V_2^{\otimes3}\cong\mathbb C^{125}, \qquad C=C^\dagger $$
$$ \operatorname{spec}(C)=\{0,2,6,12,20,30,42\}, \qquad (m_0,m_2,m_6,m_{12},m_{20},m_{30},m_{42}) =(1,9,25,28,27,22,13) $$
$$ \sum_\lambda m_\lambda=125, \qquad C=\sum_\lambda\lambda Q_\lambda, \qquad Q_\lambda Q_\mu=\delta_{\lambda\mu}Q_\lambda, \qquad \sum_\lambda Q_\lambda=I $$
$$ \mu=\frac{\operatorname{Tr}C}{125}=18, \qquad \sigma^2=\frac{\operatorname{Tr}(C-\mu I)^2}{125}=144, \qquad \sigma=12 $$
$$ K=(C-6I)(C-30I)=K^\dagger, \qquad \ker K=E_6\oplus E_{30}\equiv E_{47} $$
$$ \dim E_{47}=25+22=47, \qquad \Omega_c=\frac{47}{125}=0.376=0;22,33,36_{60} $$
$$ P_6=\prod_{\lambda\ne6}\frac{C-\lambda I}{6-\lambda}, \qquad P_{30}=\prod_{\lambda\ne30}\frac{C-\lambda I}{30-\lambda}, \qquad P_{47}=P_6+P_{30} $$
$$ P_{47}^2=P_{47}, \qquad P_{47}^\dagger=P_{47}, \qquad KP_{47}=P_{47}K=0 $$
$$ H=I-P_{47}, \qquad H^2=H, \qquad P_{47}H=HP_{47}=0, \qquad \mathcal H=E_{47}\oplus E_{47}^{\perp} $$