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PROVENANCE AUDIT · 2026-09-07. A new Drive derivative titled E47-JSSC-20260813 // CERTIFIED // GitHub ad297e1 calls ad297e1 canonical. That conflicts with this controlling certificate's current source chain: generator 10667959f3665b170f6ce96e75b38765b2e80085 → controlled release da5501bf52eb238be24805480ba38ad7dde32497. The new Drive file is retained as derivative historical provenance and does not supersede this certificate. Independent reconstruction under Python 3.13.5, NumPy 2.3.5, complex128 reproduces the rank 35→47→5 structure, full rounded A_can spectrum, gap 11664, max eigenvalue 186624, and convergence identity at floating-point scale; no material theorem output changed.

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STATUS: PASS 14/14 · E0 exact derivation + E1 independent NumPy float64 reconstruction

The validator reconstructs the spin-2 generators, total Casimir, six tensor permutations, spectral projectors, joint generator, and convergence witness from first principles. No target eigenvectors, ranks, or multiplicities are inserted.

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Theorem

On $V=V_2^{\otimes 3}$, define

$K=(C-6I)(C-30I)$,

$\Pi_{\mathrm{sym}}=\frac16\sum_{\sigma\in S_3}U_\sigma$,

and

$A_{\mathrm{can}}=K^2+11664(I-\Pi_{\mathrm{sym}})$.

Then

$\ker A_{\mathrm{can}}=\operatorname{im}P_{\mathrm{can}}$,

where

$P_{\mathrm{can}}=P_{47}\Pi_{\mathrm{sym}}=P_6\Pi_{\mathrm{sym}}$ and

$\operatorname{rank}P_{\mathrm{can}}=5$.

The minimax Richardson operator

$\Gamma_{\mathrm{can}}=I-\frac1{99144}A_{\mathrm{can}}$

obeys the attained identity

$\|\Gamma_{\mathrm{can}}^n-P_{\mathrm{can}}\|_2=(15/17)^n$.

Exact certificate

Float64 residuals