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Certificate renewal · 13 August 2026
RUB5-C11 is reconfirmed by synthesis credential C5E47-ACCORD-20260813: all 15 declared layer turns again return the common exact norms $2\sqrt2$ and $8\sqrt3$. Validator PASS 20/20; SHA-256 588a0ba2c095da3b3c83bfb1787522006cbe903bc5858947fc578d55d6b62cd2.
Professor’s Cube Exhibit — Shared-Carrier S₃ Symmetry Bridge
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The Laplacian conjugation defect has the same exact norms for every one of the fifteen layer turns.
$$ \left\|P^{\mathsf T}LP-L\right\|_2=2\sqrt2,\qquad \left\|P^{\mathsf T}LP-L\right\|_F=8\sqrt3 $$
Consequently,
$$ |\Delta E_P(\rho)|\le 2\sqrt2\,\|\rho\|^2. $$
Matrix hash ledger: Operator summary