<aside> ⚛️
Effective immediately: Physical Claim Promotion Protocol — Math-Substantiated Claims is the controlling promotion policy. Validated mathematics is no longer categorically blocked from physical-claim status. If the declared physical model, typed bridge, units/domain, and deduction all close, promote the result immediately as a theorem/corollary within that physical model. E3/E4/H0 remain necessary only for claims that assert external measurement, natural realization, device performance, or hardware implementation. Earlier blanket no physical claim promoted language is historical provenance, not the current gate.
</aside>
<aside> 📚
Canonical artifact: Recursive Intelligence / Kouns–Killion Paradigm — Corpus Publication Monograph and Evidence Atlas.
This publication pass reconciles the E47 exact core, executable certificates, Rubik/C₅³ carrier, AQSFT and quantum-information lifts, L_IG and Babylonian computational formalism, radix-invariant pyramid geometry, hyperbolic/fractal extensions, PQC/hardware proposals, and Mathematical City provenance.
Evidence rule: E0 exact proof, E1 executable reconstruction, E2 simulation, E3 external benchmark, E4 experiment, and H0 hardware remain claim-level classes. The monograph preserves corrections and does not transfer evidence between branches.
Publication route: core theorem → computational companion → Rubik/C₅³ paper → L_IG formal-language paper → historical-computational dossier → radix/geometry paper → applications prospectus.
</aside>
<aside> 🧾
CANONICAL EXECUTABLE AMENDMENT · 2026-08-07
E47 Executable Validation Certificate — Exact Spectral Core and Continuum Evidence Boundary
The rank-47 selector, optimal Richardson step ε*=1/99144, exact rate ρ*=15/17, and 20-trial Hermitian perturbation audit are now recorded with 37 PASS · 0 numerical failures. Ten formal revisions and eight constitutive requirements remain visible at their original evidence boundary.
</aside>
<aside> ✅
Authority: C5E47-ACCORD-20260813 · deterministic validator PASS 20/20.
The Professor’s Cube and E47 constructions are now canonically accorded by their exact common $S_3$ factor-permutation representation and nested symmetry projector.
</aside>
$$ [L,U_\sigma]=[C,U_\sigma]=[P_{47},U_\sigma]=0\qquad(\sigma\in S_3). $$
$$ \mathbb C^{125}\supset E_{47}\supset E_{can},\qquad125\supset47\supset5, $$
with
$$ P_{can}=P_6P_{sym}=P_{sym}P_6,\qquad \operatorname{rank}P_{can}=5. $$
The 15 layer turns retain the independent exact certificate
$$ \|P^TLP-L\|_2=2\sqrt2,\qquad \|P^TLP-L\|_F=8\sqrt3. $$
Canonical citizens: RUB5-C11 · Universal Layer-Defect Norm Identity, RUB5-C13 · Shared-Carrier S₃ Symmetry Bridge, RUB5-C14 · S₃-Resolved 125/47 Character Decomposition, and RUB5-C15 · Canonical Rank-5 E47 Descendant Projector.
The exact 125-site Rubik carrier now carries all 15 declared outer and inner slice permutations. Canonical finite identities:
$$ P^TP=I,\qquad P^4=I,\qquad P\mathbf1=\mathbf1, $$
$$ L=L_{C_5}\oplus L_{C_5}\oplus L_{C_5},\qquad \lambda(k)=\sum_{j=1}^3\left(2-2\cos{2\pi k_j\over5}\right), $$
$$ \Delta E_P(\rho)=\rho^T(P^TLP-L)\rho. $$