<aside> 🧾

Credential: RUB5-S3-COMMON-20260813 · Status: PASS · Evidence: E0 + E1

</aside>

Theorem

Let $V=\mathbb C^5\otimes\mathbb C^5\otimes\mathbb C^5$ and let $U_\sigma$ permute tensor factors for $\sigma\in S_3$. With $L=L_{C_5}\oplus L_{C_5}\oplus L_{C_5}$, total-spin Casimir $C$, and E47 projector $P_{47}$,

$$ [L,U_\sigma]=[C,U_\sigma]=[P_{47},U_\sigma]=0. $$

The lattice and E47 sectors therefore share one exact six-element symmetry representation on the common 125-state carrier.

Machine certificate

• Validator: professors_cube_s3_bridge_quantum_validation.py
• Result: PASS 20/20
• SHA-256: 588a0ba2c095da3b3c83bfb1787522006cbe903bc5858947fc578d55d6b62cd2

Dependencies

Professor’s Cube Exhibit — Shared-Carrier S₃ Symmetry Bridge

• Parent citizens: RUB5-C01, RUB5-C02, RUB5-C08, and the certified E47 projector family.

Typed scope

The citizen certifies the simultaneous $S_3$ action. The separately registered 15 layer turns retain their own permutation, defect, and energy-conjugation certificates.

Provenance reconciliation · 13 August 2026

• Canonical E47 generator dependency: GitHub 10667959; publication release anchor: GitHub da5501b.
• Canonical citizen proof: Professor’s Cube shared-carrier dossier.
• Direct repository status: no dedicated GitHub commit for professors_cube_s3_bridge_quantum_validation.py is registered in the current provenance chain; the finite-core GitHub dependency and Drive-hosted E1 witness remain explicitly separated.