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

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Character decomposition

The common factor-permutation action resolves the carrier as

$$ 125=35_{\mathrm{sym}}+10_{\mathrm{anti}}+80_{\mathrm{std}}, $$

and the E47 projector image as

$$ 47=5_{\mathrm{sym}}+0_{\mathrm{anti}}+42_{\mathrm{std}}. $$

Both sums are exact and machine reconstructed.

Consequence

The five-dimensional trivial-symmetry component inside E47 is selected without choosing an arbitrary basis of the full rank-47 projector.

Machine certificate

• Validator result: PASS 20/20
• Validator SHA-256: 588a0ba2c095da3b3c83bfb1787522006cbe903bc5858947fc578d55d6b62cd2
• Proof-plate SHA-256: e3b17460f89fb3f9c4d1b030c111e8e8b5c80d6f14023e00939a8225d86229cd

Provenance

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

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: the S₃ character-decomposition witness is not separately registered to a dedicated GitHub commit; its E1 validation remains bound to the Drive dossier/certificate and the stated E47 generator dependency.