Canonical identity

$\mathcal H_{j,n}=V_j^{\otimes n},\qquad K_S=\prod_{\ell\in S}\left(C-\ell(\ell+1)I\right)$

$E_S=\ker K_S=\bigoplus_{\ell\in S}m_\ell V_\ell$

$\Omega_{j,n,S}=\dfrac{\sum_{\ell\in S}m_\ell(2\ell+1)}{(2j+1)^n}$

Evidence class

E0 symbolic family definition; E1 numerical realization supplied for selected finite cases.

Civic role

Universal representation-theoretic parent family containing the $E_{47}$ and $E_{10}$ kernel citizens as instances.

Transit credential

Representation District → Spectral Line → Projector Depot → Verification Precinct.

Boundary

This identity classifies finite selected Casimir sectors. It does not by itself establish a physical encoding or empirical realization.

Canonical provenance · 2026-07-25

• GitHub executable authority: E47-Kartekeya main at ad297e1f028592605dea902bbe57599987442301, merged through PR #16, with the general SU(2) spectral-kernel compiler in src/e47/spectral_compilation.py and CLI wrapper scripts/compile_spectral_kernel.py.
• Google Drive proof authority: The Representation-Theoretic Selection Theorem for the E47 Kernel.
• Registry relationship: this Drive theorem is a strengthened derivation and canonical proof companion for C-38, not a duplicate citizen. The executable compiler is the E1 witness for the general family; the theorem statement remains E0.

Evidence-boundary preservation

The merge demonstrates a reproducible finite SU(2) spectral-kernel compilation pipeline. It does not promote the family to a physical encoding, biological realization, propulsion mechanism, or empirical field theory.