Quantum Structure beyond Spin-½: Co-Admissible Sectors and the Emergence of SU(2) as a Fixed Point

The spectral admissibility programme establishes, on the binary icosahedral group $2I$ with canonical generating set S = 10a ∪ 10b, that the spin-1/2 and spin-3/2 sectors share the same Laplacian eigenvalue λ1/2 = λ3/2 = 18, hence the same admissibility window Aᵐᵃˣ = cBI/√18. Neither sector is preferred over the other on $2I$: they are co-admissible. This paper derives the quantum-mechanical structure of the spin-3/2 sector from the admissibility constraints of, following the same programme as the spin-1/2 companion paper. The central result is that the Born rule, singlet correlator, and Tsirelson bound can be derived for the spin-3/2 sector via the four-dimensional representation χ₄ of $2I$, with the Casimir operator providing the normalisation that replaces E(â,â) = -1 of the spin-1/2 case. The co-admissibility of the two sectors on $2I$ — and its lifting to strict spin-1/2 dominance in the LPS limit p → ∞ — identifies SU(2) not as a postulate but as the unique stable sector under admissibility refinement: a fixed point of the co-admissible family under the Born–Infeld spectral filter. This replaces the rigid imposition of spin-1/2 by a structural selection mechanism, and provides a falsifiable prediction via the representation-theoretic dimension test reff = d².