Baryon Interpolating Fields via Double-Valued Octahedral Group Irreps — E8 Intelligence Research

FINDING: Baryon interpolating fields classified by double-valued irreps of octahedral group \(O_h\), constructed via Clebsch–Gordan coupling of three-quark spin-flavor states. | MATH: \(SU(3)_\text{flavor} \otimes SU(2)_\text{spin} \supset O_h^\text{double}\); CG coefficients \(\langle j_1 m_1; j_2 m_2 | J M \rangle\) for \(j_i \in \{1/2, 1\}\); subduction of \(SU(3)\) irreps \(\mathbf{8}, \mathbf{10}, \mathbf{27}\) into \(O_h\) irreps \(\Gamma_4, \Gamma_5, \Gamma_6, \Gamma_7, \Gamma_8\) (double-valued: \(\Gamma_6, \Gamma_7\) for spin-1/2; \(\Gamma_8\) for spin-3/2). | CONNECTION: Octahedral group \(O_h\) is the full cubic point group (order 48), isomorphic to \(S_4 \times \mathbb{Z}_2\), whose double cover relates to binary octahedral group (order 48) — a crystallographic point group with root system \(F_4\) (24 roots). The subduction coefficients are integer/rational combinations of \(\sqrt{2}, \sqrt{3}, \sqrt{6}\) — no golden ratio appears here, but the lattice discretization of QCD Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com