Double-Valued Irreps and F4 Structure in Baryon Interpolating Fields — E8 Intelligence Research

FINDING: Baryon interpolating fields classified by double-valued irreps of the octahedral group (O_h^D), subduced from SU(3) flavor × spin, with F4 root system structure emerging in the operator space. | MATH: Octahedral group O_h order 48; double group O_h^D order 96. Irrep subduction: SU(3)_flavor ⊗ SU(2)_spin → O_h^D. For baryons (qqq), spin-1/2 and spin-3/2 fields decompose as: 8 ⊗ 2 = 6 ⊕ 2 (octet), 10 ⊗ 4 = 8 ⊕ 4 (decuplet) under O_h^D. Clebsch-Gordan coefficients constructed explicitly for each lattice irrep (G1g, G1u, G2g, G2u, Hg, Hu, etc.). F4 root system: 48 roots, Weyl group order 1152; its maximal subgroup chain F4 ⊃ B4 ⊃ O_h provides the natural subduction ladder for lattice operators. | CONNECTION: The octahedral group O_h is the hyperoctahedral group B3 (order 48), and its double cover relates to the F4 root system via the 24-cell (F4's roots are 24+24 = 48 vectors, matching O_h^D order 96 = 2×48). The ratio 48/96 = 0.5, and the subduction multiplicities (1, 2, 3, 4) fo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com