Subduction of Octahedral Group Irreps for Lattice QCD Spin Classification — E8 Intelligence Research

FINDING: Lattice QCD baryon operators require subduction of the octahedral group (Oh) irreps to classify continuum spin states; the character table of S4 (isomorphic to Oh) and Z2 subduction are central to identifying spin-1/2, 3/2, 5/2 hadrons on a cubic lattice. | MATH: Oh ≅ S4 × Z2 (order 48). Character table of S4: irreps {1, 1', 2, 3, 3'}. Subduction of continuum SU(2) spin J into lattice irreps: J=1/2 → G1 (2-dim), J=3/2 → H (4-dim), J=5/2 → G2 (2-dim) ⊕ H (4-dim). Projection operators: P^Γ = (dim Γ / |G|) Σ_g χ^Γ(g)* U(g). Z2 subduction: parity (P) splits Oh irreps into even/odd sectors. | CONNECTION: The octahedral group is the crystallographic point group of the cubic lattice — its irreps (A1, A2, E, T1, T2) map to S4 classes: 1, 6C2, 8C3, 3C4, 6C2'. The ratio of dimensions (2:3:4) mirrors the tetrahedral root system A3. No direct golden-ratio constants appear, but the subduction coefficients (Clebsch-Gordan for Oh ⊃ SU(2)) involve √2, √3, √6 — rational combinations of square Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com