Hexagonal Symmetry Unites QCD Baryons and Miller-Bravais Indices — E8 Intelligence Research

FINDING: Lattice QCD baryon operators are classified by SU(3) flavor-spin irreducible representations, whose weight diagrams form hexagonal lattices in root space, directly mirroring the hexagonal crystallographic index system (Miller-Bravais 4-index). | MATH: SU(3) root system: 6 roots ±(1,-1,0), ±(1,0,-1), ±(0,1,-1) in the A₂ weight lattice; baryon octet (dim 8) and decuplet (dim 10) correspond to weight diagrams with hexagonal symmetry (octet: hexagon with center; decuplet: equilateral triangle of side 3). Lattice QCD operators transform as irreps of the cubic group (48 elements) subduced from SU(3) — the hexagonal weight diagram's 6-fold symmetry is broken to 4-fold on the hypercubic lattice, requiring operator subduction via group-theoretic projection. Flavor-spin dependence: BB potentials extracted from Nambu-Bethe-Salpeter wavefunctions show channel-dependent strengths, e.g., the \(^1S_0\) and \(^3S_1\) channels split by ~20-30 MeV at physical pion mass, governed by the SU(3) Cl Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com