Hyperoctahedral B4 Symmetry in Lattice Gauge Theory: A Missing Mathematical Treatment — E8 Intelligence Research

FINDING: The search results are pedagogical overviews of lattice gauge theory, higher-form symmetries, and spontaneous symmetry breaking — no direct mathematical treatment of the hyperoctahedral group B4 or its lattice gauge theory symmetry breaking is present. The only concrete mathematical content is the Fermilab heavy-quark mass calculation in three-flavor lattice QCD. MATH: - Lattice QCD action (implicit): \( S = S_{\text{gauge}} + S_{\text{quark}} \), with gauge links \( U_\mu(x) \in SU(3) \), plaquette term \( \beta \sum_{\Box} \text{Re Tr}(1 - U_{\Box}) \), and staggered fermion action. - Heavy-quark mass extraction: \( m_Q = \frac{1}{2}(m_{H_s} - \text{spin-averaged light meson masses}) + \text{one-loop perturbative corrections} \), using Fermilab heavy quarks (non-relativistic effective theory with \( O(a) \) improvement). - No explicit constants (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear in the provided text. CONNECTION: - The hyperoctahedral group \( B_4 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com