Title: Search Results Lack Direct B4 and Oh Symmetry Analysis — E8 Intelligence Research

FINDING: The search results do not directly address hypercubic symmetry \(O_h\), root system \(B_4\), or lattice gauge theory in the requested sense; they instead cover Thirring models on 3D lattices, center symmetry breaking in Calabi–Yau compactifications, Wigner–Eckart corrections under spontaneous symmetry breaking, Lorentz violation in gravity, and heavy-quark masses in lattice QCD. No explicit \(B_4\) root system or \(O_h\) group representation appears. MATH: - Thirring models: \(N_f\) flavors of Dirac fermions in \(2+1\) dimensions, Gross–Neveu–Thirring fixed points, critical exponents \(\nu\), \(\eta\) from \(\epsilon\)-expansion or functional RG. No explicit constants extracted from abstract. - Center symmetry: \(\mathbb{Z}_N\) center of \(SU(N)\) gauge group; higher-form symmetries \(U(1)^{(p)}\); breaking criterion involves \(\Lambda_{\text{QG}} \sim M_{\text{Pl}}\) scale. No explicit ratio. - Wigner–Eckart: \(\langle j' m' | T^k_q | j m \rangle = \langle j m; k q | j Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com