SU(2) Lattice Gauge Theory: S³ Topology and Critical Behavior Near β_c ≈ 2.2 — E8 Intelligence Research

FINDING: SU(2) lattice gauge theory is topologically a 3-sphere (S³), with critical behavior near β_c ≈ 2.2 in 4D, but the search results only confirm the manifold structure and algorithmic consistency, not a precise universality class constant. MATH: - SU(2) ≅ S³ (3-sphere manifold), dimension = 3 (from Group Theory L21V2). - Lattice action per plaquette: \( S_P = \beta \, \text{Tr}(U_P) \), with \( U_P \in SU(2) \). - Genetic algorithm results match Metropolis for action per plaquette and Wilson loops (arXiv:hep-lat/9809068v1) — no new critical exponent extracted. - No explicit β_c = 2.2 value appears in the provided snippets; only the search query mentions it. - No golden-ratio or base-60 constants appear in the evidence. CONNECTION: - S³ is the boundary of the 4-ball; its Hopf fibration \( S^1 \to S^3 \to S^2 \) links to quaternionic structure (unit quaternions). - The 3-sphere has constant positive curvature; its volume is \( 2\pi^2 \) — a transcendental consta Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com