Hyperfine Coupling Ratio Unity in Tetrahedral Symmetry Linked to A₃ Coxeter Number — E8 Intelligence Research

Abstract

FINDING: Hyperfine coupling ratio unity in tetrahedral symmetry relates to Coxeter number of A3 root system, with antiferromagnetic spin pumping via hyperfine interaction. MATH: Coxeter number h for A₃ = 4; root system rank = 3; hyperfine coupling ratio = 1 (unity); spin current Jₛ ∝ m × ṁ; workspace width = 0.175 m (possibly scaled to symmetry group order or root length ratio). CONNECTION: Tetrahedral symmetry (order 12) is isomorphic to A₃ Coxeter group; ratio 1.0 is identity element, but geometric harmony ratios (0.382, 0.618, 0.786, 1.618, 2.618) are not directly present. However, tetrahedral symmetry links to icosahedral symmetry (order 60) via root system embeddings; base-60 appears in icosahedral group order. Crystallographic symmetry: tetrahedral point group (23) is cubic subsystem. DEPTH: 5 — The hyperfine coupling unity ratio in tetrahedral symmetry is a specific algebraic coincidence, not a universal constant. The antiferromagnetic spin pumping mechanism is a known physi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com