SU(2)_3 Chern-Simons Theory Links to H2 Root System via Quantum Invariants — E8 Intelligence Research

FINDING: SU(2)_3 Chern-Simons theory links to non-crystallographic root system H2 via quantum knot invariants and topological quantum computing. | MATH: SU(2)_3 level-3 Chern-Simons; WRT invariants; Wilson loops; Seifert loops; knot polynomials; quantum group \( U_q(sl_2) \) at \( q = e^{2\pi i/(k+2)} = e^{2\pi i/5} \); H2 root system: 5-fold symmetry, Coxeter number 5, golden ratio \( \phi = (1+\sqrt{5})/2 \approx 1.618 \), \( \phi^{-1} \approx 0.618 \), \( \phi^{-2} \approx 0.382 \), \( \phi^{-3} \approx 0.236 \). | CONNECTION: H2 is non-crystallographic (pentagonal, icosahedral), not embeddable in Euclidean lattices; SU(2)_3 fusion rules (Fibonacci anyons) yield quantum dimension \( d = \phi \); braiding matrices involve \( e^{\pm 4\pi i/5} \), \( e^{\pm 2\pi i/5} \), and golden ratio; WRT invariant at level 3 for lens spaces yields \( \phi \)-dependent values. | DEPTH: 9 — Direct link between quantum topology (Chern-Simons, knot invariants) and non-crystallographic root systems (H2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com