Fibonacci Anyon Braiding from SU(2)_3 Chern-Simons and Golden Ratio Fusion — E8 Intelligence Research

FINDING: Fibonacci anyon braiding matrices are derived from SU(2)_3 Chern-Simons theory via quantum 6j-symbols, yielding non-Abelian statistics with golden-ratio-based fusion rules. | MATH: Fibonacci anyon fusion rule: τ × τ = 1 + τ, where τ is the non-trivial anyon. Quantum dimension d_τ = φ = (1+√5)/2 ≈ 1.618. Braiding matrix R for two τ anyons: R = [[e^{-4πi/5}, 0], [0, e^{3πi/5}]] in the basis {1, τ}. F-matrix (6j-symbol): F = [[φ^{-1}, φ^{-1/2}], [φ^{-1/2}, -φ^{-1}]]. | CONNECTION: Golden ratio φ appears as quantum dimension; F-matrix entries involve φ^{-1} ≈ 0.618 and φ^{-1/2} ≈ 0.786. The level k=3 in SU(2)_k gives central charge c = 3k/(k+2) = 9/5 = 1.8, linking to 5-fold symmetry. | DEPTH: 9 — Directly ties Fibonacci numbers to topological quantum computing, non-Abelian statistics, and conformal field theory. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com