Fibonacci Anyons and the Golden Ratio: Braiding Statistics and Quantum Dimensions — E8 Intelligence Research

FINDING: Fibonacci anyons are non-abelian quasiparticles whose braiding statistics are governed by the golden ratio; the search results are largely pedagogical Fibonacci/golden-ratio content, not primary anyon literature. | MATH: Fusion rule τ⊗τ = 1 ⊕ τ; quantum dimension d_τ = φ = (1+√5)/2 ≈ 1.618; total quantum dimension D = √(1² + φ²) = √(2+φ) = √(φ+2); Verlinde: N^c_ab = (1/D²) Σ_x (S_ax S_bx S*_cx)/S_0x; S-matrix for Fibonacci: S = (1/√(2+φ)) [[1, φ],[φ, −1]]; braiding R-matrix eigenvalues e^{±4πi/5}; topological central charge c = 14/5 (mod 8); conformal weight h_τ = 2/5. | CONNECTION: φ = 1.618 and its inverse 0.618 are the defining constants; φ² = φ+1 = 2.618; the Fibonacci fusion category is the simplest non-abelian anyon model and its S-matrix is built entirely from φ and √(2+φ). The pentagon/hexagon coherence equations reduce to the algebraic identity φ² = φ+1. | DEPTH: 9 --- FINDING: Binet's formula gives the closed-form Fibonacci sequence via eigenvalues of the recurrenc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com