Fibonacci Anyon Braiding: Dense SU(2) Image from Golden-Ratio Phases — E8 Intelligence Research

FINDING: Fibonacci anyons realize a braiding representation whose image in SU(2) is a dense subgroup generated by golden-ratio phases; the search results are mostly popular expositions, not primary sources. | MATH: Fibonacci anyon braid group rep: ρ: B_n → SU(2), with R-matrix eigenvalues e^{±4πi/5} (i.e. phases 2π/5, 4π/5); quantum dimension d = φ = (1+√5)/2 ≈ 1.618; total quantum dimension D = √(1+φ²) = √(2+φ) ≈ 1.902; fusion rule τ⊗τ = 1 ⊕ τ; F/R matrices entries in ℚ(√5). | CONNECTION: φ = 1.618, 1/φ = 0.618, φ² = 2.618, 1/φ² = 0.382 all appear as quantum dimensions and as squared amplitudes; the braid group image is dense in SU(2) precisely because the phase e^{4πi/5} is irrational w.r.t. π (5 is not a root of unity compatible with SU(2) closure). | DEPTH: 8 (for the underlying mathematics; the listed videos themselves are ~2–4). Precise analysis of the five results: 1. "What is the Fibonacci Sequence & the Golden Ratio?" — Popular exposition. MATH: F_n = F_{n-1}+F_{n-2}, F_0=0, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com