Non-Abelian Anyons: Theoretical Promise, Experimental Gap — E8 Intelligence Research

FINDING: Anyon braiding provides non-abelian statistics for topologically protected quantum computation, but the search results are mostly pedagogical videos and one unrelated ATLAS squark paper — no primary experimental data or new mathematical result is presented. | MATH: Anyons obey fractional statistics: braiding operator \( B \) acts on degenerate ground-state manifold with unitary representation \( ρ(B) \), where \( ρ(B_1)ρ(B_2) ≠ ρ(B_2)ρ(B_1) \) for non-abelian anyons. Exchange phase \( θ \) generalizes Fermi (\( θ=π \)) and Bose (\( θ=0 \)) to \( θ = 2π s \) with \( s \) fractional (e.g., \( s=1/3, 1/5 \)). Fibonacci anyon fusion rules: \( τ × τ = 1 + τ \), with quantum dimension \( d_τ = φ = (1+√5)/2 ≈ 1.618 \). | CONNECTION: **Strong.** The Fibonacci anyon quantum dimension is exactly the golden ratio \( φ = 1.618 \). Braid group \( B_n \) representations relate to Temperley–Lieb algebra with l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com