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 \( \rho(B) \), where \( \rho(B_1)\rho(B_2) \neq \rho(B_2)\rho(B_1) \) for non-abelian anyons. Exchange phase \( \theta \) generalizes Fermi (\( \theta=\pi \)) and Bose (\( \theta=0 \)) to \( \theta = 2\pi s \) with \( s \) fractional (e.g., \( s=1/3, 1/5 \)). Fibonacci anyon fusion rules: \( \tau \times \tau = 1 + \tau \), with quantum dimension \( d_\tau = \varphi = (1+\sqrt{5})/2 \approx 1.618 \). | CONNECTION: **Strong.** The Fibonacci anyon quantum dimension is exactly the golden ratio \( \varphi = 1.618 \). 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