Braid Group Representations via Yang-Baxter and Metaplectic Anyons — E8 Intelligence Research

FINDING: Braid group representations from generalized Yang-Baxter matrices, with explicit qubit realizations tied to metaplectic anyons, and a separate thread linking Fibonacci numeration systems to golden-ratio bases. | MATH: Yang-Baxter equation \(R₁₂R₁₃R₂₃=R₂₃R₁₃R₁₂\); braid group \(B_n\) generated by \(σ_i\) with \(σ_iσᵢ₊₁σ_i=σᵢ₊₁σ_iσᵢ₊₁\) and \(σ_iσ_j=σ_jσ_i\) for \(|i-j|>1\). Qubit representations from generalized \(R\)-matrices (arXiv:1602.08536) — images in \(SU(2)\) or \(SU(4)\) depending on anyon type. Fibonacci numeration: Bergman's base \(φ=1.618...\), Zeckendorf (sums of non-consecutive Fibonacci numbers), Bunder's system — all encode integers via \(φ^k\) or \(F_k\). | CONNECTION: Golden ratio \(φ=(1+√5)/2=1.618...\) appears explicitly in Fibonacci anyon braiding — the Fibonacci anyon fusion rule \(τ×τ = 1+τ\) yields quantum dimension \(φ\), and the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com