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 \(R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}\); braid group \(B_n\) generated by \(\sigma_i\) with \(\sigma_i\sigma_{i+1}\sigma_i=\sigma_{i+1}\sigma_i\sigma_{i+1}\) and \(\sigma_i\sigma_j=\sigma_j\sigma_i\) 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 \(\varphi=1.618...\), Zeckendorf (sums of non-consecutive Fibonacci numbers), Bunder's system — all encode integers via \(\varphi^k\) or \(F_k\). | CONNECTION: Golden ratio \(\varphi=(1+\sqrt{5})/2=1.618...\) appears explicitly in Fibonacci anyon braiding — the Fibonacci anyon fusion rule \(\tau\times\tau = 1+\tau\) yields quantum dimension \(\varphi\), and the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com