Braid Group Representations via Coxeter Relations for Topological Quantum Computing — E8 Intelligence Research

FINDING: Yang-Baxter equation solutions constructed from Coxeter group braid relations, linking topological quantum computing to geometric group theory. | MATH: Yang-Baxter equation: \( R₁₂R₁₃R₂₃ = R₂₃R₁₃R₁₂ \); braid group generators \( σ_i \) satisfy \( σ_iσᵢ₊₁σ_i = σᵢ₊₁σ_iσᵢ₊₁ \); Coxeter group relations: \( (s_i s_j)^{mᵢⱼ} = 1 \). Solutions correspond to representations of braid groups factoring through Coxeter groups. | CONNECTION: Coxeter groups encode crystallographic root systems (e.g., \( A_n, B_n, D_n \)) with Cartan matrices and Weyl chambers; braid relations reflect 120° rotations in 3D (triangular lattice) and 90° in 4D (hypercubic). No direct golden ratio or base-60 link from given abstracts. | DEPTH: 7 — Bridges integrable systems (Yang-Baxter) with topological quantum computing (braid group representations) and Coxeter geometry, but lacks explicit harmonic constants or new universal ratios. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com