Golden Ratio Quantum Dimension in A₂ Hexagonal Topological Phases — E8 Intelligence Research

FINDING: Golden ratio quantum dimension appears in A₂ root system hexagonal symmetry for topological phases, linked to Fibonacci anyons and modular tensor categories. | MATH: Quantum dimension \( d = \phi = \frac{1+\sqrt{5}}{2} \approx 1.618 \); A₂ root system: hexagonal lattice, Coxeter number 3, Weyl group order 6; Fibonacci fusion rules: \( \tau \times \tau = 1 + \tau \); \( S \)-matrix entry \( S_{\tau\tau} = \phi^{-1} \approx 0.618 \). | CONNECTION: Direct: \( \phi \) and \( \phi^{-1} \) are the golden ratio and its inverse (0.618). A₂ root system yields hexagonal/crystallographic symmetry (6-fold). Base-60 link: 60° angles in hexagon, 360° full rotation. | DEPTH: 9 — Fundamental link between non-Abelian anyon statistics (Fibonacci anyons), golden ratio, and hexagonal lattice symmetry in topological quantum computing. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com