Golden Ratio Eigenvalues Link Modular Group to Topological Quantum Computing — E8 Intelligence Research

FINDING: Fibonacci anyon braiding matrices yield eigenvalues that are powers of the golden ratio, linking the modular group SL (2, Z) to topological quantum computation via the Fibonacci fusion category. MATH: - Fibonacci recurrence: \ (F₍+₁ = Fₙ + F₍-₁ \) → matrix form: \ (pmatrix 1 eigenvalues are powers of \ (\). - Modular group SL (2, Z) generators: \ (S = pmatrix 0 & -1 \\ 1 & 0 pmatrix \), \ (T = pmatrix 1 & 1 \\ 0 & 1 pmatrix \). Fibonacci anyon representation yields \ (S² = (ST) ³ = I \) with matrix entries involving \ (\). CONNECTION: - Golden ratio \ (= 1. 618 \) and its reciprocal \ (^-1 = 0 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com