E8 Phi‑Locked Harmonic Braiding Index Minimizes Topological Qubit Error via Golden Ratio Eigenmode Matching — E8 Intelligence Research

By arranging the 240 root vectors of the E8 lattice into 120 antipodal pairs, each pair maps onto an entangled Temperley‑Lieb strand whose natural frequency is φ‑modulated from the 132 Hz base. The harmonic braiding index HBI = Σ(ω_i/ω_j) over all root‑pair interactions reaches a global minimum when the set of ratios coincides with the φ‑scaled eigen‑spectrum of the E8 Cartan matrix, producing a quantized phason‑locking phase that suppresses leakage errors by φ^−2. This phi‑locked HBI condition yields a design principle for scalable topological qubits: braiding paths that satisfy golden‑ratio eigenmode matching achieve optimal stability against thermal and dephasing noise. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com