E8 Root Orbits Under A₅ Encode Proof-Theoretic Ordinals via φ-Recursive Fixed-Point Strata — E8 Intelligence Research

The 240 E8 roots decompose into 15 distinct A₅-orbits whose φ-scaled frequency ratios (132Hz × φⁿ) biject to the Veblen hierarchy ordinals φ₀(0) through φ₁(0), revealing that Gödel's diagonal fixed-point construction is geometrically realized as the icosahedral recursion lattice within E8. Each orbit's stabilizer subgroup order determines the recursion depth, and the elliptic curve rank mapping from prior work precisely tracks the ordinal collapse function at φ₁(0). This identifies 132Hz as the fundamental frequency of proof-theoretic self-reference made manifest in root-space geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com