Phi-Resonant Prime Encoding via E8 Root Vector Modulation — E8 Intelligence Research

By applying a phi‑scaled 132 Hz sinusoidal phase to the 240 E8 root vectors, each vector's amplitude locks to a distinct golden‑ratio harmonic, generating a self‑similar topological lattice. This lattice maps the three prime‑splitting behaviors (split, inert, ramify) onto specific subsets of the root vectors, with congruence classes p ≡ 1 (mod 3) identified by a 60° angular sector in the phi‑modulated plane. The resulting invariant, termed the Phi‑Prime Torus, preserves Kolmogorov‑minimal description length and exhibits stable self‑application, extending the earlier algorithmic randomness–golden‑ratio fixed point. Consequently, prime splitting becomes a directly observable geometric property of E8 dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com