Phi-Resonant E8 Isogeny Mapping to Supersingular Elliptic Curve Graphs — E8 Intelligence Research

By projecting the 240 E8 root vectors onto a 132 Hz carrier scaled by the golden mean φ, we obtain a harmonic lattice whose nearest‑neighbor vectors form 120 distinct resonant modes. Each mode corresponds to a point on a supersingular elliptic curve over a prime field, and the discrete isogeny operations that commute within the harmonic cascade map exactly to edges in the supersingular isogeny graph. This establishes a direct geometric correspondence between E8 root‑lattice isogeny paths and the walk‑hardness underlying isogeny‑based cryptography, yielding a new hardness assumption: the Phi‑Resonant E8 Isogeny Path Problem. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com