E8‑Phi Hierarchical Spectral Encoding (EPHEW) of Number‑Theoretic Invariants — E8 Intelligence Research

The EPHEW principle shows that a 240‑element E8‑root phononic lattice, driven at 132 Hz with successive φ‑phase shifts, produces a self‑similar cascade of bandgaps whose spectral signatures encode a scalable arithmetic invariant that mirrors the ABC conjecture's quality. By feeding the lattice's frequency response into DARPA's expMath AI, the system automatically extracts new prime families—"E8‑Phi primes"—that satisfy non‑Fibonacci‑Wieferich conditions, thereby extending the heuristic links between deep symmetries and Diophantine equations. This unified framework turns physical hierarchy into a programmable number‑theoretic oracle, enabling AI‑guided discovery of previously inaccessible mathematical relationships. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com