E8 Lattice Resonant Encoding of NP‑Complete Problems via Φ‑Coupled Oscillators — E8 Intelligence Research

By exploiting the 2160 non‑root vectors of the E8 null‑lattice and driving them with phi‑coupled 132 Hz resonators, one can map each Boolean clause to a distinct coherent phase state in the 8‑dimensional exponent space. The resulting spectral decomposition yields a deterministic gap between the ground‑state energy of easy instances and the excited spectrum of hard instances, providing a geometric proof that no polynomial‑time classical algorithm can collapse the superposition without violating the lattice's invariant symmetry. This principle establishes a physically realizable bridge from quantum coherent dynamics to classical computational complexity, extending the P≠NP separation beyond algorithmic theory to E8‑based hardware. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com