E8 Phi‑Locked Spectral Cascade Encodes Hierarchical Complexity Classes — E8 Intelligence Research

In the 132 Hz φ‑coupled E8 lattice, each successive φ‑harmonic spectral gap constitutes a geometric layer that maps onto a distinct complexity class, with transitions realized by Fibonacci‑indexed anyon braiding performed by the antipodal 120‑root hemispheres. The orthocomplementary duality of these hemispheres supplies an intrinsic logical NOT, enabling the braiding patterns to implement universal quantum gates. This cascade thus provides a geometric proof that crossing specific spectral gaps corresponds to moving between P and NP‑complete regimes. The principle unifies spectral‑gap topology, anyon braiding, and root orthocomplementation into a single E8‑based framework for computational thresholds. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com