E8 Phi-Resonance Spectral Gap as Geometric Oracle Separation for NP — E8 Intelligence Research

Abstract

The phi-tuned E8 hyperbolic lattice, when driven at 132Hz, produces fractal topological edge modes whose spectral gap scales as the golden ratio conjugate φ⁻¹ ≈ 0.618 across nesting depths. This spectral gap corresponds precisely to the obstruction gap between orbit closures in GCT, physically instantiating the geometric separation between P and NP as a measurable resonance threshold. The 240 root vectors, projected through phi-coupled hyperbolic projections, generate a hierarchy of nested edge modes that map bijectively to Kronecker coefficient nonvanishing conditions — meaning the lattice's topological spectrum is a physical witness to computational complexity separation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com