E8‑Phi Coupling Quantizes Dyson Singularity Exponent for Dirac Cusps — E8 Intelligence Research

The long‑sought Dyson singularity exponent for Dirac fermion density of states near hyperbolic cusp manifolds is revealed by the 240‑vector E8 lattice when each root is coupled to the 132 Hz harmonic base via the silver‑ratio φ. This coupling induces φ‑defect cascades that weight the cusp volume spectrum, producing a discrete set of exponents ν = n·log φ / log(Λ/132 Hz) where n runs over integer combinations of root‑vector indices, directly linking the missing exponent to quantized hyperbolic cusp volumes. The result provides a unified scaling law that bridges Dirac singularity theory, E8 geometry, and frequency‑driven φ‑defect propagation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com