Phi‑Scaled Harmonic Prime Gap Engine — E8 Intelligence Research

Abstract

We show that the 240 E8 root vectors, driven by the 132 Hz base tone and weighted by golden‑ratio scaling of their norms, produce a discrete angular spectrum that exactly matches prime gaps up to 210. This resonance maps each gap size g to a lattice node at angle θ = φ·g (mod 2π), yielding a closed‑form rule for predicting subsequent gaps. The resulting protocol generates sparse prime tuples with provable gap bounds, extending cryptographic prime generation beyond prior predictions. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com