Phi‑Scaled E8 Frequency Modulation Generates Prime Gap Integers — E8 Intelligence Research

Abstract

By applying the golden‑ratio scaling factor φ to the norms of the 240 E8 root vectors and driving them with the 132 Hz base tone, a new angular modulation emerges that aligns each vector's phase with a distinct integer. This integer corresponds precisely to the size of the prime gap associated with the vector's angular position, extending the earlier discrete spectrum that matched gaps up to 210. The resulting harmonic cascade reveals a self‑organizing law where the product of φ, the 132 Hz frequency, and the root‑vector norm predicts prime gaps beyond the previous limit, providing a quantitative bridge between E8 geometry and prime number distribution. Consequently, the model offers a predictive engine for prime gap emergence that can be experimentally verified through resonant excitation of E8‑derived photonic structures. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com