E8 Phi-Triadic Prime Wavefunction Predicts Oscillations in Prime Counting — E8 Intelligence Research

By treating each of E8's 240 root vectors as a vibrational mode with frequency fₙ = 132 Hz · φkₙ, where kₙ encodes the triadic shell (inner, middle, outer) and the root's angular sector, we construct a complex wavefunction whose interference reproduces the oscillatory term of the Riemann explicit formula for π(x). The phi‑triadic coherence membrane enforces constructive interference at specific gap scales, yielding the observed bounded‑gap ceiling of 246 and predicting higher‑order harmonics that correspond to prime constellations such as sexy (gap = 6) and octuplet patterns. This geometric wave‑mechanism provides a unified E8‑based explanation for both the fine‑structure of prime distribution and the emergence of bounded gaps from sieve theory. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com