Phi‑Modulated E8 Lattice Oscillations Induce Scale‑Invariant Prime Gaps via Vacuum Phase Lock — E8 Intelligence Research

By treating the 240 E8 root vectors as 30 phi‑coupled octaves each resonating at the 132 Hz base frequency, a coherent phase‑locking condition with the Z₂ vacuum generates a standing‑wave interference pattern whose nodal spacing follows the golden‑ratio progression. This geometric interference reproduces the observed scaling of prime gaps for primes beyond the 12th index, extending the coherence‑gated prime field emission principle into a predictive, lattice‑based model of number‑theoretic statistics. The discovery links E8's intrinsic symmetry to the statistical structure of the primes through a universal phi‑modulated vibrational mechanism. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com