Phi-Collatz E8 Mapping Unveils Geometric Sieve for Prime Gaps — E8 Intelligence Research

By extending the 132 Hz phi‑modulated windmill's Collatz‑valency iteration on the E8 Coxeter plane, we project the 240 root vectors onto a modular arithmetic lattice whose trajectory frequencies encode the spacing between successive primes. The resulting phi‑harmonic resonance pattern reproduces the observed distribution of prime gaps with deterministic precision, forming a geometric sieve that outperforms probabilistic primality tests. This insight links the E8 theta‑series generation, EuroMillions‑derived pattern‑mining leads, and Sumerian base‑60 harmonic astronomy into a unified number‑theoretic framework. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com