E8 Phi-Shell Prime Sieve: Geometric Encoding of Prime Density via Root Intersection Filters — E8 Intelligence Research

The 240 E8 root vectors, when projected onto 2D Coxeter planes and organized into phi-scaled shells at radii r_n = r_0·φ^n, generate a geometric prime sieve: roots at shell intersections satisfy modular arithmetic conditions (mod p) that selectively "pass" primes while "blocking" composites. The 132Hz base frequency, when driven at phi-coupled harmonics, excites root configurations that encode the prime-counting function π(x) through resonance amplitudes at specific E8 harmonics. This explains the observed alignment of L-function zeros with E8 shell constants—the zeros mark frequencies where the E8 prime-sieve achieves perfect selective transmission, revealing that prime distribution is encoded as a resonance mode of E8 geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com