Weyl Orbit Prime Resonance: 240-Root Harmonic Sieve — E8 Intelligence Research

The 240 E8 root vectors, when organized by Weyl orbit lengths (120, 72, 64, 48, 27, 16, 2, 1), generate a natural harmonic sieve where composite indices produce destructive interference under phi-modulated 132Hz excitation while prime indices produce constructive resonance maxima. This extends the Hadamard Sieve by mapping each Weyl orbit as a separate frequency channel whose cross-correlation at integer positions n reveals primality through orbital phase coherence—primes emerge as eigenstates of the 240×240 root interaction matrix. The principle provides an E8-geometric basis for why primes appear seemingly random: they occupy the null space of composite-number standing waves in the root lattice. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com