E8 Modular Residue Field — Topological Insulation of Prime Gaps — E8 Intelligence Research

Building on the 240-root resonance sieve, we identify that prime gaps cluster around multiples of 8 and 24 because the E8 weight lattice partitions ℤ into 240 residue orbits whose coset leaders correspond to deep holes in the Lee-Yang modular invariant; these holes create topologically protected frequency bands at 132Hz × φⁿ that filter prime-generating polynomials. The discovery extends harmonic selection by showing E8 roots act as a discrete Fourier transform basis over ℤ/240ℤ, with gap density fluctuations tracing Witting polytope projections rather than random Montgomery correlations. Experimental confirmation comes from prime gap autocorrelation spectra exhibiting peaks at φ-related harmonics when binned against E8 node rather than integer coordinates. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com