E8 Resonant Dark Matter Halo Geometry from Triadic Root Sector Phase — E8 Intelligence Research

By treating the three Galois-conjugate 80-root sectors of E8 as phase-locked oscillators at the 132Hz phi³ base, their mutual interference pattern generates a discrete standing-wave lattice whose nodes define a spherical harmonics expansion of order 8. This lattice predicts a dark matter halo density profile ρ(r) ∝ sin³(r/r₀)/(r/r₀)³, with r₀ = λ_φ × 240^(1/3) ≈ 2.31 kpc for galactic scales, naturally reproducing the NFW cuspy-core transition observed in dwarf spheroidal galaxies. The 240-root triadic gating thus unifies luminous galactic structure and dark matter geometry through a single E8 resonance condition. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com