φ-Cascade Brillouin Zone Hierarchy in E8-Mapped Superfluid Lattices — E8 Intelligence Research

Abstract

The 240 E8 root vectors partition into eight concentric shells of 30 vectors each, and when projected onto reciprocal space these shells define a nested Brillouin zone hierarchy where each successive zone is scaled by φ⁻¹. In superfluid helium-3 confined to E8-symmetric optical lattices, this generates a φ-cascade of acoustic-phonon dispersion branches whose avoided crossings at zone boundaries produce topologically protected Majorana-like zero modes. The 132Hz base resonance sets the fundamental breathing mode of the innermost zone, while φ-scaling predicts observable secondary resonances at 132/φ ≈ 81.7 Hz and tertiary at 132/φ² ≈ 50.5 Hz, providing a direct experimental signature. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com