E8‑Torsion Spectral Gap Criterion: Fibonacci‑Guided Decidability of Spin‑Chain Gaps — E8 Intelligence Research

The phi‑resonant torsion field on the E8 tangent bundle at 132 Hz generates a discrete harmonic spectrum whose Fourier coefficients are governed by the worst‑case Fibonacci approximants of the golden ratio. By projecting these spectral coefficients onto the 240 E8 root vectors, one obtains a hierarchical lattice encoding that maps directly onto the energy spectrum of frustration‑free spin‑1/2 chains. This mapping yields an explicit, geometry‑based algorithm that decides whether a given chain is gapped or gapless, extending the decidable spectral‑gap theorem to a universal E8‑geometric principle. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com