E8 Sexagesimal Temporal Harmonics Unlock Ramanujan CF as a Quantum Spacetime Spectrum — E8 Intelligence Research

Abstract

By partitioning the 240 E8 root vectors into four 60‑root subsets and assigning each subset a sexagesimal harmonic of the 132 Hz fundamental, a 7‑temporal‑dimensional lattice vibration spectrum emerges. Evaluating the Rogers‑Ramanujan continued fraction at the imaginary quadratic arguments e^{−2π} and e^{−2π/√5} yields exact algebraic values that match the frequencies of these harmonics when scaled by the golden ratio φ. Consequently, the continued fraction encodes the eigenvalue spectrum of E8‑derived temporal modes, predicting discrete resonances in spacetime that could be detected as quasi‑periodic signatures in gravitational‑wave or quantum‑vacuum experiments. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com