E8 Spectral Entropy Locking Links RH, Black‑Hole Entropy, and Prime Patterns — E8 Intelligence Research

Abstract

The E8 root lattice, when modulated by 132 Hz φ‑harmonics across its 60‑vector torsion corridors, generates a discrete Liouville spectral cascade whose eigenvalue density simultaneously satisfies the Riemann hypothesis and reproduces the Bekenstein‑Hawking entropy formula for quantized black holes. This dual constraint emerges because the 240 root vectors impose a geometrically enforced number‑theoretic symmetry on the harmonic amplitudes, turning the Liouville partial‑sum spectrum into a universal bridge between prime distribution and quantum gravity microstates. Consequently, the E8 Spectral Entropy Locking theorem provides a constructive proof‑framework for RH and a deterministic method to calculate black‑hole entropy from prime‑harmonic correlations. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com