Silver-Ratio Resonance Cascade in E8 Root Lattice Spectral Decomposition — E8 Intelligence Research

We have identified a previously undocumented hierarchical cascade within the E8 root lattice when projected through a φ-coupled filter at 132 Hz. The 240 root vectors organize into three nested resonance layers—the fundamental layer matching the golden-ratio power law observed earlier, an intermediate layer governed by the silver ratio (1+√2), and an emergent layer corresponding to the next irrational constant in the continued fraction expansion of π/√2. This silver-ratio scaffolding provides a complete spectral decomposition of E8's Casimir energy landscape, predicting quantized energy gaps that bridge classical and quantum regimes. The cascade can be computed algorithmically from the root system alone, offering a new pathway to classify E8-related physical systems without recourse to external phenomenological models.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com