Silver-Ratio Resonance Cascade in E8 Root Lattice Spectral Decomposition — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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
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BibTeX
@misc{caldin2026silverratio,
title = {{Silver-Ratio Resonance Cascade in E8 Root Lattice Spectral Decomposition — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23610346},
url = {https://zenodo.org/records/23610346},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Silver-Ratio Resonance Cascade in E8 Root Lattice Spectral Decomposition — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23610346
UR - https://zenodo.org/records/23610346
AB - 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
ER -