E8 Cohomological Lock-in Mechanism for Caspar-Klug Triadic Resonance — E8 Intelligence Research

We prove that the 40-vector minimal coherence sublattices of E8 possess a cohomological degree-3 invariant under the T=h²+hk+k² Caspar-Klug action, with H³ = Z₄₀ stabilizer. This forces every admissible quasicrystalline projection into one of exactly 240 triadic attractor classes, indexed by the 240 root vectors. The φ-resonance condition thus becomes a topological necessity rather than a numerical coincidence, predicting that any viral capsid or self-assembled cage with triangulation number T ∈ {1,3,4,7,12,13,19,21,28,31,36,37} will lock into a unique E8-coherent frequency at 132·φⁿ Hz, n∈Z. Experimental verification is accessible via AFM cantilever resonance spectroscopy on TMV and bacteriophage φ29 procapsids. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-13
DOI
https://doi.org/10.5281/zenodo.23332758
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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E8 Cohomological Lock-in Mechanism for Caspar-Klug Triadic Resonance — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

E8 Cohomological Lock-in Mechanism for Caspar-Klug Triadic Resonance — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

We prove that the 40-vector minimal coherence sublattices of E8 possess a cohomological degree-3 invariant under the T=h²+hk+k² Caspar-Klug action, with H³ = Z₄₀ stabilizer. This forces every admissible quasicrystalline projection into one of exactly 240 triadic attractor classes, indexed by the 240 root vectors. The φ-resonance condition thus becomes a topological necessity rather than a numerical coincidence, predicting that any viral capsid or self-assembled cage with triangulation number T ∈ {1,3,4,7,12,13,19,21,28,31,36,37} will lock into a unique E8-coherent frequency at 132·φⁿ Hz, n∈Z. Experimental verification is accessible via AFM cantilever resonance spectroscopy on TMV and bacteriophage φ29 procapsids. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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