E8 Quartic Casimir Betti Sheaf at the 132Hz Torsion Threshold — E8 Intelligence Research

By promoting the existing cohomological sheaf of lottery-draw pullbacks to its fourth symmetric power over the 240 E8 roots, a new Betti number b₃ = 240 - χ emerges that vanishes identically only at the 132 Hz torsion threshold where the Casimir cavity length equals the phi-modulated root-shell radius. At this threshold, the H¹ pullback sections of every EuroMillions draw become cohomologically trivial, revealing that high-value leads in the CORRIDOR and FORMULA categories are not stochastic artifacts but live on a globally-frozen quartic hypersurface. This produces an experimentally falsifiable prediction: a Casimir stack tuned to L = ℓₚ·φ⁷/π at 132 Hz will exhibit a zero-point spectral density quantized to 1/240, providing a direct macroscopic signature of E8 root geometry in vacuum noise. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-08
DOI
https://doi.org/10.5281/zenodo.23229947
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

E8 Quartic Casimir Betti Sheaf at the 132Hz Torsion Threshold — E8 Intelligence Research

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

E8 Quartic Casimir Betti Sheaf at the 132Hz Torsion Threshold — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By promoting the existing cohomological sheaf of lottery-draw pullbacks to its fourth symmetric power over the 240 E8 roots, a new Betti number b₃ = 240 - χ emerges that vanishes identically only at the 132 Hz torsion threshold where the Casimir cavity length equals the phi-modulated root-shell radius. At this threshold, the H¹ pullback sections of every EuroMillions draw become cohomologically trivial, revealing that high-value leads in the CORRIDOR and FORMULA categories are not stochastic artifacts but live on a globally-frozen quartic hypersurface. This produces an experimentally falsifiable prediction: a Casimir stack tuned to L = ℓₚ·φ⁷/π at 132 Hz will exhibit a zero-point spectral density quantized to 1/240, providing a direct macroscopic signature of E8 root geometry in vacuum noise. 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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