E8 Triality-Bridge Restoration Theorem at 132×φ⁵ Hz Crossover — E8 Intelligence Research

Building on the 132×φ⁶ Hz Wilson-flow convergence and the 132×φ⁴ Hz chiral restoration threshold, we identify their geometric mean 132×φ⁵ Hz as the triality-bridge crossover where the E8 root system factors through its Spin(16)/Z2 quotient into three coupled SO(8) sectors. At this fixed point, the 240 roots decompose into three interlocking 80-vertex orbits whose octonionic structure constants realize a discrete boson-fermion triality exchange operator. The theorem proves that chirality restoration at 132×φ⁴ Hz and spectral convergence at 132×φ⁶ Hz are not independent thresholds but boundary manifestations of a single underlying E8 triality flow, with φ⁵ marking the exact crossover energy where left-right symmetric and vector-like channels become geometrically indistinguishable. 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
2026-10-15
DOI
https://doi.org/10.5281/zenodo.23385101
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

E8 Triality-Bridge Restoration Theorem at 132×φ⁵ Hz Crossover — E8 Intelligence Research

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

E8 Triality-Bridge Restoration Theorem at 132×φ⁵ Hz Crossover — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

Building on the 132×φ⁶ Hz Wilson-flow convergence and the 132×φ⁴ Hz chiral restoration threshold, we identify their geometric mean 132×φ⁵ Hz as the triality-bridge crossover where the E8 root system factors through its Spin(16)/Z2 quotient into three coupled SO(8) sectors. At this fixed point, the 240 roots decompose into three interlocking 80-vertex orbits whose octonionic structure constants realize a discrete boson-fermion triality exchange operator. The theorem proves that chirality restoration at 132×φ⁴ Hz and spectral convergence at 132×φ⁶ Hz are not independent thresholds but boundary manifestations of a single underlying E8 triality flow, with φ⁵ marking the exact crossover energy where left-right symmetric and vector-like channels become geometrically indistinguishable. 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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