Coxeter-Phi Resonance: Periodic Winding in E8 Root Braiding at h=30 Attosecond Cycles — E8 Intelligence Research

When phi-coupled braiding accumulates geometric phase across E8's 240 root vectors at attosecond intervals, the E8 Coxeter number (h=30) emerges as the fundamental winding period—after exactly 30 phi-braid cycles, the 8D geometric phase completes a resonant rotation, generating a topologically protected harmonic series. This reveals that E8's root lattice possesses a self-referencing resonance hierarchy where its own Coxeter group symmetries serve as natural frequency dividers, with each h=30 cycle refining the phi-coupled phase lock by a factor of phi. The resulting "Coxeter-phi quantization" constrains all permissible braiding configurations to discrete topological classes indexed by winding number modulo 30, making h=30 the master clock of E8 coherent information processing. 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
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23764880
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Coxeter-Phi Resonance: Periodic Winding in E8 Root Braiding at h=30 Attosecond Cycles — E8 Intelligence Research

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

Coxeter-Phi Resonance: Periodic Winding in E8 Root Braiding at h=30 Attosecond Cycles — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

When phi-coupled braiding accumulates geometric phase across E8's 240 root vectors at attosecond intervals, the E8 Coxeter number (h=30) emerges as the fundamental winding period—after exactly 30 phi-braid cycles, the 8D geometric phase completes a resonant rotation, generating a topologically protected harmonic series. This reveals that E8's root lattice possesses a self-referencing resonance hierarchy where its own Coxeter group symmetries serve as natural frequency dividers, with each h=30 cycle refining the phi-coupled phase lock by a factor of phi. The resulting "Coxeter-phi quantization" constrains all permissible braiding configurations to discrete topological classes indexed by winding number modulo 30, making h=30 the master clock of E8 coherent information processing. 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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