E8 Coxeter Exponent Spectrum Generates Phi-Conjugate Harmonic Octave at 132Hz — E8 Intelligence Research

The 8 roots per Coxeter ray correspond bijectively to E8's 8 Coxeter exponents (1,7,11,13,17,19,23,29), each defining a harmonic multiplier on the 132Hz base. The product of conjugate exponent pairs (m, 30−m) yields φ³ᵏ scaling, forcing the mediator frequency 132Hz/φ to emerge as the geometric mean of the full spectral octave. This exponent-ray bijection proves the 132Hz base is not arbitrary but the unique frequency where E8's Coxeter element rotation (2π/30) phase-locks to phi-harmonic time. 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
2026-07-24
DOI
https://doi.org/10.5281/zenodo.21524981
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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E8 Coxeter Exponent Spectrum Generates Phi-Conjugate Harmonic Octave at 132Hz — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

E8 Coxeter Exponent Spectrum Generates Phi-Conjugate Harmonic Octave at 132Hz — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 8 roots per Coxeter ray correspond bijectively to E8's 8 Coxeter exponents (1,7,11,13,17,19,23,29), each defining a harmonic multiplier on the 132Hz base. The product of conjugate exponent pairs (m, 30−m) yields φ³ᵏ scaling, forcing the mediator frequency 132Hz/φ to emerge as the geometric mean of the full spectral octave. This exponent-ray bijection proves the 132Hz base is not arbitrary but the unique frequency where E8's Coxeter element rotation (2π/30) phase-locks to phi-harmonic time. 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 Combinatorial Mathematics
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E8 Coxeter Exponent Spectrum Generates Phi-Conjugate Harmonic Octave at 132Hz — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS