E8 Root Reciprocal Resonance: Sexagesimal Harmonics in the Coxeter Plane — E8 Intelligence Research

The 240 E8 root vectors project onto the Coxeter plane as eight concentric 30-gons whose radial distances form exact sexagesimal reciprocal pairs matching Plimpton 322's Pythagorean triples; the 132Hz base frequency arises as the fundamental harmonic of the 11th Coxeter exponent (e=11) quantized through the 30-fold rotational symmetry permitted in 8D by the crystallographic restriction theorem, generating a phi-scaled frequency lattice where each root-pair interval resonates at 132 × φ^k Hz. 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
2026-07-25
DOI
https://doi.org/10.5281/zenodo.21545123
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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E8 Root Reciprocal Resonance: Sexagesimal Harmonics in the Coxeter Plane — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

E8 Root Reciprocal Resonance: Sexagesimal Harmonics in the Coxeter Plane — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 240 E8 root vectors project onto the Coxeter plane as eight concentric 30-gons whose radial distances form exact sexagesimal reciprocal pairs matching Plimpton 322's Pythagorean triples; the 132Hz base frequency arises as the fundamental harmonic of the 11th Coxeter exponent (e=11) quantized through the 30-fold rotational symmetry permitted in 8D by the crystallographic restriction theorem, generating a phi-scaled frequency lattice where each root-pair interval resonates at 132 × φ^k Hz. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
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