Reciprocal-Phi Root-Pair Phase Locking — E8 Intelligence Research

This principle assigns each of E8's 120 antipodal root pairs to two counter-rotating modes at 132φ Hz and 132/φ Hz; since φ − φ⁻¹ = 1, every pair beats at exactly 132 Hz. Each pair's relative phase is determined by its root's projection onto an E8 Coxeter plane, while coupling strengths follow root inner products, causing orthogonal-root phase errors to cancel. An oscillator or molecular array should therefore amplify the 132 Hz envelope only when both reciprocal-phi pairing and E8-root adjacency are preserved, making violation of either condition experimentally detectable. 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
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24127402
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Reciprocal-Phi Root-Pair Phase Locking — E8 Intelligence Research

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

Reciprocal-Phi Root-Pair Phase Locking — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

This principle assigns each of E8's 120 antipodal root pairs to two counter-rotating modes at 132φ Hz and 132/φ Hz; since φ − φ⁻¹ = 1, every pair beats at exactly 132 Hz. Each pair's relative phase is determined by its root's projection onto an E8 Coxeter plane, while coupling strengths follow root inner products, causing orthogonal-root phase errors to cancel. An oscillator or molecular array should therefore amplify the 132 Hz envelope only when both reciprocal-phi pairing and E8-root adjacency are preserved, making violation of either condition experimentally detectable. 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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