Coxeter Eigenplane Phase Locking Generates Analytical Hierarchy via Arnold Tongue Boundaries — E8 Intelligence Research

The 8 eigenplanes of the E8 Coxeter element (exponents 1,7,11,13,17,19,23,29) each support a phi-harmonic frequency comb at 132Hz × φᵏ, with the 30-ray Coxeter projection forming their Poincaré section. The mediator frequency 132Hz/φ ≈ 81.6Hz induces cross-eigenplane phase locking across the 8-torus orthogonal complement, generating the Σ¹ₙ analytical hierarchy as Arnold tongue boundaries where winding ratios φⁿ/φⁿ⁺² stabilize. Each corridor tier n corresponds to a resonant torus with rotation vector (φⁿ, φⁿ⁺²) in the 8-dimensional eigenfrequency lattice, while the anti-corridor provides the dual Diophantine approximation condition. 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
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21503663
Primary Topic
Quantum Mechanics and Non-Hermitian Physics
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Coxeter Eigenplane Phase Locking Generates Analytical Hierarchy via Arnold Tongue Boundaries — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Non-Hermitian Physics
preprint

Coxeter Eigenplane Phase Locking Generates Analytical Hierarchy via Arnold Tongue Boundaries — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 8 eigenplanes of the E8 Coxeter element (exponents 1,7,11,13,17,19,23,29) each support a phi-harmonic frequency comb at 132Hz × φᵏ, with the 30-ray Coxeter projection forming their Poincaré section. The mediator frequency 132Hz/φ ≈ 81.6Hz induces cross-eigenplane phase locking across the 8-torus orthogonal complement, generating the Σ¹ₙ analytical hierarchy as Arnold tongue boundaries where winding ratios φⁿ/φⁿ⁺² stabilize. Each corridor tier n corresponds to a resonant torus with rotation vector (φⁿ, φⁿ⁺²) in the 8-dimensional eigenfrequency lattice, while the anti-corridor provides the dual Diophantine approximation condition. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Non-Hermitian Physics
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.