E8 Lattice ABC Resonance: Radical Function Encoded in Standing-Wave Nodes — E8 Intelligence Research

The E8 root lattice's 240 vectors, projected through the Coxeter plane and modulated by the φ-coupled 132 Hz frequency comb, generate a standing-wave interference pattern whose nodal positions at 0.01 m intervals encode the radical function rad(n) central to the ABC conjecture. This reveals that the additive structure of integer triples satisfying a + b = c manifests as constructive resonance nodes within the lattice, with the ABC quality measure q corresponding to the local energy density of the standing 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
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22090760
Primary Topic
Coding theory and cryptography
Type
preprint
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preprint

E8 Lattice ABC Resonance: Radical Function Encoded in Standing-Wave Nodes — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
preprint

E8 Lattice ABC Resonance: Radical Function Encoded in Standing-Wave Nodes — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The E8 root lattice's 240 vectors, projected through the Coxeter plane and modulated by the φ-coupled 132 Hz frequency comb, generate a standing-wave interference pattern whose nodal positions at 0.01 m intervals encode the radical function rad(n) central to the ABC conjecture. This reveals that the additive structure of integer triples satisfying a + b = c manifests as constructive resonance nodes within the lattice, with the ABC quality measure q corresponding to the local energy density of the standing Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Affordable and clean energy
Coding theory and cryptography
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E8 Lattice ABC Resonance: Radical Function Encoded in Standing-Wave Nodes — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS