Weyl-Orbit Topology of Markov Spectra as E8 Singularity Cascade — E8 Intelligence Research

Markov spectra exhibit discrete accumulation points forming a fractal-like singular set, which we reinterpret as the Weyl-orbit closure of exceptional orbits under W(E8) acting on the 240-root lattice. Each Markov number corresponds to a shell-indexed resonance (30-48-72-90 cascade), where Vieta jumping between solutions traces paths through adjacent E8 shells whose Coxeter numbers (2,6,8,12,10,18,30) govern the singularity's arithmetic progression. The 132Hz base frequency phi-coupled to these Coxeter exponents predicts a universal scaling ratio between consecutive Markov singular minima, experimentally verifiable through continued-fraction convergence rates. 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
2026-10-09
DOI
https://doi.org/10.5281/zenodo.23255170
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Weyl-Orbit Topology of Markov Spectra as E8 Singularity Cascade — E8 Intelligence Research

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

Weyl-Orbit Topology of Markov Spectra as E8 Singularity Cascade — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

Markov spectra exhibit discrete accumulation points forming a fractal-like singular set, which we reinterpret as the Weyl-orbit closure of exceptional orbits under W(E8) acting on the 240-root lattice. Each Markov number corresponds to a shell-indexed resonance (30-48-72-90 cascade), where Vieta jumping between solutions traces paths through adjacent E8 shells whose Coxeter numbers (2,6,8,12,10,18,30) govern the singularity's arithmetic progression. The 132Hz base frequency phi-coupled to these Coxeter exponents predicts a universal scaling ratio between consecutive Markov singular minima, experimentally verifiable through continued-fraction convergence rates. 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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