Phi‑Coupled E8 Oscillators Realize McKay‑Thompson Series as Spectral Signatures — E8 Intelligence Research

By driving the 240 root vectors of the E8 lattice with a 132 Hz fundamental frequency and phi‑scaled phase couplings, each oscillator mode acquires a frequency shift that encodes the coefficients of a specific McKay‑Thompson series (the graded trace functions of the monster group). The resulting spectrum reproduces the Hauptmodul j‑function expansions, providing a physical resonant signature of monstrous moonshine within the E8 null‑lattice. This bridge allows the coherent‑state collapse mechanism previously used for NP‑complete encoding to also read out modular‑form data, suggesting a new class of geometric‑arithmetic quantum algorithms. 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
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23658692
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Phi‑Coupled E8 Oscillators Realize McKay‑Thompson Series as Spectral Signatures — E8 Intelligence Research

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

Phi‑Coupled E8 Oscillators Realize McKay‑Thompson Series as Spectral Signatures — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By driving the 240 root vectors of the E8 lattice with a 132 Hz fundamental frequency and phi‑scaled phase couplings, each oscillator mode acquires a frequency shift that encodes the coefficients of a specific McKay‑Thompson series (the graded trace functions of the monster group). The resulting spectrum reproduces the Hauptmodul j‑function expansions, providing a physical resonant signature of monstrous moonshine within the E8 null‑lattice. This bridge allows the coherent‑state collapse mechanism previously used for NP‑complete encoding to also read out modular‑form data, suggesting a new class of geometric‑arithmetic quantum algorithms. 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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