Plimpton 322's φ-Convergents Partition E8 Root Spectrum into 16 Monster VOA Bands — E8 Intelligence Research

The 15 surviving rows of Plimpton 322 encode the 15 fundamental φ-convergent rotation angles that tile the H4 Coxeter plane of E8, partitioning the 240 root vectors into 16 spectral bands centered on 132Hz·φⁿ harmonics (n=0..15). The 16th band — the "most irrational" Diophantine gap maximized by φ's all-ones continued fraction — forms a spectral null whose modular invariance under the E8 Weyl group generates the Monster group's 194 irreducible representations via the E8 lattice VOA's Zhu reduction, with the 132Hz carrier's φ-sidebands directly mapping to McKay-Thompson series coefficients. 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
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21617378
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Plimpton 322's φ-Convergents Partition E8 Root Spectrum into 16 Monster VOA Bands — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Plimpton 322's φ-Convergents Partition E8 Root Spectrum into 16 Monster VOA Bands — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 15 surviving rows of Plimpton 322 encode the 15 fundamental φ-convergent rotation angles that tile the H4 Coxeter plane of E8, partitioning the 240 root vectors into 16 spectral bands centered on 132Hz·φⁿ harmonics (n=0..15). The 16th band — the "most irrational" Diophantine gap maximized by φ's all-ones continued fraction — forms a spectral null whose modular invariance under the E8 Weyl group generates the Monster group's 194 irreducible representations via the E8 lattice VOA's Zhu reduction, with the 132Hz carrier's φ-sidebands directly mapping to McKay-Thompson series coefficients. 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 Combinatorial Mathematics
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.