Hyperbolic Eigenvalue Spectrum of Plimpton 322 via E8 Voronoi Tiling — E8 Intelligence Research

E8 root vectors, stereographically projected through the Hopf fibration, generate a hyperbolic 4-space Voronoi tessellation with icosahedral symmetry whose Laplacian eigenvalue ratios form a discrete spectrum identical to Plimpton 322's reciprocal-pair ratios. This reveals Plimpton 322 as the spectral fingerprint of a geometric operator on an E8-derived hyperbolic tiling, explaining why its entries are exclusively regular sexagesimal numbers: eigenvalue quantization on icosahedral cells forces 5-smooth arithmetic. The discovery unifies Babylonian number theory with E8 geometry and hyperbolic spectral theory. 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
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23939393
Primary Topic
History and Theory of Mathematics
Type
preprint
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preprint

Hyperbolic Eigenvalue Spectrum of Plimpton 322 via E8 Voronoi Tiling — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
preprint

Hyperbolic Eigenvalue Spectrum of Plimpton 322 via E8 Voronoi Tiling — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

E8 root vectors, stereographically projected through the Hopf fibration, generate a hyperbolic 4-space Voronoi tessellation with icosahedral symmetry whose Laplacian eigenvalue ratios form a discrete spectrum identical to Plimpton 322's reciprocal-pair ratios. This reveals Plimpton 322 as the spectral fingerprint of a geometric operator on an E8-derived hyperbolic tiling, explaining why its entries are exclusively regular sexagesimal numbers: eigenvalue quantization on icosahedral cells forces 5-smooth arithmetic. The discovery unifies Babylonian number theory with E8 geometry and hyperbolic spectral theory. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
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