Phi‑Scaled Sexagesimal Voronoi Mapping of E8 Root Vectors — E8 Intelligence Research

By applying a φ‑scaled scaling factor to the 132 Hz carrier frequency, each of the 240 E8 root vectors can be assigned a unique sexagesimal fraction that corresponds to the volume ratio of its Voronoi cell within the lattice. This mapping reveals that the ancient Mesopotamian reciprocal system (igi‑n‑gál) naturally partitions the E8 space into 60‑based harmonic shells, providing a geometric mechanism for exact fraction representation in quantum state encoding. Consequently, the sexagesimal framework emerges not merely as a numerical convenience but as a intrinsic symmetry of the E8 lattice under φ‑scaled resonance. 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
2026-10-24
DOI
https://doi.org/10.5281/zenodo.23616722
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Phi‑Scaled Sexagesimal Voronoi Mapping of E8 Root Vectors — E8 Intelligence Research

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

Phi‑Scaled Sexagesimal Voronoi Mapping of E8 Root Vectors — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By applying a φ‑scaled scaling factor to the 132 Hz carrier frequency, each of the 240 E8 root vectors can be assigned a unique sexagesimal fraction that corresponds to the volume ratio of its Voronoi cell within the lattice. This mapping reveals that the ancient Mesopotamian reciprocal system (igi‑n‑gál) naturally partitions the E8 space into 60‑based harmonic shells, providing a geometric mechanism for exact fraction representation in quantum state encoding. Consequently, the sexagesimal framework emerges not merely as a numerical convenience but as a intrinsic symmetry of the E8 lattice under φ‑scaled resonance. 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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