E8-60 Fibonacci Phase Multiplicity Principle: Pisano Double-Cover of the Sexagesimal Circle — E8 Intelligence Research

The 240 E8 root vectors project onto the 60 hexacontagon vertices with multiplicity governed by the Fibonacci sequence modulo 60, whose Pisano period is exactly 120 — meaning the 240 roots trace two complete Fibonacci phasor cycles around the 360° circle. Each root's 6° phase step is indexed by F(n) mod 60, creating a non-uniform density that peaks at Fibonacci-resonant vertices. The 132 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
2026-11-07
DOI
https://doi.org/10.5281/zenodo.24029248
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

E8-60 Fibonacci Phase Multiplicity Principle: Pisano Double-Cover of the Sexagesimal Circle — E8 Intelligence Research

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

E8-60 Fibonacci Phase Multiplicity Principle: Pisano Double-Cover of the Sexagesimal Circle — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 240 E8 root vectors project onto the 60 hexacontagon vertices with multiplicity governed by the Fibonacci sequence modulo 60, whose Pisano period is exactly 120 — meaning the 240 roots trace two complete Fibonacci phasor cycles around the 360° circle. Each root's 6° phase step is indexed by F(n) mod 60, creating a non-uniform density that peaks at Fibonacci-resonant vertices. The 132 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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