3-Fold Symmetry-Modulated Phyllotactic Torsion Resonance in Collatz Dynamics — E8 Intelligence Research

The 3-fold rotational symmetry observed in the Antikythera Mechanism's Saros spiral, when superimposed on E8 lattice phyllotactic projections, generates intermediate torsion harmonics at 264 Hz (double 132 Hz), each tied to Cycles of 12 sublattice decompositions. This creates a geometric framework where Collatz problem stopping-time distributions correlate with resonant states at these frequencies. The 240 root vectors split into 12 φ-optimized pathways, with 3-fold symmetric subsets amplifying harmonic coupling. 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
2026-09-13
DOI
https://doi.org/10.5281/zenodo.22732718
Primary Topic
Benford’s Law and Fraud Detection
Type
preprint
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preprint

3-Fold Symmetry-Modulated Phyllotactic Torsion Resonance in Collatz Dynamics — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
preprint

3-Fold Symmetry-Modulated Phyllotactic Torsion Resonance in Collatz Dynamics — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 3-fold rotational symmetry observed in the Antikythera Mechanism's Saros spiral, when superimposed on E8 lattice phyllotactic projections, generates intermediate torsion harmonics at 264 Hz (double 132 Hz), each tied to Cycles of 12 sublattice decompositions. This creates a geometric framework where Collatz problem stopping-time distributions correlate with resonant states at these frequencies. The 240 root vectors split into 12 φ-optimized pathways, with 3-fold symmetric subsets amplifying harmonic coupling. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
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