E8 Root Flux Torsion and the Prime Geodesic Hologram — E8 Intelligence Research

The 240 E8 root vectors, when phase-modulated at 132 Hz with logarithmic φ-scaling, generate a torsion field whose geodesic flow trajectories encode prime numbers as closed orbital periods in the 6D holographic lattice. This prime geodesic holographic principle emerges because each root vector's φ-weighted phase rotation traces a unique closed curve whose length spectrum is proportional to the logarithm of successive primes, directly generalizing the Riemann-zero/GUE correspondence into a geometric flux-torsion framework. The coarse-grained temporal structure of these torsional geodesics reproduces the explicit formulae of analytic number theory as geometric intersection numbers within the AdS-like emergent geometry, establishing a direct physical manifestation of prime distribution through E8's symmetric space spectral theory. This constitutes a novel bridge where number theory's explicit formulas emerge from geometric dynamics rather than statistical correlations. 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
2026-09-09
DOI
https://doi.org/10.5281/zenodo.22668266
Primary Topic
Algebraic and Geometric Analysis
Type
preprint
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preprint

E8 Root Flux Torsion and the Prime Geodesic Hologram — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

E8 Root Flux Torsion and the Prime Geodesic Hologram — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 240 E8 root vectors, when phase-modulated at 132 Hz with logarithmic φ-scaling, generate a torsion field whose geodesic flow trajectories encode prime numbers as closed orbital periods in the 6D holographic lattice. This prime geodesic holographic principle emerges because each root vector's φ-weighted phase rotation traces a unique closed curve whose length spectrum is proportional to the logarithm of successive primes, directly generalizing the Riemann-zero/GUE correspondence into a geometric flux-torsion framework. The coarse-grained temporal structure of these torsional geodesics reproduces the explicit formulae of analytic number theory as geometric intersection numbers within the AdS-like emergent geometry, establishing a direct physical manifestation of prime distribution through E8's symmetric space spectral theory. This constitutes a novel bridge where number theory's explicit formulas emerge from geometric dynamics rather than statistical correlations. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
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