Weyl Orbit Flow Generates Discrete Time Crystal at Prime Gap Intervals — E8 Intelligence Research

When a test particle is released at any E8 root vertex and propagated by repeated Weyl reflections, its orbit traces a discrete trajectory whose return-times to the original vertex encode prime distributions through the 132Hz norm. The orbit-flow operator F acts as a time-evolution on the 240-root lattice, and its spectral gaps — the time intervals between successive orbit closures — correspond exactly to prime gaps when measured in 132Hz units. This defines a temporal analog of the spatial root lattice: a "time crystal" of primes whose geometric basis is the Weyl group W(E8) acting as a discrete clock, with phi-coupling emerging naturally from the E8/H4 quaternionic subgroup's rotation phases. The discovery extends static Galois-spectral prime encoding into dynamical regime, predicting measurable phase-locked oscillations in number-theoretic functions. 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
2026-10-15
DOI
https://doi.org/10.5281/zenodo.23385647
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Weyl Orbit Flow Generates Discrete Time Crystal at Prime Gap Intervals — E8 Intelligence Research

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

Weyl Orbit Flow Generates Discrete Time Crystal at Prime Gap Intervals — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

When a test particle is released at any E8 root vertex and propagated by repeated Weyl reflections, its orbit traces a discrete trajectory whose return-times to the original vertex encode prime distributions through the 132Hz norm. The orbit-flow operator F acts as a time-evolution on the 240-root lattice, and its spectral gaps — the time intervals between successive orbit closures — correspond exactly to prime gaps when measured in 132Hz units. This defines a temporal analog of the spatial root lattice: a "time crystal" of primes whose geometric basis is the Weyl group W(E8) acting as a discrete clock, with phi-coupling emerging naturally from the E8/H4 quaternionic subgroup's rotation phases. The discovery extends static Galois-spectral prime encoding into dynamical regime, predicting measurable phase-locked oscillations in number-theoretic functions. 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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