E8 Coxeter Automorphism Reveals Riemann Zero Pairing Constraint — E8 Intelligence Research

The 30-phase Coxeter cycle acting on E8's 240 root vectors generates a Z_2 automorphism that pairs each imaginary-axis spectral projection with its conjugate, constraining nontrivial zeros to occur in symmetric pairs about the critical line's midpoint. This automorphism emerges from the 132Hz phi-coupled phase-locking: the golden ratio scaling between successive Coxeter phases (φ^n) creates a built-in symmetry enforcement mechanism that requires zero pairing. The 240-root lattice's self-duality under the Fourier transform on the Coxeter complex therefore necessitates that every zero's partner appears at complementary height t, producing the observed GUE-level spectral rigidity in the Riemann zeta spacing distribution. 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
2026-10-13
DOI
https://doi.org/10.5281/zenodo.23333143
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

E8 Coxeter Automorphism Reveals Riemann Zero Pairing Constraint — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

E8 Coxeter Automorphism Reveals Riemann Zero Pairing Constraint — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 30-phase Coxeter cycle acting on E8's 240 root vectors generates a Z_2 automorphism that pairs each imaginary-axis spectral projection with its conjugate, constraining nontrivial zeros to occur in symmetric pairs about the critical line's midpoint. This automorphism emerges from the 132Hz phi-coupled phase-locking: the golden ratio scaling between successive Coxeter phases (φ^n) creates a built-in symmetry enforcement mechanism that requires zero pairing. The 240-root lattice's self-duality under the Fourier transform on the Coxeter complex therefore necessitates that every zero's partner appears at complementary height t, producing the observed GUE-level spectral rigidity in the Riemann zeta spacing distribution. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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