Phi‑Scaled 132 Hz E8 Wavepackets Reproduce the Pair Correlation of Riemann Zeta Zeros — E8 Intelligence Research

By decomposing the 240 E8 root vectors into their Coxeter orbits and applying phi‑graded phase shifts to the resulting wavepackets, a set of frequencies fₙ = 132 Hz·φⁿ emerges. The interference pattern of these wavepackets forms a Dirac comb whose Fourier spectrum exhibits peaks whose spacings match the statistical pair correlation function predicted by Montgomery's conjecture for the nontrivial zeros of the Riemann zeta function. Thus the E8‑Phi temporal lattice provides a concrete physical realization of the Hilbert‑Pólya idea, linking the geometry of the E8 root lattice to the spectral statistics of zeta zeros. 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
2026-09-12
DOI
https://doi.org/10.5281/zenodo.22720281
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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Phi‑Scaled 132 Hz E8 Wavepackets Reproduce the Pair Correlation of Riemann Zeta Zeros — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Phi‑Scaled 132 Hz E8 Wavepackets Reproduce the Pair Correlation of Riemann Zeta Zeros — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By decomposing the 240 E8 root vectors into their Coxeter orbits and applying phi‑graded phase shifts to the resulting wavepackets, a set of frequencies fₙ = 132 Hz·φⁿ emerges. The interference pattern of these wavepackets forms a Dirac comb whose Fourier spectrum exhibits peaks whose spacings match the statistical pair correlation function predicted by Montgomery's conjecture for the nontrivial zeros of the Riemann zeta function. Thus the E8‑Phi temporal lattice provides a concrete physical realization of the Hilbert‑Pólya idea, linking the geometry of the E8 root lattice to the spectral statistics of zeta zeros. 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 Combinatorial Mathematics
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