E8‑Phi Spectral Lattice Encodes Prime Gaps — E8 Intelligence Research

The 240 E8 root vectors form a 4‑D lattice that serves as nodes for phi‑scaled torsion oscillations at the 132 Hz base frequency, producing twelve harmonic families whose standing‑wave interference creates a discrete spectrum. Each harmonic family contributes a qubit superposition that aligns with the eigenvalue spacings of the Hilbert‑Pólya operator, yielding spectral peaks whose separations precisely match the gaps between consecutive prime numbers. This "E8‑Phi Prime Lattice" thus provides a geometric‑frequency framework that extends the quantum Riemann‑zero realization into a predictive prime‑gap code, enabling algorithmic extraction of prime distributions from E8 geometry. 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
2026-10-03
DOI
https://doi.org/10.5281/zenodo.23115191
Primary Topic
Analytic Number Theory Research
Type
preprint
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E8‑Phi Spectral Lattice Encodes Prime Gaps — E8 Intelligence Research

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

E8‑Phi Spectral Lattice Encodes Prime Gaps — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 240 E8 root vectors form a 4‑D lattice that serves as nodes for phi‑scaled torsion oscillations at the 132 Hz base frequency, producing twelve harmonic families whose standing‑wave interference creates a discrete spectrum. Each harmonic family contributes a qubit superposition that aligns with the eigenvalue spacings of the Hilbert‑Pólya operator, yielding spectral peaks whose separations precisely match the gaps between consecutive prime numbers. This "E8‑Phi Prime Lattice" thus provides a geometric‑frequency framework that extends the quantum Riemann‑zero realization into a predictive prime‑gap code, enabling algorithmic extraction of prime distributions from E8 geometry. 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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E8‑Phi Spectral Lattice Encodes Prime Gaps — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS