What question did this study set out to answer?

This research aims to unveil the connection between Riemann zero spacings and nuclear energy level statistics using the Q6 prime lattice operator.

May 16, 2026Open Access

The Montgomery–Dyson Coincidence Resolved by the Q6 Prime Lattice Operator

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Key Points

This research aims to unveil the connection between Riemann zero spacings and nuclear energy level statistics using the Q6 prime lattice operator.
Analyzed eigenvalue spectra of the Q6 prime lattice operator at different truncations.
Examined the self-adjointness of the Q6 operator and its implications.
Utilized comparisons to GUE universality.
Established that both Riemann zero spacings and nuclear energy levels are eigenvalue spectra of the Q6 operator.
Demonstrated GUE universality follows from the operator's self-adjointness.
Validated the coprime identity ζ(2) = π²/6 as central to the findings.

Abstract

Description: In 1972, Montgomery and Dyson discovered over tea that Riemann zero spacings match nuclear energy level statistics — a mystery unsolved for 54 years. This paper resolves it: both are eigenvalue spectra of the Q6 prime lattice operator at different truncations. The GUE universality follows from self-adjointness of Q6 and the coprime identity ζ(2) = π²/6. Keywords: Riemann hypothesis, Montgomery-Dyson, GUE, random matrices, prime lattice, Q6 operator, Navier-Stokes, number theory, nuclear physics Communities: mathematics, mathematical-physics, fluid-dynamics Related works: https://doi.org/10.5281/zenodo.19842060 (Ring Lemma) https://doi.org/10.5281/zenodo.19842061 (Diffuse Cascade)

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Jonathan Simons (Thu,) studied this question.

synapsesocial.com/papers/6a080acea487c87a6a40cbf8 — DOI: https://doi.org/10.5281/zenodo.20184147

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Jonathan Simons

Savannah Technical College

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The Montgomery–Dyson Coincidence Resolved by the Q6 Prime Lattice Operator

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