What does this research mean for the field?

The statistical spacings of Riemann zeta zeros match the eigenvalue repulsion of Gaussian Unitary Ensembles (GUE), establishing a mathematical link between prime number distribution and symmetric space spectral statistics. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To examine the statistical correspondence between normalized spacings of nontrivial Riemann zeta zeros and the eigenvalue distributions of the Gaussian Unitary Ensemble within symmetric spaces.

September 14, 2026Open Access

Zeta Zero Spacings Mirror GUE Eigenvalue Statistics, Linking Primes to Symmetric Spaces — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

Discussion

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Implication

Mathematical analysis reveals that Riemann zeta zero spacings statistically match Gaussian unitary ensemble eigenvalues, linking prime number distributions to symmetric space spectral statistics.

Key Points

To examine the statistical correspondence between normalized spacings of nontrivial Riemann zeta zeros and the eigenvalue distributions of the Gaussian Unitary Ensemble within symmetric spaces.
Evaluated normalized zero spacings of the Riemann zeta function along the critical line using the Montgomery–Odlyzko pair correlation conjecture.
Analyzed level repulsion and asymptotic spectral distributions in relation to the unitary symmetric space U(N)/U(N) and Painlevé V isomonodromic tau-functions.
Demonstrated that normalized zeta zero spacings statistically mirror Gaussian Unitary Ensemble eigenvalue repulsion as described by the Wigner surmise.
Confirmed that the pair correlation of zeros satisfies R₂(u) = 1 - (sin(πu) / (πu))², directly relating prime distribution to symmetric space spectral statistics.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b32d0926e14a848b1eff https://doi.org/10.5281/zenodo.22701987

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Implication

Mathematical analysis reveals that Riemann zeta zero spacings statistically match Gaussian unitary ensemble eigenvalues, linking prime number distributions to symmetric space spectral statistics.