Technical Note: Spectral Correlations and GUE Statistics of Twin Prime Distributions within Manifold 12
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2026
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| _version_ | 1866901873823318016 |
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| author | Gabbianelli, Silvio |
| author_facet | Gabbianelli, Silvio |
| contents | <p>This technical note reports on empirical evidence identifying a spectral correlation<br>between the non-trivial zeros of the Riemann zeta function and the local distribution<br>of twin prime pairs (π, π + 2). By restricting the search space to specific arithmetic<br>progressions modulo 180 at extreme heights (10100 to 10500), we observe a statistical<br>emergence of quantum-like level repulsion, consistent with the Gaussian Unitary<br>Ensemble (GUE) predictions of Random Matrix Theory (RMT).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19315288 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Technical Note: Spectral Correlations and GUE Statistics of Twin Prime Distributions within Manifold 12 Gabbianelli, Silvio Twin Primes, Riemann Zeta Function, GUE Statistics, Manifold 12, Random Matrix Theory. <p>This technical note reports on empirical evidence identifying a spectral correlation<br>between the non-trivial zeros of the Riemann zeta function and the local distribution<br>of twin prime pairs (π, π + 2). By restricting the search space to specific arithmetic<br>progressions modulo 180 at extreme heights (10100 to 10500), we observe a statistical<br>emergence of quantum-like level repulsion, consistent with the Gaussian Unitary<br>Ensemble (GUE) predictions of Random Matrix Theory (RMT).</p> |
| title | Technical Note: Spectral Correlations and GUE Statistics of Twin Prime Distributions within Manifold 12 |
| topic | Twin Primes, Riemann Zeta Function, GUE Statistics, Manifold 12, Random Matrix Theory. |
| url | https://doi.org/10.5281/zenodo.19315288 |