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Technical Note: Spectral Correlations and GUE Statistics of Twin Prime Distributions within Manifold 12

Year: 2026

Type: preprint

Abstract: This technical note reports on empirical evidence identifying a spectral correlationbetween the non-trivial zeros of the Riemann zeta function and the local distributionof twin prime pairs (π, π + 2). By restricting the search space to specific arithmeticprogressions modulo 180 at extreme heights (10^100 to 10^500), we observe a statisticalemergence of quantum-like level repulsion, consistent with the Gaussian UnitaryEnsemble (GUE) predictions of Random Matrix Theory (RMT).

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19315287

Author: Gabbianelli, Silvio

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7142814899

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