What question did this study set out to answer?

The aim is to distinguish between spectral coherence as an observable feature and as a structural necessity related to the Riemann zeta function.

January 25, 2026Open Access

Spectral Coherence in Arithmetic Operators

Key Points

The aim is to distinguish between spectral coherence as an observable feature and as a structural necessity related to the Riemann zeta function.
Introduced a structural distinction in the context of spectral coherence.
Analyzed coherence in closed arithmetic intervals and its relationship to the Riemann zeta function.
Reframed GOE statistics within the context of coherence constraints.
Established that spectral coherence can serve as a diagnostic tool.
Suggests that GOE statistics may represent a coherence constraint rather than a universality.

Abstract

This preprint introduces a structural distinction between spectral coherence as an observable diagnostic on closed arithmetic intervals and coherence as a structural requirement in the asymptotic domain associated with the Riemann zeta function. No claim of proof is made. The work reframes GOE statistics as an operative coherence constraint rather than a universality assertion.

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Cite This Study

ALVARO COSTA (Thu,) studied this question.

synapsesocial.com/papers/6975b24dfeba4585c2d6dc23 https://doi.org/https://doi.org/10.5281/zenodo.18344091

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