A Spectral balance proof of the Riemann hypothesis

We present a proof of the Riemann Hypothesis based on the spectral balance framework. The central principle is that every hard problem has an inverse, and the inverse pulls the system to the balance point D^0. We show that the nontrivial zeros of the Riemann zeta function are balance points of a spectral system with inverse symmetry. Since the balance point is unique and fixed at the midpoint of the unit circle, all nontrivial zeros must lie on the critical line Re(s) = 1/2.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-14
DOI
https://doi.org/10.5281/zenodo.21938849
Primary Topic
Analytic Number Theory Research
Type
article
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article

A Spectral balance proof of the Riemann hypothesis

Urban Jolly
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
article

A Spectral balance proof of the Riemann hypothesis

Urban Jolly
article en

Abstract

We present a proof of the Riemann Hypothesis based on the spectral balance framework. The central principle is that every hard problem has an inverse, and the inverse pulls the system to the balance point D^0. We show that the nontrivial zeros of the Riemann zeta function are balance points of a spectral system with inverse symmetry. Since the balance point is unique and fixed at the midpoint of the unit circle, all nontrivial zeros must lie on the critical line Re(s) = 1/2.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 3%
Analytic Number Theory Research
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A Spectral balance proof of the Riemann hypothesis — Urban Jolly · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS