A Topodynamic Field Theory and the Resolution of the Riemann Hypothesis via Invariant Geometric Operators

We present a topodynamic framework wherein the distribution of the non-trivial zeros of the Riemann zeta function \\zeta(s) is governed by the interaction between a non-local linear super-wave and invariant geometric constraints. By establishing \\pi not merely as a static ratio but as an active torsion operator equivalent to a fundamental harmonic frequency of f_0 = 210.42\\text{ Hz} under appropriate dimensional scaling, we demonstrate that any deviation from the critical line \\operatorname{Re}(s) = 1/2 induces an unrecoverable curvature divergence. Consequently, all non-trivial zeros are strictly constrained to reside upon the critical axis.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-21
DOI
https://doi.org/10.5281/zenodo.22873056
Primary Topic
Black Holes and Theoretical Physics
Type
preprint
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preprint

A Topodynamic Field Theory and the Resolution of the Riemann Hypothesis via Invariant Geometric Operators

albert cruañas pardo
Zenodo (CERN European Organization for Nuclear Research)
Black Holes and Theoretical Physics
preprint

A Topodynamic Field Theory and the Resolution of the Riemann Hypothesis via Invariant Geometric Operators

albert cruañas pardo
preprint en

Abstract

We present a topodynamic framework wherein the distribution of the non-trivial zeros of the Riemann zeta function \zeta(s) is governed by the interaction between a non-local linear super-wave and invariant geometric constraints. By establishing \pi not merely as a static ratio but as an active torsion operator equivalent to a fundamental harmonic frequency of f_0 = 210.42\text{ Hz} under appropriate dimensional scaling, we demonstrate that any deviation from the critical line \operatorname{Re}(s) = 1/2 induces an unrecoverable curvature divergence. Consequently, all non-trivial zeros are strictly constrained to reside upon the critical axis.

Zenodo (CERN European Organization for Nuclear Research)
Black Holes and Theoretical Physics
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