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Preprint . 2025
License: CC BY
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image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
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Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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The Riemann Hypothesis as a Harmonic Collapse Theorem in a Logarithmic Resonance Field

Authors: Reavis, Matthew;

The Riemann Hypothesis as a Harmonic Collapse Theorem in a Logarithmic Resonance Field

Abstract

Version 1 – Foundational Harmonic Collapse ModelThis initial version introduces the harmonic collapse framework for the Riemann Hypothesis, demonstrating destructive interference alignment along the critical line through frequency-phase superposition. It outlines the core intuition, functional equation symmetry, and spectral collapse behavior that set the stage for the full operator formalism in Version 2. Version 2 – Complete Formalization and Operator ExtensionThis second version presents a full formalization of the harmonic collapse proof of the Riemann Hypothesis, including expanded lemmas, theorem structure, numerical simulations, and operator-based spectral validation. It introduces an eigenfrequency detection operator T\mathcal{T}T, whose residuals dynamically confirm collapse points aligned with known Riemann zeros. The proof integrates Li coefficient positivity, field trench stability, and Nyman–Beurling compatibility, framing the critical line Re(s)=12\text{Re}(s) = \frac{1}{2}Re(s)=21 as the unique corridor for total interference cancellation. This version is intended as the definitive model-based submission for peer review and independent replication.

Keywords

harmonic collapse, Physics, Wave Mechanics, Riemann Hypothesis, zeta function, Quantum field theory, number theory, Spectral Theory, Mathematical physics, FOS: Mathematics, Field Theory, Foundational Mathematics, Mathematical Physics, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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