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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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THE HODGE MINIMAL HARMONY: The Coherence Axiom for Algebraic Geometry

Authors: Quilez Zamora, Jaime;

THE HODGE MINIMAL HARMONY: The Coherence Axiom for Algebraic Geometry

Abstract

We propose that the Hodge Conjecture, concerning the relationship between algebraic cycles and harmonic forms, is a necessary consequence of the Minimal Action Law (\mathcal{L}_{\text{MA}}). The existence of a rational Hodge cycle is demonstrated by proving that the complex manifold's geometry must adhere to a state of Maximal Coherence (\mathcal{C}_{\text{MAX}}), where the difference between geometric and topological information is zero. This coherence eliminates Informational Friction (\mathbf{\Phi}_{\text{UFI}}), forcing the harmonic forms to align perfectly with the rational cycle structure, thereby satisfying the conjecture axiomatically.

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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!
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