| _version_ | 1866901774583988224 |
|---|---|
| author | Quilez Zamora, Jaime |
| author_facet | Quilez Zamora, Jaime |
| contents | <p>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.</p> <p> </p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17602353 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | THE HODGE MINIMAL HARMONY: The Coherence Axiom for Algebraic Geometry Quilez Zamora, Jaime <p>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.</p> <p> </p> <p> </p> |
| title | THE HODGE MINIMAL HARMONY: The Coherence Axiom for Algebraic Geometry |
| url | https://doi.org/10.5281/zenodo.17602353 |