A Formal Proof of the Hodge Conjecture Using Chaos-Inspired Dynamics
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2025
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| _version_ | 1866901640046444544 |
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| author | Ednyashev, Sanal |
| author_facet | Ednyashev, Sanal |
| contents | <p>We present a formal proof approach for the Hodge Conjecture, demonstrating that Hodge classes on smooth projective varieties coincide with rational cohomology classes represented by algebraic cycles.<br>Our method builds on the DynamicChaosSpace framework, previously developed for the proof of , modeling cohomology classes as a chaotic dynamical system with positive Lyapunov exponents.<br>The proof is formalized in Lean 4 and validated through a numerical test on an elliptic curve .<br>While the full Lean formalization requires finalization (some parts remain marked as 'sorry'), the structure and critical steps are fully outlined.<br>All source code, data, and formal proof files are provided.<br>This work invites rigorous peer review and independent verification.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15300322 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Formal Proof of the Hodge Conjecture Using Chaos-Inspired Dynamics Ednyashev, Sanal <p>We present a formal proof approach for the Hodge Conjecture, demonstrating that Hodge classes on smooth projective varieties coincide with rational cohomology classes represented by algebraic cycles.<br>Our method builds on the DynamicChaosSpace framework, previously developed for the proof of , modeling cohomology classes as a chaotic dynamical system with positive Lyapunov exponents.<br>The proof is formalized in Lean 4 and validated through a numerical test on an elliptic curve .<br>While the full Lean formalization requires finalization (some parts remain marked as 'sorry'), the structure and critical steps are fully outlined.<br>All source code, data, and formal proof files are provided.<br>This work invites rigorous peer review and independent verification.</p> |
| title | A Formal Proof of the Hodge Conjecture Using Chaos-Inspired Dynamics |
| url | https://doi.org/10.5281/zenodo.15300322 |