A Formal Resolution of the Birch and Swinnerton-Dyer Conjecture: Spectral Stability in Arithmetic Manifolds and the Deterministic Synchronization of Rank
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866902327441489920 |
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| author | Antun Šantak |
| author_facet | Antun Šantak |
| contents | <p> </p> <p>This scientific paper provides a formal resolution to the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves defined over the field of rational numbers. By introducing a framework of non-perturbative spectral anchoring, the author demonstrates that the analytical rank of an elliptic curve is intrinsically equivalent to the algebraic rank of its Mordell-Weil group. The proof establishes that any discrepancy between these indices induces a catastrophic divergence in the manifold's information density, which is precluded by a fundamental principle of topological exclusion, thereby ensuring the global stability of the arithmetic substrate.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19943906 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Formal Resolution of the Birch and Swinnerton-Dyer Conjecture: Spectral Stability in Arithmetic Manifolds and the Deterministic Synchronization of Rank Antun Šantak Birch and Swinnerton-Dyer Conjecture, Spectral Stability, Arithmetic Manifolds, Deterministic Synchronization, Analytic Rank, Algebraic Rank, Elliptic Curves, Topological Integrity, Information Density, Mathematical Physics <p> </p> <p>This scientific paper provides a formal resolution to the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves defined over the field of rational numbers. By introducing a framework of non-perturbative spectral anchoring, the author demonstrates that the analytical rank of an elliptic curve is intrinsically equivalent to the algebraic rank of its Mordell-Weil group. The proof establishes that any discrepancy between these indices induces a catastrophic divergence in the manifold's information density, which is precluded by a fundamental principle of topological exclusion, thereby ensuring the global stability of the arithmetic substrate.</p> <p> </p> |
| title | A Formal Resolution of the Birch and Swinnerton-Dyer Conjecture: Spectral Stability in Arithmetic Manifolds and the Deterministic Synchronization of Rank |
| topic | Birch and Swinnerton-Dyer Conjecture, Spectral Stability, Arithmetic Manifolds, Deterministic Synchronization, Analytic Rank, Algebraic Rank, Elliptic Curves, Topological Integrity, Information Density, Mathematical Physics |
| url | https://doi.org/10.5281/zenodo.19943906 |