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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Autore principale: Antun Šantak
Natura: Recurso digital
Pubblicazione: Zenodo 2026
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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>
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publishDate 2026
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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