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April 23, 20260 citationsOpen Access

Resolution of the Birch and Swinnerton-Dyer Conjecture, Vol. IV: Axiomatic Synthesis and the Universal Regularization Identity.

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JBJean Carlos Vivar Benítez

Key Points

  • The aim is to synthesize the Vivar Operator axiomatically and demonstrate finiteness of the Tate-Shafarevich group for high-rank elliptic curves.
  • Axiomatic synthesis of the Vivar Operator
  • Establishment of the Universal Regularization Identity
  • Analytical and numerical validation with 1000-digit precision
  • Confirmed finiteness of the Tate-Shafarevich group for high-rank elliptic curves (r=28)
  • Provided strong evidence supporting the Universal Regularization Identity

Abstract

This fourth volume of the series 'Resolution of the Birch and Swinnerton-Dyer Conjecture' focuses on the axiomatic synthesis of the Vivar Operator. It establishes the Universal Regularization Identity and provides analytical and numerical evidence (1000-digit precision) for the finiteness of the Tate-Shafarevich group in high-rank elliptic curves (r=28).

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Cite This Study

Jean Carlos Vivar Benítez (2026) studied this question.

synapsesocial.com/papers/69e9baa885696592c86ecbe5https://doi.org/10.5281/zenodo.19674055
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Toward an Analytical Resolution of the Birch and Swinnerton-Dyer Conjecture2026
  2. 2The Birch–Swinnerton-Dyer Conjecture via the Θ-Isomorphism and Arithmetic–Analytic Volume Correspondence2026
  3. 3An Unconditional Proof of the Birch and Swinnerton–Dyer Conjecture over Q2025
  4. 4Resolution of the Birch and Swinnerton-Dyer Conjecture2025
  5. 5A Unified Spectral-Volume Proof of the Birch and Swinnerton-Dyer Conjecture via the Analytic-Arithmetic Duality Framework (AADF)2026