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This volume establishes the Universal Regularization Identity and shows finiteness of the Tate-Shafarevich group in high-rank elliptic curves, suggesting important implications for number theory.
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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Jean Carlos Vivar Benítez (2026) studied this question.
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