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This work aims to resolve the Birch and Swinnerton-Dyer conjecture by linking analytic and algebraic ranks of elliptic curves.

August 2, 2026Open Access

[Smt-Vol10 & STCT-Vol6] the Spectral Resolution of the Birch and Swinnerton-Dyer Conjecture via Seonggil Operator Algebra

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This work aims to resolve the Birch and Swinnerton-Dyer conjecture by linking analytic and algebraic ranks of elliptic curves.
Introduced an exact analytic bound using critical roughness index to prove convergence.
Constructed path-integral isomorphism to connect analytic kernel and discrete rational points.
Embedded Galois cohomology classes into Sobolev subspace to address Tate-Shafarevich finiteness.
Proved absolute convergence for the Birch and Swinnerton-Dyer conjecture at s=1.
Established non-degeneracy of the isomorphism using Strict Positive Definiteness of the pairing.
Derived leading Taylor coefficient with Universal Arithmetic Friction constant η ≈ 10^−22.

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Randomized trial addresses the Birch and Swinnerton-Dyer conjecture, indicating new mathematical insights.

Lee Seonggil (2026) studied this question.

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