What question did this study set out to answer?

This research aims to prove the Birch and Swinnerton-Dyer Conjecture through a novel approach in information theory.

February 16, 2026Open Access

Birch and Swinnerton-Dyer Conjecture: A Proof via Holographic Information Theory

Key Points

This research aims to prove the Birch and Swinnerton-Dyer Conjecture through a novel approach in information theory.
Embedded elliptic curves within the Entropix MESA holographic framework.
Analyzed rational points as stable information states on the 2D holographic screen.
Defined L function as the partition function over these information states.
Demonstrated that the order of vanishing of L(E,s) at s = 1 equals the rank of the Mordell-Weil group.
Proved the finiteness of the Tate-Shafarevich group using the Write Tax mechanism.

Abstract

We prove the Birch and Swinnerton-Dyer Conjecture by embedding elliptic curveswithin the Entropix MESA holographic framework. The key insight is that rationalpoints on an elliptic curve E/Q correspond to stable information states on the 2Dholographic screen, and the rank of the Mordell-Weil group measures the dimension ofthe free information subspace. We show that the L function L(E,s) is the partitionfunction over these states, and its order of vanishing at s = 1 equals the rank. Furthermore, we prove the finiteness of the Tate-Shafarevich group using the informationtheoretic ”Write Tax” mechanism

Birch and Swinnerton-Dyer Conjecture: A Proof via Holographic Information Theory

Key Points

Abstract

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