What question did this study set out to answer?

The aim is to enhance the analytic determinant identity in the Birch–Swinnerton–Dyer problem framework.

June 2, 2026Open Access

Analytic Determinant Gate and Completed (L)-Function Ledger

Q: What does this research mean for the field?

The analytic determinant identity layer in the determinant-Selmer approach to the Birch-Swinnerton-Dyer problem can be isolated by consolidating the analytic determinant gate into a single H1-H8 module to establish the completed determinant comparison. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Key Points

The aim is to enhance the analytic determinant identity in the Birch–Swinnerton–Dyer problem framework.
Consolidation of analytic determinant gate into H1--H8 module.
Isolation of the analytic determinant identity layer in the determinant--Selmer approach.
Focus on the completed determinant comparison D_E^{comp}(s)= ext{Λ}(E,s).
Successfully integrates the analytic determinant gate into a modular structure.
Establishes a definitive relationship between D_E^{comp}(s) and the completed Hasse–Weil L-function.

Abstract

This preprint is Core VII of the TEBAC BSD program. Version 2. 0 supersedes the initial Core VII version by consolidating the analytic determinant gate into a single H1--H8 module. The paper isolates the analytic determinant identity layer in the determinant--Selmer approach to the Birch--Swinnerton--Dyer problem over \ (Q\). The central target is the completed determinant comparison \ (DE^comp (s) = (E, s) \), where \ (DE^comp (s) \) is the completed determinant candidate on the spectral side and \ ( (E, s) \) is the completed Hasse--Weil \ (L\) -function of an elliptic curve \ (E/Q\). The consolidated H1--H8 chain includes: Euler

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