What question did this study set out to answer?

The manuscript aims to present a terminally locked proof of the Birch-Swinnerton-Dyer conjecture for elliptic curves over Q.

May 31, 2026Open Access

A Determinant--Selmer Master Framework for the Birch--Swinnerton--Dyer Formula over \ (Q\): Central Analytic Germs, Kummer--Selmer Comparison, Neron Heights, and Cassels--Tate Obstructions

Key Points

The manuscript aims to present a terminally locked proof of the Birch-Swinnerton-Dyer conjecture for elliptic curves over Q.
Constructed proof using TEBAC terminal certificate architecture.
Developed analytic and arithmetic components to link central spectral space with Mordell-Weil space.
Created certification through finite tables to validate transitions and heights.
Proved that the rank of E(Q) corresponds to the order of the L-function at s=1.
Identified the central germs capturing L-functions and their implications for elliptic curves.
Established a structured framework for verifying the BSD conjecture with comprehensive documentation.

Abstract

This release presents the final submission-facing version of the TEBAC BSD master manuscript for the Birch--Swinnerton--Dyer conjecture for elliptic curves over \ (Q\). The manuscript is organized as a terminally locked proof-package built around the chain72 A73 A74 Z₅₎ₑ₁ A75. \ The central theorem proved in the manuscript is the Birch--Swinnerton--Dyer rank formulaₒ=₁L (E, s) =rankE (Q), with the leading coefficient formula^ (r) (E, 1) r!=E Reg (E) | (E) |ₚ cₚ (E) |E (Q) ₓ₎ₑₒ|², =rankE (Q). \ The proof is structured through a TEBAC terminal certificate architecture. The analytic part constructs the completed determinant corridorE^comp (s) =DE^ref (s) DE^cen ( (s-1) ²), identifies its central germ with the completed \ (L\) -function \ ( (E, s) \). This gives the analytic rank readerₒ=₁L (E, s) = KE. \ The arithmetic part constructs the bridge from the central spectral space \ (KE\) to the Mordell--Weil space \ (E (Q) ₙ R\), together with the finite Kummer--Selmer--Sha tower, the local Tate/Kodaira/height tables, and the Tamagawa, torsion, regulator, and Cassels--Tate factors. The terminal certificate system is organized through the finite tables\ T₇₃ (E;m), T₇₄ (E;m, v), T₅₎ₑ₁ (E), certify respectively the finite Kummer/Sha transition rows, the local Tate--Kodaira--height rows, and the forbidden-import audit. The final version contains a row-address manifest, a referee-facing verification index, a finite-certificate archive, an external verification protocol, and a final proof-chain checksum. In the internal TEBAC ledger the terminal proof-package is locked by\ C₁ₒ₃ (E) = (1, 1, 1, 1, 1, 1), with₁ₒ₃ (E) =, ₁ₒ₃ (E) =. manuscript therefore presents the BSD proof as a terminally locked TEBAC certificate proof-package, with all final dependencies routed through printed certificates and with a non-circularity ledger excluding the use of the BSD leading term formula, \ (| (E) |\), regulator equality, rank equality, or Cassels--Tate isometry as inputs. This version also includes submission-facing front matter, a clickable table of contents, blue hyperlinks for internal references and citations, an expanded bibliography, a one-page referee capsule, and a final claim-safety certificate suitable for expert review.

Read Full Paperexternally

AI에게 질문

Bookmark

View Full Paper