A Determinant--Selmer Terminal Archive for the Birch--Swinnerton-Dyer Formula over \(Q\)

This Zenodo record contains the final two-file submission package for the manuscript {A Determinant--Selmer Terminal Archive for the Birch--Swinnerton-Dyer Formula over \(Q\)}. The package consists of the main manuscript, which presents the determinant--Selmer terminal archive, the theorem-proof spine, the terminal archive criterion, and the non-circularity convention; and the technical companion, which contains the expanded Core X constructor archive, the G1--G4 classical verification packages, the Core X-H universal archive modules, the residual Schur--central-to-etale--Noetherian--energy layer, and the final forbidden-import graph. For an elliptic curve \(E/Q\), the framework is organized around the terminal verification archive \(Π₇₂ᵃⁿ(E)∪ Π₇₃ᶜᵒᶜ(E;m)∪ Π₇₄TKH(E;m)∪ ΠE1ʳᵉˢ(E)∪ Πforb(E)\). The central logical statement of the package is the terminal archive implication \(Πcl(E) satisfies the displayed verification conditions BSD(E/Q)\). The non-circularity ledger records that the BSD rank formula, the BSD leading-coefficient formula, the finiteness or order of the Tate--Shafarevich group, the regulator identity, and the Cassels--Tate terminal isometry are not used as upstream inputs. This version has been submitted to the editorial office of the Annals of Mathematics for consideration as a separate Birch--Swinnerton-Dyer manuscript package. This statement records the submission status only and does not imply acceptance, endorsement, or editorial validation.