TEBAC Birch--Swinnerton--Dyer Program: Expanded Annals/JAMS Master Architecture with Central-Germ Analytic Determinant and Selmer--Height--Sha Certificates

This preprint presents the expanded Annals/JAMS-facing master architecture of the TEBAC Birch--Swinnerton--Dyer program for elliptic curves over \ (Q\). The target statements areₒ=₁L (E, s) =rankE (Q), for=rankE (Q), \^ (r) (E, 1) r!=E\, Reg (E) \, | (E) |ₚ cₚ (E) |E (Q) ₓ₎ₑₒ|². \ The manuscript is written as a claim-safe master reduction paper rather than as a completed \ (100\%\) unconditional proof. It records the current state of the TEBAC determinant--Selmer--height--Sha architecture and isolates the remaining terminal certificates required for a full unconditional proof. The analytic side is organized around the central-germ determinant route near \ (s=1\). The completed determinant is written asE^comp (s) =DE^ref (s) \, DE^cen ( (s-1) ²), the central analytic target is the germ identityE^comp (s) = (E, s) \ (s=1\). This is reduced to central log-derivative ledger matching, no-spurious-center control, central unit normalization, and independent central spectral multiplicity. The arithmetic side develops a finite response-matrix bridge\E (K₄, ₐ) =E (M₄, ₐ) S^red₄, ₂₄₍, ₄, ₐ=E (Q) ₅ₑ₄₄ ₙ Q. bridge is reduced to detector no-loss, primitive packet spanning, and the spectral full-rank certificate (TEZE) = ₐ^prim₄, ₂₄₍. \ The Selmer--Kummer comparison is organized place by place: good primes, bad primes, primes dividing the level, the Archimedean place, and the global Kummer image. The height/regulator block is reduced to local Néron-symbol calibration^raw₄, ₗ, ₒ₏₄₂ (u, v) = D₂₄ₔ, D₂₄ₕₓ^Ner every place \ (x\). The final BSD-V assembly records the remaining Sha, Tamagawa, torsion, and Cassels--Tate certificates needed to convert the formal coefficient ledger into the classical BSD leading-term formula. An earlier, incomplete architectural chain of this TEBAC BSD proof attempt received a desk rejection from the Journal of the American Mathematical Society because the proof architecture was not yet complete as a full unconditional proof. The present version is a substantially expanded and claim-safe master architecture. It is estimated by the author to contain approximately \ (60\%\) classical unconditional closure of the intended proof, with the remaining part reduced to explicitly stated terminal certificates. The remaining terminal certificates include: E^comp (s) = (E, s) central germs at s=1, \ (TEZE) = ₐ^prim₄, ₂₄₍, \^raw₄, ₗ, ₒ₏₄₂=\, \ ₓ^Ner all places x, \ OE^spec (E), ^spec=\, \ ₂ₓ. \ Once these terminal blocks are completed to a fully unconditional proof, the manuscript is planned for submission to Annals of Mathematics around mid-October 2026, or earlier as a completed revised version for possible resubmission to JAMS. No claim in this upload should be interpreted as using the BSD rank formula, the BSD leading coefficient formula, or the equality\| (E) |=Pf (T) ² an input. These are intended terminal outputs, conditional on the explicitly listed certificates.