TEBAC BSD-IV: Final Closure and Export Manuscript

This preprint is the final closure and export manuscript for Module BSD-IV in the TEBAC Birch--Swinnerton--Dyer program. Its purpose is to collect the BSD-IV split sequence into a short referee-facing handoff document and to state precisely what the arithmetic-bridge module exports downstream to BSD-V. The manuscript records the source-complete raw verification closure of BSD-IV: D^=EB^=ET^=EM^=EH^=0, hence^₁ₒ₃₈ₕ (E) = (0, 0, 0, 0, 0) the source-complete raw verification sense. The exported BSD-IV package consists of the arithmetic bridgeE^: (-1) (Q) ₙ R, rank bridge\ (-1) =rankE (Q), raw height comparison^₄, =BE^, *\, , \, _, the regulator identity\_ (E) = (E). \ This upload should be read as the BSD-IV arithmetic-bridge export document for the downstream BSD-V assembly. It does not claim to prove the full Birch--Swinnerton--Dyer conjecture by itself, and it does not replace the terminal leading-term assembly that belongs to BSD-V.