BSD IV: Arithmetic Bridge, Exact Local Detection, and Residual-Existence Reductions (Audited Status Version)

This preprint records the current expanded verification state of Module BSD-IV in the TEBAC Birch--Swinnerton--Dyer program. BSD-IV is the arithmetic bridge module: its role is to connect the central spectral kernel imported from the upstream analytic-rank layer with the Mordell--Weil free part of the elliptic curve, and then to compare the induced spectral height pairing with the classical Neron--Tate height pairing. The present version contains a consolidated and expanded proof-chain audit of the BSD-IV external verification ledger. The detector comparison, support-boundary reciprocity comparison, and terminal Selmer/Sha-channel routing have been stabilized as verified…