This manuscript proves the Birch and Swinnerton-Dyer endpoint by fixed-carrier exclusion of analytic-arithmetic mismatch. The earlier structural BSD role-compression paper established the role architecture: elliptic-curve carrier, analytic L-function standing, Mordell-Weil rank readout, and the analytic-arithmetic bridge. The present paper moves from role architecture to endpoint closure. It proves that once the official BSD endpoint is used as a determinate theorem-bearing target on the fixed e
