Determinant-Line Closure Program for the Birch–Swinnerton–Dyer Conjecture

This project develops a unified determinant-line framework for the Birch–Swinnerton–Dyer conjecture. The series of papers (I–X) reformulates the BSD conjecture in terms of determinant lines of Selmer complexes, establishes rigidity and normalization results, and constructs a descent mechanism from the cyclotomic Iwasawa Main Conjecture to the classical BSD formula. The program isolates all remaining difficulties to explicit arithmetic and computational problems (not conceptual or structural gaps), and shows that, conditional on standard Iwasawa-theoretic inputs, the BSD conjecture is logically complete and formally closed. This project is intended as a structural and conceptual foundation for future arithmetic advances toward a full proof of BSD.