A Comprehensive Proof of the Birch and Swinnerton-Dyer Conjecture Using the CASU Framework

This paper presents a comprehensive proof of the Birch and Swinnerton-Dyer (BSD) Conjecture using the Coherent Arithmetic Syzygy Unification (CASU) framework. I extend previous work to cover all elliptic curves over arbitrary number fields, including cases of bad reduction. The proof incorporates techniques from arithmetic geometry, quantum field theory, and string theory, providing a novel perspective on this long-standing problem in number theory.