← AMRAL · PROGRAM-BSD

BSD Conjecture

Birch and Swinnerton-Dyer Conjecture · One of the Clay Millennium Prize Problems

Does not claim to prove BSD, nor treats numerical matches as proofs. The core tool is a curve-level certificate ladder (C0 identity → C6 weak BSD → C7 single-prime strong form → C8 Sha finite and exact → C9 full strong BSD → C10 family theorem)—for every curve and every prime, it precisely marks exactly which level has been proven, rather than just storing a boolean "BSD true/false" value. During the research process, the system conducted a formal audit on the researcher's own old claims ("lattice rank convergence") and rejected them, which is the point of highest discipline in this line.

All four sub-threads are now online: Phase 0, P5, Phase 1, Phase 2 (40/40 COMPLETE) — the current true status of each line is listed below; the P5 core comparison remains OPEN, and completion is not claimed in advance. An independent stress-test audit of the existing content, concluding VERIFIED_ADVANCE, exists on the Chinese site and is not yet translated to English.