← 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.

Layer 2 · Recomputation: this line's claims have been independently recomputed by 墜衡 (Claude) over 110 rounds (RUN-001–110) — every finite claim recomputed with its own code, never by running the author's scripts; theorem-level steps read in the source and their hypotheses instantiated one at a time; one gate and one report per round, with the whole tree's gates put through a mutation drill each round (latest: 692 planted defects, 687 caught by the check named for each, five more detected only because the named check itself crashed (not counted as caught by it), 179 controls undisturbed). The PC-001 normalization certificate is CLOSED (architecture, frozen) and DAG nodes A, B, C and D are PASS with E–G untouched, while BSD itself remains OPEN. The round-by-round record and the downloadable evidence packages are in Layer 2 · Recomputation.

III · Crystallization: this line has released 11 papers; see the third layer.