Domain 04 · Birch–Swinnerton-Dyer

Campaign ID: BSD-001
Mathematical status: open conjecture
Canonical field: elliptic curves over Q
Governance: ADR-0005

Canonical challenge

The campaign separates three nearby obligations that must not be conflated:

• equality of Mordell–Weil rank and complex analytic rank;
• finiteness of the Tate–Shafarevich group;
• the strong leading-term formula with all normalization data explicit.

A parity statement, family result, one-prime theorem, finite computation, or p-adic formula does not by itself establish the universal complex conjecture.

Programme posture

WP00–WP04 have completed source normalization, false-proof analysis, theorem-ledger construction, computational/formal substrate review, and restricted-target selection. The selected target BSD-R2-A1 remains unproved. No WP05 or theorem-strengthening stage is inferred from promotion of the documentary stack.

Canonical artifacts

• Canonical Domain 04 entry
• Detailed historical master-plan filename
• Campaign directory
• Review records
• Governing decision ADR-0005

Claim boundary

The programme has not proved BSD, a new rank theorem, finiteness of Sha, or a new leading-term formula. The current selected target is a bounded research obligation inside the normalized theorem ledger.