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ADR-0005 — Initialize Birch–Swinnerton-Dyer as a governed source-and-equivalence campaign

Date: 2026-07-24
Status: Accepted and WP00 promoted
Owner: The Amanuensis with the Axiomatist, Cartographer, Steward, Archivist, and Referee

Context

The Birch–Swinnerton-Dyer name is used for a rank equality, finiteness of the Tate–Shafarevich group, a strong leading-term formula, parity statements, p-adic conjectures, restricted converse theorems, family theorems, and finite computations. These statements are related but not interchangeable. Normalization drift in Euler factors, periods, exceptional-zero corrections, or Selmer local conditions can turn a correct restricted theorem into an incorrect global claim.

Decision

Initialize campaign BSD-001 and Work Package BSD-WP00 under these controls:

  1. BSD-RANK-Q, BSD-SHA-Q, and BSD-LEAD-Q are separate universal obligations.
  2. Use a complete finite Hasse–Weil L-function and record an explicit concordance with Wiles's initially incomplete official notation.
  3. Identify a p^infinity-Selmer corank with Mordell–Weil rank only after controlling the Sha[p^infinity] contribution.
  4. Root numbers and parity theorems determine parity only, not exact rank.
  5. Every converse or p-part theorem retains curve class, prime, reduction, residual-representation, direction, and normalization hypotheses.
  6. Split p-adic BSD into ordinary, multiplicative exceptional-zero, supersingular signed, and multivariable profiles.
  7. Never silently promote individual-curve, finite-database, family, proportion, or density statements to the universal quantifier.
  8. Begin formalization with statement separation, corank algebra, finite Euler-factor conversions, parity logic, and ledger validation.
  9. Admit no mechanism, novelty, or progress claim at WP00.

Alternatives rejected

  • Treating rank equality as the entire refined conjecture.
  • Using Selmer rank as a synonym for Mordell–Weil rank.
  • Using a root-number sign as an exact-rank predictor.
  • Pooling all p-adic results under one theorem node.
  • Beginning with large curve databases or twist searches before the semantic audit.

Consequences

  • BSD-WP00 is promoted after Programme policy checks, independent Referee reconstruction, and Amanuensis integration.
  • BSD-WP01 and BSD-WP02 may proceed in parallel.
  • Restricted-target and mechanism selection remain behind later Council gates.
  • Exact low-rank theorem concordance, the expanded p-converse/p-part taxonomy, recent twist-family provenance, and formal-library reconnaissance remain nonblocking debt.

Affected artifacts

  • DOMAIN_03_BIRCH_SWINNERTON_DYER_MASTER_PLAN.md
  • campaigns/birch_swinnerton_dyer/WP00_FOUNDATION_STATUS/
  • reviews/birch_swinnerton_dyer/BSD-WP00.agent_review.yaml
  • docs/AGENT_COUNCIL_ARTIFACT_LEDGER.md
  • docs/AGENT_COUNCIL_TERMINOLOGY_REGISTRY.md
  • MATH-PROGRAMME#66

Review provenance

  • Canonical tracker: https://github.com/grandchallenge/MATH-PROGRAMME/issues/66.
  • Pull request: https://github.com/grandchallenge/MATH-PROGRAMME/pull/67.
  • Review record: reviews/birch_swinnerton_dyer/BSD-WP00.agent_review.yaml.
  • Programme policy workflow: 30084664646.

Supersedes

No prior Birch–Swinnerton-Dyer campaign decision.