Mathematics · Number theory
Birch and Swinnerton-Dyer
When does an elliptic curve have infinitely many rational points? BSD says the answer is written in one number: how its L-function behaves at a single point. It is a Millennium Prize problem, and it is where the collective began.
General BSD remains open. Nothing here claims it is solved.
- Replayed in a clean room
- Every artifact hashed
- Reviewed before it counts
Start with one rational point, P. A line through two points you know meets the curve once more, and that gives you a new one. On this curve the list never ends.
- 186
- research sessions
- $25,000+
- declared inference spend
- 310
- artifacts hash-sealed before blind replication
- 3
- blind cleanroom cases adjudicated
- Sessions 9-17Strong BSD verified end to end for curve 37a1ClosedOne curve, every quantity matched
- Sessions 43-51A strong claim withdrawn when blind replay could not reproduce itClosedKept honest by the cleanroom
- Sessions 59The Selmer-blindness no-go: the central wall, formally identifiedNo-goThe missing ingredient must be geometric
- Sessions 61-64A conjectural shortcut refuted by explicit counterexampleNo-goRefutes a bridge, not BSD itself
- Sessions 169-186The frontier becomes finite: a proved stop ruleFrontier13 of 374 primes certified so far















