What is recorded here?
For an elliptic curve over the rational numbers, the manuscript claims the complete Birch–Swinnerton-Dyer leading-term formula whenever its full q-power Selmer group has corank zero or one at some prime q. It includes finiteness of the Tate–Shafarevich group and all prime factors of the formula. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The hypothesis is on the full Selmer group, not merely Mordell–Weil rank. This is not BSD in every rank. The paper imports the unrestricted converse and the two-primary formula from separate manuscripts. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.
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People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed The recorded author list is incomplete.
OpenAI research model · OpenAI · Unreleased internal frontier model; exact identifier not disclosed
Source-reported mathematical argument generation; human preparation/editing roles retained separately where disclosed. Source-reported attribution; provider attestation is unavailable.
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English catalogue narrative
OpenAI: Exact BSD formula under Selmer corank zero or one
For an elliptic curve over the rational numbers, the manuscript claims the complete Birch–Swinnerton-Dyer leading-term formula whenever its full q-power Selmer group has corank zero or one at some prime q. It includes finiteness of the Tate–Shafarevich group and all prime factors of the formula. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
Scientific scope
The hypothesis is on the full Selmer group, not merely Mordell–Weil rank. This is not BSD in every rank. The paper imports the unrestricted converse and the two-primary formula from separate manuscripts. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed
OpenAI research model / OpenAI / Unreleased internal frontier model; exact identifier not disclosed: Source-reported mathematical argument generation; human preparation/editing roles retained separately where disclosed (source reported).