{"representations":[{"hash_profile":"rfc8785","id":"visual-birch-and-swinnerton-dyer-conjecture-overview","version":3,"sha256":"8354c73b20ae1771e9459eb34135b0c5b9f35d4ba82dab0ffefd49f511343ae4"}],"problem_id":"problem-birch-and-swinnerton-dyer-conjecture","version":9,"sha256":"eeb755ad246dd5cc7e7d48387eefd81a59ccc2b6274d65f5bdd0fb8544f3bb9b","claims":[{"id":"claim-bsd-analytic-rank-at-most-one","version":2},{"id":"claim-bsd-rank-one-converse-finite-sha","version":2},{"id":"claim-bsd-semistable-rank-one-p-part","version":1},{"id":"claim-bsd-supersingular-p-part","version":1},{"id":"claim-bsd-46a1-quadratic-twists","version":1},{"id":"claim-bsd-miller-finite-computations","version":1},{"id":"claim-bsd-rank-target","version":1},{"id":"claim-bsd-full-target","version":1},{"id":"claim-bsd-sha-finiteness-target","version":1},{"id":"claim-bsd-mordell-weil","version":1},{"id":"claim-bsd-strong-implies-rank","version":1},{"id":"claim-bsd-finite-points-consequence","version":1},{"id":"claim-bsd-congruent-number-consequence","version":1},{"id":"claim-bsd-sha-order-consequence","version":1},{"id":"claim-bsd-openai-low-selmer-proposal","version":1},{"id":"claim-bsd-openai-goldfeld-proposal","version":1}],"source_version_ids":["clay-millennium@observed-2026-10-01","clay-millennium@observed-2026-10-10","clay-wiles-bsd@official-description","skinner-annals-2020@published-online-2020-02-13","arxiv-1512.06894@arxiv-v1","arxiv-2409.01350@arxiv-v2","arxiv-2601.16044@arxiv-v3","arxiv-1010.2431@arxiv-v3","kent-bsd-project@0e9519aaeb5c8b8c524f95925eecb970d86bc5b1-metadata-2026-10-10","icarm-curve-273@observed-2026-10-10","openai-bsd-low-selmer@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","openai-goldfeld@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb"],"entry_ids":["birch-and-swinnerton-dyer-conjecture:entry:0:v1","birch-and-swinnerton-dyer-conjecture:entry:0:v2","birch-and-swinnerton-dyer-conjecture:bsd-analytic-rank-at-most-one:v2","birch-and-swinnerton-dyer-conjecture:bsd-official-rank-description:v1","birch-and-swinnerton-dyer-conjecture:bsd-rank-one-converse-finite-sha:v2","birch-and-swinnerton-dyer-conjecture:bsd-semistable-rank-one-p-part:v1","birch-and-swinnerton-dyer-conjecture:bsd-supersingular-p-part:v1","birch-and-swinnerton-dyer-conjecture:bsd-46a1-quadratic-twists:v1","birch-and-swinnerton-dyer-conjecture:bsd-effective-families-2026:v1","birch-and-swinnerton-dyer-conjecture:bsd-46a1-corroboration:v1","birch-and-swinnerton-dyer-conjecture:bsd-miller-finite-computations:v1","birch-and-swinnerton-dyer-conjecture:bsd-ai-project-kent:v2","birch-and-swinnerton-dyer-conjecture:bsd-high-rank-witness-2026:v1","birch-and-swinnerton-dyer-conjecture:bsd-rank-target:v1","birch-and-swinnerton-dyer-conjecture:bsd-full-target:v1","birch-and-swinnerton-dyer-conjecture:bsd-mordell-weil:v1","birch-and-swinnerton-dyer-conjecture:bsd-finite-points-consequence:v1","birch-and-swinnerton-dyer-conjecture:bsd-congruent-number-consequence:v1","birch-and-swinnerton-dyer-conjecture:bsd-openai-selmer:v1","birch-and-swinnerton-dyer-conjecture:bsd-openai-goldfeld:v1","birch-and-swinnerton-dyer-conjecture:bsd-origin-history:v1","birch-and-swinnerton-dyer-conjecture:bsd-gross-zagier-history:v1","birch-and-swinnerton-dyer-conjecture:bsd-modularity-history:v1"],"report_ids":["birch-and-swinnerton-dyer-conjecture:report:0:v1","birch-and-swinnerton-dyer-conjecture:report:0:v2","birch-and-swinnerton-dyer-conjecture:bsd-analytic-rank-at-most-one:v2:report","birch-and-swinnerton-dyer-conjecture:bsd-rank-one-converse-finite-sha:v2:report","birch-and-swinnerton-dyer-conjecture:bsd-semistable-rank-one-p-part:v1:report","birch-and-swinnerton-dyer-conjecture:bsd-supersingular-p-part:v1:report","birch-and-swinnerton-dyer-conjecture:bsd-46a1-quadratic-twists:v1:report","birch-and-swinnerton-dyer-conjecture:bsd-miller-finite-computations:v1:report","birch-and-swinnerton-dyer-conjecture:bsd-rank-target:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-full-target:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-sha-finiteness-target:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-mordell-weil:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-strong-implies-rank:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-finite-points-consequence:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-congruent-number-consequence:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-sha-order-consequence:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-openai-low-selmer-proposal:report:v1","birch-and-swinnerton-dyer-conjecture:bsd-openai-goldfeld-proposal:report:v1"]}