{"representations":[{"id":"visual-hodge-conjecture-overview","version":1,"sha256":"7d6846e5f5f2cb4ffa8b8ead84646542471e2134c05a19ccef0f2d0e2e2f3a26"}],"problem_id":"problem-hodge-conjecture","version":6,"sha256":"8189c80c87b63a7e34ec900031085914db53a3d018b8de52a96f875e9c567fc5","claims":[{"id":"claim-hodge-divisor-classes","version":1},{"id":"claim-hodge-dimension-at-most-three","version":2},{"id":"claim-hodge-abelian-fourfolds","version":1},{"id":"claim-hodge-weil-fourfold-powers","version":2},{"id":"claim-hodge-motivated-transfer","version":1},{"id":"claim-integral-hodge-counterexamples","version":1},{"id":"claim-hodge-rational-target","version":1},{"id":"claim-hodge-kunneth-consequence","version":1},{"id":"claim-hodge-inverse-lefschetz-consequence","version":1},{"id":"claim-hodge-kahler-extension","version":1},{"id":"claim-hodge-broe-tate-fourfolds","version":1},{"id":"claim-hodge-openai-cm-proposal","version":1},{"id":"claim-hodge-openai-milne-proposal","version":1}],"source_version_ids":["clay-millennium@observed-2026-10-01","clay-millennium@observed-2026-10-10","clay-deligne-hodge@official-description","arxiv-2502.03415@arxiv-v2","arxiv-2504.13607@arxiv-v2","arxiv-math-0501348@arxiv-v3","arxiv-2609.27916@arxiv-v2-withdrawn","arxiv-2608.28651@arxiv-v1","arxiv-2504.13607@journal-2026-103876","openai-hodge-cm@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","openai-milne-rationality@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb"],"entry_ids":["hodge-conjecture:entry:0:v1","hodge-conjecture:entry:0:v2","hodge-conjecture:hodge-divisor-classes:v1","hodge-conjecture:hodge-dimension-at-most-three:v2","hodge-conjecture:hodge-abelian-fourfolds:v1","hodge-conjecture:hodge-weil-fourfold-powers:v1","hodge-conjecture:hodge-motivated-transfer:v1","hodge-conjecture:integral-hodge-counterexamples:v1","hodge-conjecture:hodge-withdrawal-2026:v1","hodge-conjecture:hodge-rational-target:v1","hodge-conjecture:hodge-projector-consequence:v1","hodge-conjecture:hodge-lefschetz-consequence:v1","hodge-conjecture:hodge-kahler-boundary:v1","hodge-conjecture:hodge-broe-tate-fourfolds:v1","hodge-conjecture:hodge-weil-journal:v1","hodge-conjecture:hodge-openai-cm:v1","hodge-conjecture:hodge-openai-milne:v1","hodge-conjecture:hodge-origin-history:v1","hodge-conjecture:hodge-divisor-history:v1","hodge-conjecture:hodge-cycle-obstruction:v1"],"report_ids":["hodge-conjecture:report:0:v1","hodge-conjecture:report:0:v2","hodge-conjecture:hodge-divisor-classes:v1:report","hodge-conjecture:hodge-dimension-at-most-three:v2:report","hodge-conjecture:hodge-abelian-fourfolds:v1:report","hodge-conjecture:hodge-weil-fourfold-powers:v1:report","hodge-conjecture:hodge-motivated-transfer:v1:report","hodge-conjecture:integral-hodge-counterexamples:v1:report","hodge-conjecture:hodge-rational-target:report:v1","hodge-conjecture:hodge-kunneth-consequence:report:v1","hodge-conjecture:hodge-inverse-lefschetz-consequence:report:v1","hodge-conjecture:hodge-kahler-extension:report:v1","hodge-conjecture:hodge-broe-tate-fourfolds:report:v1","hodge-conjecture:hodge-weil-journal:report:v1","hodge-conjecture:hodge-openai-cm-proposal:report:v1","hodge-conjecture:hodge-openai-milne-proposal:report:v1"]}