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OpenAI: A claimed Hodge theorem for all CM abelian varieties

Reported result · significance if the exact claim is established

If verified · conditional significanceClaim scope and evidenceReported result · not independently verified.
If verified · reference score700,000Editorial revision range 400,000–950,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.

Provisional assessment of the stated contribution scope. Scientific evidence and contributor attribution are separate.

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What is claimed?

The manuscript claims algebraic representatives for every rational Hodge class on every complex abelian variety with complex multiplication, in all dimensions and codimensions. It states further implications for Tate and Hodge standard conjectures for abelian varieties.

Scientific scope

This is not the Hodge conjecture for every smooth projective variety. Three withdrawn Weil/K3 manuscripts remain separate records of unsupported proofs; this manuscript was not named in those withdrawal notices, which does not establish its validity or independence from every affected dependency. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.

Evidence state

The manuscript reports a proof. WRS has not independently audited the complete argument or replayed the reported formalization. The grade and score here express conditional significance; they do not certify correctness. The provisional value enters the main reference rankings with an unverified label, but not achieved-science progress totals.

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