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OpenAI reports: The rational Hodge conjecture for CM abelian varieties

OpenAI claims that rational Hodge classes on any complex CM abelian variety admit algebraic-cycle representatives with rational coefficients, in all codimensions.

Sources for this record

What was already known

Known low-dimensional and special Weil-class cases do not provide algebraic cycles for all CM abelian varieties in every dimension and codimension.

What changed and why it matters

Advances the stated target relative to the recorded baseline.

The AI contribution

OpenAI attributes the manuscript to its internal model; individual human contributions remain unspecified.

Limitations

The claim is limited to CM abelian varieties, not all smooth projective varieties. The unrestricted K3 and split-eightfold manuscripts withdrawn in the release are not included. Consequences using other theorems require their hypotheses. Preprint. AIProofWatch read the source statement and context; it has not refereed the proof, compiled a formal development, or established community acceptance.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The original source reports this scoped result; AIProofWatch reviewed its statement, not the full proof.

Accessible artifact / proof

A research manuscript or proof artifact is publicly accessible; availability is not independent checking.

Correction and publication history