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OpenAI reports: Serre’s positivity conjecture

OpenAI claims strict positivity of the Tor Euler characteristic for nonzero finite modules of complementary dimension over a regular local ring, when their tensor product has finite length.

Sources for this record

What was already known

Equicharacteristic and unramified cases, nonnegativity, and further special mixed-characteristic cases were known.

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 theorem assumes nonzero finite modules with finite-length tensor product and complementary dimensions. The paper records another same-scope AI-assisted claim; sole priority is not asserted. 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