What was already known
The Lipman–Zariski conjecture predicted smoothness from a locally free tangent sheaf. Positive cases included characteristic-zero hypersurfaces and local complete intersections, log-canonical spaces, and isolated singularities in dimension at least three; positive-characteristic surface counterexamples did not settle the complex case (manuscript introduction, pp. 1–2).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Disproves the characteristic-zero Lipman–Zariski conjecture in the first dimension left by the cited isolated-singularity result.
Limitations
The example is a normal complex affine surface, smooth away from one marked singular point. It does not make a claim about hypersurfaces or log-canonical singularities.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion.
Read this published revision