What was already known
Trudinger and Wang had a singular dimension-ten example, which was not smooth at the origin or positive definite everywhere. Their two-dimensional entire-graph rigidity result and the companion three-through-nine complete-graph theorem did not settle this smooth dimension-ten case.
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 smooth entire-graph affine Bernstein assertion in dimension ten under pointwise Hessian positivity.
Limitations
No global uniform Hessian lower bound or Berwald–Blaschke completeness is claimed. The linked Lean note checks a different dimension-three-through-nine complete-graph rigidity theorem, not this counterexample.
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, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision