What was already known
Jerison and Savin proved flatness of stable smooth-cross-section cones through dimension four, giving a lower bound of five for the critical dimension. De Silva and Jerison had already constructed a nonflat global minimizing cone in dimension seven. The unresolved cases were dimensions five and six.
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
Closes the five-and-six-dimensional gap and, with the known dimension-seven example, identifies seven as the critical dimension.
Limitations
The linked Lean note verifies only existence of a dimension-seven nonflat minimizer, which the manuscript credits to De Silva and Jerison. It does not check the new flatness classification through dimension six.
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