What was already known
Dimension-dependent volume gaps above the equator were known; the sharp next threshold was known in dimension two through the Willmore theorem. The all-dimensional sharp Clifford threshold remained the Solomon–Yau conjecture.
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
Resolves the least-volume conjecture for minimal hypersurfaces of round spheres in all dimensions.
Limitations
Volume is measured on the domain, including covering multiplicity. The claim is a lower bound; it does not assert a full classification of equality cases.
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; technical verification remains Reported.
Read this published revision