What was already known
Evans and Smart proved differentiability everywhere in all dimensions, while Savin and Evans–Savin established planar gradient continuity and a planar Hölder estimate. General higher-dimensional uniform interior gradient Hölder bounds remained open.
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
Upgrades pointwise differentiability to uniform local C¹,α regularity in every higher dimension.
Limitations
The exponent is dimension-dependent and nonexplicit; no endpoint 1/3 or boundary estimate is claimed. No independent formal proof check is documented for this manuscript.
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