What was already known
Ghoussoub–Gui and Ambrosio–Cabré proved lower-dimensional cases. Savin proved the assertion through dimension eight with added directional end-limit assumptions; nonplanar monotone solutions exist from dimension nine onward.
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 remaining dimension-eight monotone rigidity case of De Giorgi’s conjecture for the scalar quartic Allen–Cahn equation.
Limitations
The theorem is for values strictly between the two wells and a strictly positive directional derivative. 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