What was already known
Bourgain’s counterexample requires Sobolev regularity s >= 1/3 in the plane. Du, Guth, and Li proved convergence for s > 1/3, leaving equality open (manuscript introduction, History and significance, pp. 2–3).
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
Settles the sharp planar Sobolev endpoint of Carleson’s Schrödinger convergence problem.
Limitations
The theorem specifies Gaussian regularization before the time limit and does not assert the stronger endpoint local L3 maximal estimate.
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.
Read this published revision