What was already known
Sogge conjectured the improvement over sharp fixed-time bounds produced by averaging over time. Earlier square-function, wave-packet, and decoupling methods obtained partial ranges; the critical p = 3 estimate was the missing interpolation point (manuscript introduction, 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
Resolves Sogge’s Euclidean local-smoothing conjecture in three spatial dimensions.
Limitations
At p = 3 the theorem allows every positive Sobolev loss but does not assert the lossless epsilon = 0 endpoint. A Bochner–Riesz bound is a consequence, not an additional separately counted contribution here.
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