What was already known
Bakry–Émery gave dimension-free log-Sobolev bounds under a positive curvature lower bound. Under log-concavity, Gaussian concentration for all Lipschitz functions also implies such a bound; the open question was whether subgaussian control of linear functions alone suffices (manuscript introduction, pp. 1–2).
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 dimension-free logarithmic Sobolev question for subgaussian log-concave measures.
Limitations
The measure must be centered, log-concave, absolutely continuous, and linearly a-subgaussian. The inequality is stated for compactly supported smooth test functions; no log-concavity-free result is claimed.
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