What was already known
Uniform Urysohn-width results were developed under pointwise positive scalar-curvature bounds. The manuscript extends the uniform conclusion to a lower bound on the scalar Schrödinger operator.
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
Strengthens the macroscopic-width theorem from pointwise to spectral scalar curvature.
Limitations
The bound is measured in the original metric and applies to compact or noncompact manifolds without orientability, spin or bounded-geometry assumptions.
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; technical verification remains Reported.
Read this published revision