What was already known
The manuscript distinguishes earlier hardness for nonuniform demands and conditional connections through Unique Games from unconditional hardness for the uniform-demand problem.
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
Rules out every fixed constant approximation ratio for Uniform Sparsest Cut unless P=NP.
Limitations
The demand is uniform and capacities are nonnegative rationals. The linked Lean scope checks a semidefinite integrality gap, not this NP-hardness reduction; a completed check of the reduction remains undocumented.
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 Lean-scope mismatch review for non-notifying local inclusion.
Read this published revision