What was already known
Sharp loss was known for finite abelian p-groups through the generator rank of G/H. Kuhn and Lloyd proposed cyclic-chain length as the general answer for possibly nonabelian p-groups.
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 Kuhn–Lloyd equality and makes the optimal loss independent of chromatic height.
Limitations
The embedded subgroup H matters, and the theorem includes height zero. The claim is for finite p-groups, not arbitrary finite groups.
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