What was already known
Gaboriau’s fixed-price problem asked whether all essentially free probability-measure-preserving actions of the same group have the same cost. No general counterexample was established in the manuscript’s prior-work account.
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
Gives a negative answer to Gaboriau’s general fixed-price problem.
Limitations
The construction compares specified essentially free actions of one finitely generated amalgamated group; it does not assert that every action has one of those costs.
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