What was already known
Rokhlin’s 1949 question asked whether ordinary mixing implies higher-order mixing for one transformation. The manuscript distinguishes prior positive results for special group transformations and counterexamples for multi-parameter actions.
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
Answers Rokhlin’s longstanding multiple-mixing problem for a single invertible transformation.
Limitations
The result concerns one invertible probability-preserving transformation, not arbitrary multi-parameter actions.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every invertible mixing probability-preserving transformation is mixing of every finite order: for any k≥3 measurable sets, their translated intersection tends to the product of their measures as successive time gaps diverge.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
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 scoped checking review for non-notifying local inclusion.
Read this published revision