What was already known
Finite-entropy ergodic systems could be realized by toral automorphisms with full-support invariant Borel probabilities, but full support does not imply a smooth positive invariant density.
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
Shows that even zero entropy does not guarantee smooth positive-volume realization in any finite dimension.
Limitations
The obstruction concerns a smooth strictly positive density; models with singular invariant measures remain possible. The linked Lean scope constructs only a finite-entropy no-model example, not the claimed zero-entropy one.
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