What was already known
Earlier constructions gave Lebesgue spectral components or related group actions; the manuscript distinguishes these from one bilateral Lebesgue orbit spanning the whole centered space of a smooth probability-preserving system.
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
Solves the probability-preserving form of Banach’s simple Lebesgue-spectrum problem in smooth dynamics.
Limitations
The claim concerns standard volume on the three-torus and the mean-zero L² space, excluding the constant functions.
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
- A C∞ diffeomorphism of the three-torus preserves standard volume and has simple Lebesgue Koopman spectrum on its entire mean-zero L² space.
- 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