What was already known
Earlier constructions gave infinite finitely generated simple amenable groups. Finite presentation remained the obstacle, and some dynamical constructions were known not to have it.
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 the long-standing existence question for infinite finitely presented simple amenable groups.
Limitations
The selected claim is existence of one group; later claims about central kernels and enlargements across families are outside the pinned Lean statement.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note establishes one group that simultaneously has all four properties, with amenability expressed by the Følner condition.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There exists an infinite group that is finitely presented, simple and amenable.
- 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