What was already known
Residual finiteness held for several established classes of hyperbolic groups, while the general question for word-hyperbolic groups remained open.
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 the long-standing residual-finiteness question for hyperbolic groups.
Limitations
The selected formalized statement is the group construction; nonlinearity over every field is not part of it.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note constructs a torsion-free word-hyperbolic group that is not residually finite.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There exists a torsion-free word-hyperbolic group that is not residually finite.
- 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