What was already known
Quasi-isometric recognition was established for virtually nilpotent groups and several solvable Lie models, including Sol and selected split abelian-by-abelian groups. The general virtually polycyclic class 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
Resolves the Eskin–Fisher–Whyte lattice-recognition conjecture in its full virtually polycyclic form.
Limitations
The comparison group need only be finitely generated. A lattice realization may use a different simply connected solvable Lie group from the original.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves virtually polycyclic recognition and the finite-index uniform-lattice consequence.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is itself virtually polycyclic.
- 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