Group theory·OpenAI Math·Result 255·Lean formalisation listed
Quasi-isometric recognition of virtually polycyclic groups
One of the 372 results in OpenAI's public mathematics catalogue, filed under group theory: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a result titled ‘Quasi-isometric recognition of virtually polycyclic groups’ (group theory) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More, is on YouTube.
Chapter 69 of 84 in Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More · starts at 23:35 · watch from there on YouTube →
What OpenAI claims
Proves that every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic, resolving the Eskin–Fisher–Whyte lattice-recognition conjecture. Equivalently, a group quasi-isometric to a lattice in a connected simply connected solvable Lie group is virtually a uniform lattice in some such Lie group, possibly a different one. (Lean)
Paper
Quasi-isometric recognition of virtually polycyclic groups
OpenAI's abstract We prove that every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic. This resolves the lattice-recognition conjecture of Eskin, Fisher and Whyte, which allows the ambient solvable Lie group in the conclusion to differ from the one in the hypothesis.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Proves that every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic, resolving the Eskin–Fisher–Whyte lattice-recognition conjecture. Equivalently, a group quasi-isometric to a lattice in a connected simply connected solvable Lie group is virtually a uniform lattice in some such Lie group, possibly a different one. (Lean)
- Where is the proof?
- In the paper, Quasi-isometric recognition of virtually polycyclic groups (PDF).
- Is there a video?
- Yes, on YouTube (29:10, chapter 69).
Also in
- Chapter 8 of 9 in Cannon's Conjecture, Thompson's Group F and 7 More in Group Theory · starts at 2:25 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 2 of 4: PCP for PPAD, Birkhoff Conjecture and 82 More · Compilation · 29:10 · chapter 69 from 23:35 · description, sources and chapters →
Related results in Group theory
- 256Nonsingular systems of equations over arbitrary groupsVideoLean
- 257A hyperbolic group without a geometric CAT(0) actionVideoLean
- 258Gersten’s conjecture and virtual compact specialness of one-relator groupsVideo
- 259A group without fixed priceVideo
- 246Cannon's conjectureVideoLean
- 247An infinite finitely presented residually finite 2-group and a finitely presented nil algebraVideoLean
