lean artifact · pending
Artifact ↗Source authenticated
Quasi-isometric rigidity of virtually polycyclic groups (the Eskin-Fisher-Whyte lattice-recognition conjecture)
Theorem 1.1: every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic; Corollary 1.2: a finitely generated group quasi-isometric to a lattice in a connected simply connected solvable Lie group has a finite-index subgroup that is a uniform lattice in some (possibly different) such Lie group. The key input is a uniform bounded-height theorem: every self quasi-isometry of a unimodular real-triangulable solvable Lie group preserves the exponential height map up to bounded error and one of finitely many linear symmetries. Amenability then gives elementary amenability, and finiteness and duality give virtual polycyclicity. It does not classify solvable groups up to quasi-isometry or describe their quasi-isometry groups in general.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Quasi-isometric rigidity of virtually polycyclic groups (the Eskin-Fisher-Whyte lattice-recognition conjecture) · QI recognition of polycyclic groups
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
VibeMathed record: Quasi-isometric rigidity of virtually polycyclic groups (the Eskin-Fisher-Whyte lattice-recognition conjecture) evidence for this event
Theorem 1.1: every finitely generated group quasi-isometric to a finitely generated virtually polycyclic group is virtually polycyclic; Corollary 1.2: a finitely generated group quasi-isometric to a lattice in a connected simply connected solvable Lie group has a finite-index subgroup that is a uniform lattice in some (possibly different) such Lie group. The key input is a uniform bounded-height theorem: every self quasi-isometry of a unimodular real-triangulable solvable Lie group preserves the exponential height map up to bounded error and one of finitely many linear symmetries. Amenability then gives elementary amenability, and finiteness and duality give virtual polycyclicity. It does not classify solvable groups up to quasi-isometry or describe their quasi-isometry groups in general. parent of this event
Quasi-isometric rigidity of virtually polycyclic groups (the Eskin-Fisher-Whyte lattice-recognition conjecture) evidence for this event
This event attributed to Unreleased internal OpenAI model
Lean: OAI/GroupTheory/PolycyclicRecognition/Recognition.lean (group_recognition) evidence for this event
Quasi-isometric rigidity of virtually polycyclic groups (the Eskin-Fisher-Whyte lattice-recognition conjecture) parent of this event
Eskin, Fisher, Whyte, Quasi-isometries and rigidity of solvable groups (PAMQ 2007) evidence for this event
Act on this frontier