# Coarse-group recognition contract

Family 255: Quasi-isometric recognition of virtually polycyclic groups. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track virtual polycyclicity under quasi-isometry and the companion solvable-Lie-lattice recognition statement.

## Applicability and commercial boundary

A quasi-isometry assumption is not obtained merely from sampled metric similarity; the resulting Lie group can differ.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Inspect effective recognition and explicit quasi-isometry input requirements.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Quasi-isometric recognition of virtually polycyclic groups](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/quasi-isometric-recognition-of-virtually-polycyclic-groups-September-24-2026/paper.pdf).