# One-relator hyperbolicity conditional adapter

Family 258: Gersten’s conjecture and virtual compact specialness of one-relator groups. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Organize hyperbolicity and virtual specialness consequences when a one-relator group contains no specified Baumslag–Solitar subgroup.

## Applicability and commercial boundary

Verifying the absence of all such subgroups and constructing a finite special cover may remain difficult.

## 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

Read decision procedures and witness-size bounds before implementing recognition.

## 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).

[Baumslag-Solitar-free one-relator groups are hyperbolic](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Baumslag-Solitar-free-one-relator-groups-are-hyperbolic-September-25-2026/paper.pdf).