# Residual-finiteness versus torsion fixture

Family 247: An infinite finitely presented residually finite 2-group and a finitely presented nil algebra. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Give group and algebra software a reference for an infinite finitely presented residually finite two-group and related nil algebra.

## Applicability and commercial boundary

Infinite existence does not provide an efficient generic membership or finite-quotient search algorithm.

## 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

Extract finite presentations and independently check finite truncation invariants.

## 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).

[An infinite finitely presented residually finite 2-group](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-infinite-finitely-presented-residually-finite-2-group-October-5-2026/residually-finite-torsion.pdf).