# Finite-group poset homology contract

Family 310: Quillen's conjecture in rational homology. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Cross-check nonzero augmented rational homology of the elementary-abelian subgroup poset when the largest normal p-subgroup is trivial.

## Applicability and commercial boundary

Enumeration of subgroups can dominate runtime; noncontractibility is weaker than a complete homology computation.

## 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

Compare explicit small groups with an existing poset homology implementation.

## 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).

[Rational homology and Quillen's conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rational-homology-and-Quillens-conjecture-September-24-2026/paper.pdf).