# Cohomological versus geometric dimension fixture

Family 249: A finitely generated Eilenberg–Ganea counterexample. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Prevent software from equating cohomological dimension two with existence of a two-dimensional classifying space.

## Applicability and commercial boundary

The finitely generated residually finite example concerns infinite complexes, including arbitrarily many cells.

## 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 the group presentation and exact obstruction.

## 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).

[A finitely generated counterexample to the Eilenberg–Ganea conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-finitely-generated-counterexample-to-the-Eilenberg-Ganea-conjecture-September-23-2026/paper.pdf).