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.

A finitely generated counterexample to the Eilenberg–Ganea conjecture.