# Homological dimension counterexample library

Family 198: A counterexample to finitistic-dimension finiteness. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Algebra researchers can test claims of uniformly bounded finite projective dimensions for one finite-dimensional complex algebra.

## Applicability and commercial boundary

Finite dimensionality of the algebra is not a practical finite computation bound for every module; the result gives no new resolution engine.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.

## Next verification action

Extract the algebra and explicit module family for a finite research fixture.

## Evidence scope

The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[An algebra of infinite little finitistic dimension](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-algebra-of-infinite-little-finitistic-dimension-September-23-2026/paper.pdf).