# Division-ring local-finiteness limitation reference

Family 201: A counterexample to Kurosh’s division-ring problem. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Algebra researchers can preserve a two-generator algebraic-over-center example with infinite dimension.

## Applicability and commercial boundary

The countable division-ring existence result is not a finite-field compression method or a practical noncommutative solver.

## 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 an effective finite description if one exists.

## 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).

[A Counterexample to Kurosh’s Division-Ring Problem](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Counterexample-to-Kuroshs-Division-Ring-Problem-September-23-2026/paper.pdf).