# Computability-degree rigidity reference

Family 241: Rigidity of the Turing degrees. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Logic researchers can record the exact order-rigidity result for Turing degrees.

## Applicability and commercial boundary

Degree rigidity does not classify arbitrary program runtime, provide an effective equivalence decider or optimize a compiler.

## 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 a teaching example and proof-dependency record rather than a direct commercial product.

## 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).

[Rigidity of the Turing degrees](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Rigidity-of-the-Turing-degrees-September-24-2026/paper.pdf).