Mathematical logic·OpenAI Math·Result 241·Lean formalisation listed
Rigidity of the Turing degrees
One of the 372 results in OpenAI's public mathematics catalogue, filed under mathematical logic: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Rigidity of the Turing degrees
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What OpenAI claims
Every order automorphism of the Turing degrees is the identity, resolving their rigidity problem. Thus no nontrivial relabeling of degrees preserves the ordering by relative computability. (Lean)
Paper
Rigidity of the Turing degrees
We prove that every order automorphism of the full partial order of Turing degrees is the identity, resolving the rigidity conjecture for the Turing degrees positively.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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