OpenAI · 241-01 · 2026-09-24 · Mathematical logic
Rigidity of the Turing degrees
preprints/Rigidity-of-the-Turing-degrees-September-24-2026
Family 241. Rigidity of the Turing degrees.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
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.
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.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 241: Rigidity of the Turing degrees. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.