What was already known
Jockusch proved every c.e. truth-table degree contains an irreducible many-one degree without requiring that degree to be c.e. Odifreddi asked whether the stronger c.e. version held.
AI involvement
The author's acknowledgment states that Gemini Deep Think discovered the main negative result. The published structural argument was then fully reworked by Cintioli, so the AI credit is for the decisive result and initial route, not for the final wording or unchecked independent proof.
The named model discovered the main negative result, while the human author substantially reworked the entire argument before publication; the source does not document an autonomous complete final proof.
Importance
Shows that the proposed c.e. strengthening fails.
Limitations
Gemini Deep Think found the negative result; Cintioli reworked and verified the published argument. The model’s original intermediate proof is not available.
Technical verification
Cintioli explicitly says he fully reworked and verified all arguments of the published proof. This is a source-reported completed human check by the named author.
Formal checking
Full reworking and verification of every argument in the published structural proof
- Checker
- Patrizio Cintioli, author
- Scope
- The existence of a c.e. tt-degree without any c.e. irreducible m-degree
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Cintioli explains how rigid complements imply simplicity, why simple sets are not cylinders and how Degtev's uniqueness theorem gives the negative example.
Correction and publication history
Shows that the proposed c.e. strengthening fails.
Read this published revision