What was already known
The general Černý conjecture remains open. Dubuc settled the circular level-zero class; positive-level classes had weaker bounds, and the relative extension property was conjectured.
AI involvement
Zhu says he obtained the proof through interaction with OpenAI Codex (GPT-5.6 Sol Ultra), then verified and presented it; the source does not assign each lemma or sharpness example to a contributor.
The first-person disclosure assigns the central proof to interaction with Codex. It does not support AI autonomy or a more precise division of the proof ideas.
Importance
The proof settles this substantial automata class and the stronger relative extension statement.
Limitations
The result does not settle the general Černý conjecture. Zhu does not separate the model’s individual proof steps from his own.
Technical verification
Zhu explicitly reports verifying the proof. This is an author-reported complete human proof check; no independent reproduction or machine formalization is documented.
Independent checking
Verified the proof obtained in interaction with Codex
- Checker
- Yinfeng Zhu, author
- Scope
- Positive-level relative extension and resulting Černý bound for one-cluster automata
- Basis
- Reported by the linked checker
Human understanding
Zhu gives a detailed account of the Fitting, annular-descent and reset-accounting mechanism in §§3–9.
Correction and publication history
The proof settles this substantial automata class and the stronger relative extension statement.
Read this published revision