What was already known
Kim and Roush gave the block candidate, a row-stochastic upper bound 2^k and the n=3 case. The doubly stochastic maximum and equality cases for n≥5 remained open.
AI involvement
Yair Lavi guided the project and wrote the paper. He credits GPT-5.6 Sol and Claude Fable 5 jointly with carrying out the proof; their individual steps are not separated.
The author expressly says the two models carried out the proof under his guidance.
Importance
The proof settles the odd-order maximum and characterizes equality cases.
Limitations
Lavi reports reviewing the model-produced arguments, but does not describe a complete rigorous check of the full proof.
Technical verification
Lavi reports reviewing the resulting proof arguments, but does not specify a completed rigorous check of the entire maximum and equality classification. The source-reported human review is recorded only at its documented scope.
Independent checking
Author review of the resulting proof arguments
- Checker
- Yair Lavi
- Scope
- The model-produced arguments for the Kim–Roush maximum and equality cases
- Basis
- Reported by the linked checker
Human understanding
The author's paper explains the functional-digraph expansion, top-layer charge bound and support argument classifying equality.
Correction and publication history
The proof settles the odd-order maximum and characterizes equality cases.
Read this published revision