What was already known
Foregger and Sinkhorn proposed the implication in 1986. A special complex or multiplex family had been checked, but no earlier general counterexample was identified.
AI involvement
Yair Lavi credits GPT-5.6 Sol and Claude Fable 5 with proving the counterexample under his guidance. He reviewed the resulting arguments and took responsibility for the final paper.
The author attributes the proof of the counterexample theorem to the two models under his guidance.
Importance
Provides a counterexample to a long-standing named conjecture about permanent minimizers.
Limitations
The paper does not show that eight is the smallest counterexample dimension. The author reports reviewing the proof arguments but does not specify whether that review covered every global-minimum and cofactor step.
Technical verification
Lavi reports reviewing the AI-derived proof arguments for Theorem 1, but does not say that he completed a rigorous check of the full global-minimum and cofactor calculations. The documented review supports a human check of unspecified scope; a complete check is not established.
Independent checking
Author review of AI-derived proof arguments; precise coverage not stated
- Checker
- Yair Lavi, author
- Scope
- Theorem 1 order-eight counterexample to the tie-point implication
- Basis
- Reported by the linked checker
Human understanding
A human proof review is reported, but no distinct account by Lavi explains the central AI-derived minimization mechanism. Few is the evidence default, not a claim of inability.
Correction and publication history
Provides a counterexample to a long-standing named conjecture about permanent minimizers.
Read this published revision