What was already known
Tuza stated the case without a published proof. The prior Haxell–Scott bound implies at most seven.
AI involvement
GPT-5.6 Sol supplied the retained projection lemma and proof idea after White found errors in earlier rounds. White directed the search, checked cases and wrote the final proof.
GPT-5.6 Sol supplied the retained projection lemma and final proof idea, while White directed the search, corrected outputs and completed the paper.
Importance
Closes the named (4,2) case of Ryser’s covering inequality.
Limitations
White checked the projection lemma on classified finite cases and tested examples, but a completed rigorous check of the universal proof is not documented. The general conjecture remains separate.
Technical verification
White reports exact computational checks of the projection lemma on five classified intersecting extremals under all six two-plus-two splits, plus checks of the bipartite identity on six examples. These are bounded checks; no completed rigorous check of every step of the universal theorem is documented.
Human understanding
White's short proof and Remark 4.3 explain how the projection lemma, Gyárfás's theorem and Kőnig's theorem fit together; the model's discarded rounds are not needed to explain the retained contribution.
Correction and publication history
Closes the named (4,2) case of Ryser’s covering inequality.
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