What was already known
Babai posed the unbounded-chromatic-number question in 1978. The authors previously constructed related no-lonely-colour graphs, but not minimal Cayley graphs.
AI involvement
Given the authors' earlier no-lonely-colour paper, ChatGPT 5.6 Sol found an initial proof. Substantial parts of the final Section 2 construction come from an interactive model draft. The authors edited and improved that draft, so the proof is model-centered rather than independent of human strategic input.
The disclosure credits ChatGPT with finding the initial proof and substantial retained Section 2 mathematics, while the authors' earlier related framework and interactive editing constrain autonomy.
Importance
Answers Babai’s question with an unbounded family.
Limitations
Davies, Hatzel and Yepremyan supplied the prior framework and edited the model draft. No completed check of the final proof is documented.
Technical verification
The final paper gives a full proof, but its authorship and responsibility statement does not document a completed independent human check or a machine check.
Human understanding
The human authors edited and improved the proof and explain the inductive permutation-group construction and Hales–Jewett coloring contradiction.
Correction and publication history
Answers Babai’s question with an unbounded family.
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