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Sivaraman asked whether perfect divisibility is characterized by its chromatic consequence: is a graph $G$ perfectly divisible if and only if $\chi(H) \le \binom{\omega(H)+1}{2}$ for every induced subgraph $H$ of $G$? False: the Paley graph $P(17)$ satisfies the chromatic bound hereditarily but is not perfectly divisible.
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The acknowledgement states that the Paley graph P(17) - the counterexample witness - was identified during exploratory use of ChatGPT and subsequently verified by the authors, with ChatGPT also used for language polishing and generating the verification code. All arguments and computations were checked by the authors.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Checked by this site on 17 August 2026 against the paper's LaTeX (arXiv:2608.14519, Wang-Xia): the question is stated as Question 1 with attribution to Sivaraman by personal communication, the negative answer via P(17) is Theorem-level, and the acknowledgement is verbatim as quoted. The P(17) computation was not re-run here. The paper's larger content - perfect and linear divisibility of chair-free graphs - is human work outside this entry's claim. Days old, no independent review.
Correctness: unknown · statement fidelity: unaudited · peer review: none
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VibeMath has not independently audited the mathematical statement, proof, or novelty claim.