Problem detail · source-aware
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Chromatic quasisymmetric functions of natural unit interval graphs were conjectured to have log-concave coefficients in the elementary basis. A connected $13$-vertex example refutes it: for the Hessenberg function $h=(2,4,4,6,7,10,10,10,10,12,12,13,13)$ and $\lambda=(6,5,1,1)$ the coefficients of $q^5,q^6,q^7$ are $1,6,38$, and $6^2 < 1 \cdot 38$. The coefficient is still positive, palindromic and unimodal, so log-concavity is separated from the weaker shape properties that motivated the conjecture.
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The disclosure describes a computer-assisted investigation in which the model was used extensively as an interactive research assistant: it generated and revised the exploratory and verification code, ran independent computational cross-checks, searched the literature, and helped organize and draft the manuscript. The author states that no assertion is accepted on the authority of model output.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The counterexample is a single explicit graph and partition, and the paper ships an exact standard-library Python verifier with a recorded SHA-256 digest. arXiv preprint, not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
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Source-reported tools: computation.
Independent: unknown · difference confidence: 0
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