Problem detail · source-aware
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Let $\mu$ be a probability measure on the unit circle with Verblunsky coefficients $\alpha$. Lukic conjectured that a weighted entropy condition with finitely many critical points is equivalent to a decomposition of $\alpha$ into components localized at those points. A counterexample with two critical points of multiplicity three refutes it: the sequence satisfies the decomposition conditions while the corresponding weighted entropy is $-\infty$.
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The counterexample - two phase modes with common power-decay exponent $3/20$ - was found by GPT-5.6, as the abstract states directly; the author developed and verified the construction.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint with the counterexample stated explicitly; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.