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Does the natural trace estimate hold for kinetic energy spaces in the unrestricted Gaussian velocity model on bounded domains (Question 1.8 of Albritton, Armstrong, Mourrat and Novack)? No: for each $1 \le p < 2$ there are counterexamples on every bounded $\mathrm{C}^{1,1}$ domain in dimension $d \ge 2$. The paper also identifies the sharp boundary-regularity threshold $\mathrm{C}^{1,1/2}$ for the natural trace weight.
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GPT-5.5 Pro provided preliminary counterexamples and GPT-5.6 Sol an initial proof of the natural half-space trace estimate; generative AI was also used in developing some of the subsequent arguments. The authors developed and verified the final theory.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
the named open question is answered negatively; the paper's positive theory goes further
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.