Kinetic Trace Estimates in the Gaussian Model
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 there are counterexamples on every bounded domain in dimension . The paper also identifies the sharp boundary-regularity threshold for the natural trace weight.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Kinetic theory
- Posed by
- Dallas Albritton, Scott Armstrong, Jean-Christophe Mourrat, Matthew Novack
- Year posed
- 2024
- Years open
- 2y
- Solved
- 2026-07-27
- Model
- GPT-5.5 Pro, GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Lukas Niebel, Lisa Valentini
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the named open question is answered negatively; the paper's positive theory goes further
What the AI did
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.
Verification
arXiv preprint; not yet peer-reviewed.