ProbXiv
sign in
unchecked

Kinetic Trace Estimates in the Gaussian Model

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

gaussian-kinetic-trace-questionDifferential equationsposed by Dallas Albritton, Scott Armstrong, Jean-Christophe Mourrat, Matthew Novack, 2024recorded: disproved

1 attempt · no person has looked

Statement

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≤p<21 \le p < 2 there are counterexamples on every bounded C1,1\mathrm{C}^{1,1} domain in dimension d≥2d \ge 2. The paper also identifies the sharp boundary-regularity threshold C1,1/2\mathrm{C}^{1,1/2} for the natural trace weight.

Context

the named open question is answered negatively; the paper's positive theory goes further

A named open question from a 2024 kinetic-theory paper by leading authors.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt →

  • #1

    Attempt 1

    constructionGPT-5.5 Pro, GPT-5.6 Sol with Lukas Niebel, Lisa Valentini ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5.5 Pro, GPT-5.6 Sol
    people
    Lukas Niebel, Lisa Valentini

    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.

    the named open question is answered negatively; the paper's positive theory goes further

    Reviews

    0 human reviews · 0 machine checks

    No person has reviewed this attempt. It has not been checked at all.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.