The Jauslin-Kreiss-Moser Vanishing-Viscosity Selection Problem
resolvedconfidence 70%
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Precise statement
For the ergodic problem $\tfrac12|D\varphi^\varepsilon|^2 + F(x) - \varepsilon\Delta\varphi^\varepsilon = c(\varepsilon)$ on the torus, normalized by $\varphi^\varepsilon(0) = 0$, Jauslin, Kreiss and Moser asked whether the vanishing-viscosity limit $\lim_{\varepsilon \to 0}\varphi^\varepsilon$ always exists. It need not: there is a one-dimensional example with $F \in C^3$ for which the limit fails to exist.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
ChatGPT
Generic rather than itemised, and prominent enough that the authors put it in the arXiv comment as well as the acknowledgement: they used ChatGPT during the development of the work, including for suggesting proof strategies and assisting with calculations, and then completed and rigorously checked every statement, proof and verification themselves. No model version is named and no individual step is attributed, which is what keeps this at the assistive end rather than higher.
arXiv preprint, not peer-reviewed. The result is an explicit one-dimensional counterexample built from local Dirichlet ground-state energies and a localization lemma, so it is checkable, but nobody independent has checked it.
arXiv:2605.10478 - Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.