A counterexample to the Howland-Kato problem for positive commutators
Statement
The Howland-Kato conjecture that every nonzero positive commutator must arise from functions in appropriate Kato classes is false: is nonzero and nonnegative.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Rupert L. Frank and Paata Ivanisvili, using Grok 4.5That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The paper discloses only "The authors acknowledge the use of AI tools. All mathematical arguments and proofs in the final manuscript were checked and written by the authors." Co-author Paata Ivanisvili (@PI010101, Professor of Mathematics at UC Irvine) has since said publicly that "AI deserves a fair amount of credit for finding" the key identity, and, asked which model: "Grok 4.5 in Cursor with an agent found a non-symmetric counterexample f(x) = arctan(x/2) and g(x) = tanh(x)/2 + tanh(3x)/2 which works and is correct. However, in the final manuscript we implemented symmetric example." So the model found a valid counterexample, but not the symmetric one the paper is built around, and the positivity proof is the authors' own.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.