A counterexample to the Howland-Kato problem for positive commutators
The Howland-Kato conjecture that every nonzero positive commutator $i[f(P),g(Q)]$ must arise from functions in appropriate Kato classes is false: $i[\arctan(P),\arctan(Q)]$ is nonzero and nonnegative.
Exact FrontierDelta
Scope and record
Occurred: Aug 7, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: A counterexample to the Howland-Kato problem for positive commutators · Howland-Kato problem
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Rupert L. Frank
human · human collaborator
Paata Ivanisvili
human · human collaborator
Grok 4.5
model · ai model contributor · xAI
Lineage and corrections
This event attributed to Paata Ivanisvili
This event attributed to Rupert L. Frank
This event attributed to Grok 4.5