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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

Prior state unknowndisproved

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

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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

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