ChatGPT 5
The acknowledgements state the counterexamples were found with the assistance of ChatGPT 5.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
The Quantum Wasserstein Semidistance Is Not a Distance
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Friedland and coauthors proposed a quantum analogue of the $p$-Wasserstein distance and conjectured that, though only a semidistance in general, it is a true distance for a particular quantum cost matrix and for cost matrices near it. The paper disproves both conjectures with an explicit family of triples of states violating the triangle inequality.
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
Verification boundary
No independent review, but the refutation is an explicit family of state triples and the triangle inequality can be checked directly. Preprint, not refereed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv
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.