GPT-5.5, GPT-5.6 Sol
The proof by Fu, Gao and Park was AI-assisted and independently verified by the authors.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Two-Copy Distillability of Werner States
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
Is a Werner state that is not one-copy distillable ever two-copy distillable? The first open rung of the NPT bound-entanglement ladder, open since 2000.
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
Author-verified arXiv preprint. Within days, two further groups posted independent proofs of the same theorem (arXiv:2607.24309, arXiv:2607.24479), which strengthens confidence but none is yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv:2607.21367 - A solution to 2-copy distillability of Werner states
Two-copy distillable if and only if already one-copy distillable. Four independent papers settled this within five days of each other, and no single one of them is the account of record. Fu, Gao and Park posted first on 23 July (arXiv:2607.21367), followed by Song and Chen on 26 July (arXiv:2607.23416), then on 27 July both Fraser, Huber, Pozsgay and Vona (arXiv:2607.24309) and Bharti, Gajjala and Haug (arXiv:2607.24479). The headline axes here follow the first posting, which is a filing convention and not a claim about who solved it. Pozsgay has stated publicly that his group had their AI-assisted proof before the first paper appeared. This site cannot verify a private completion date, so that is recorded as his account rather than as a finding. All four are linked below.
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.