{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:werner-two-copy-distillability",
  "title": "Two-Copy Distillability of Werner States",
  "canonical_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.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:werner-two-copy-distillability:event",
      "problem_id": "vibemathed:werner-two-copy-distillability",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-23T00:00:00.000Z",
      "title": "arXiv:2607.21367 - A solution to 2-copy distillability of Werner states",
      "summary": "Two-copy distillable if and only if already one-copy distillable.\n\nFour 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.\n\nPozsgay 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.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:werner-two-copy-distillability:attempt"
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    }
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  "attempts": [
    {
      "id": "vibemathed:werner-two-copy-distillability:attempt",
      "problem_id": "vibemathed:werner-two-copy-distillability",
      "model": "GPT-5.5, GPT-5.6 Sol",
      "provider": "OpenAI",
      "attempted_at": "2026-07-23T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The proof by Fu, Gao and Park was AI-assisted and independently verified by the authors.",
      "failed_routes": [],
      "artifacts": [
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          "label": "Song and Chen - A partial-trace matrix inequality and Werner-state distillability (26 Jul)",
          "url": "https://arxiv.org/abs/2607.23416",
          "kind": "independent",
          "license": null
        },
        {
          "label": "Fraser, Huber, Pozsgay and Vona - two-copy distillability and a new partial trace bound (27 Jul)",
          "url": "https://arxiv.org/abs/2607.24309",
          "kind": "independent",
          "license": null
        },
        {
          "label": "Bharti, Gajjala and Haug - sharp partial-trace inequalities (27 Jul)",
          "url": "https://arxiv.org/abs/2607.24479",
          "kind": "independent",
          "license": null
        }
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          "kind": "primary-mathematical-source",
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        },
        {
          "label": "VibeMathed: Two-Copy Distillability of Werner States",
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      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "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.",
      "sources": [
        {
          "label": "VibeMathed: Two-Copy Distillability of Werner States",
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          "label": "arXiv:2607.21367 - A solution to 2-copy distillability of Werner states",
          "url": "https://arxiv.org/abs/2607.21367",
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      "label": "arXiv:2607.21367 - A solution to 2-copy distillability of Werner states",
      "url": "https://arxiv.org/abs/2607.21367",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Two-Copy Distillability of Werner States",
      "url": "https://vibemathed.com/problem/werner-two-copy-distillability",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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      "generated_at": "2026-09-13T16:28:40.178Z"
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  "uncertainties": [
    "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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}