{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:npt-two-copy-distillability-divincenzo-family",
  "title": "Finite-Copy Distillability of NPT States in the DiVincenzo Family",
  "canonical_statement": "Whether negative-partial-transpose states undistillable from one copy become distillable from finitely many copies is a basic open problem in entanglement theory. In the canonical two-parameter DiVincenzo family used as its symmetry-reduced testbed, a distinguished one-copy-undistillable state is shown to be two-copy distillable in every local dimension d >= 3, disproving the conjecture that the family's whole one-copy-undistillable region stays undistillable for arbitrarily many copies.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
  "solution_events": [
    {
      "id": "vibemathed:npt-two-copy-distillability-divincenzo-family:event",
      "problem_id": "vibemathed:npt-two-copy-distillability-divincenzo-family",
      "type": "disproved",
      "status": "partial",
      "occurred_at": "2026-08-09T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Partial deliberately: the NPT bound entanglement problem itself is untouched. What falls is the conjecture about the canonical family, and the paper is explicit that a substantial neighbouring region remains unresolved while another is known two-copy undistillable.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:npt-two-copy-distillability-divincenzo-family:attempt"
      ],
      "method_family_ids": [
        "vibemathed:npt-two-copy-distillability-divincenzo-family:method"
      ],
      "source_assertion_ids": [
        "vibemathed:npt-two-copy-distillability-divincenzo-family:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:npt-two-copy-distillability-divincenzo-family:attempt",
      "problem_id": "vibemathed:npt-two-copy-distillability-divincenzo-family",
      "model": "GPT-5.6 Thinking",
      "provider": "OpenAI",
      "attempted_at": "2026-08-09T00:00:00.000Z",
      "human_collaborators": [
        "Gelo Noel M. Tabia",
        "Kai-Siang Chen",
        "Min-Hsiu Hsieh"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The disclosure lists the specific work: \"GNMT acknowledges substantial assistance from OpenAI's ChatGPT, using the GPT-5.6 Thinking model, in the discovery and development of this work. The tool helped with scientific reasoning, the numerical filter search, the derivation of exact two-copy and three-copy certificates, and the organization of the arguments. The interaction was initiated and directed by GNMT.\" An appendix gives a fuller account of the AI-assisted discovery process.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.08836",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Finite-Copy Distillability of NPT States in the DiVincenzo Family",
          "url": "https://vibemathed.com/problem/npt-two-copy-distillability-divincenzo-family",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:npt-two-copy-distillability-divincenzo-family:verification",
      "problem_id": "vibemathed:npt-two-copy-distillability-divincenzo-family",
      "solution_event_id": "vibemathed:npt-two-copy-distillability-divincenzo-family:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A preprint days old. The witnesses are explicit Schmidt-rank-two certificates that the authors independently reconstructed and verified, but no outside party has checked them.",
      "sources": [
        {
          "label": "VibeMathed: Finite-Copy Distillability of NPT States in the DiVincenzo Family",
          "url": "https://vibemathed.com/problem/npt-two-copy-distillability-divincenzo-family",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.08836",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2608.08836",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Finite-Copy Distillability of NPT States in the DiVincenzo Family",
      "url": "https://vibemathed.com/problem/npt-two-copy-distillability-divincenzo-family",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:npt-two-copy-distillability-divincenzo-family:signal:recent_partial_result",
      "problem_id": "vibemathed:npt-two-copy-distillability-divincenzo-family",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "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"
}