{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:klopp-zadik-node-private-community",
  "title": "Klopp-Zadik Question on Polynomial-Time Node-Private Recovery",
  "canonical_statement": "Klopp and Zadik gave an exponential-time node-private algorithm for exact community recovery in stochastic block models and asked whether a polynomial-time algorithm could match it. One can: a Lipschitz surrogate for the penalized likelihood plus an accept-reject sampler gives a high-probability polynomial-time node-private algorithm that nearly matches the exponential-time guarantee.",
  "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:klopp-zadik-node-private-community:event",
      "problem_id": "vibemathed:klopp-zadik-node-private-community",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-10T00:00:00.000Z",
      "title": "arXiv:2607.09441 - Near-optimal node-private community estimation in polynomial-time",
      "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.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:klopp-zadik-node-private-community:attempt"
      ],
      "method_family_ids": [
        "vibemathed:klopp-zadik-node-private-community:method"
      ],
      "source_assertion_ids": [
        "vibemathed:klopp-zadik-node-private-community:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:klopp-zadik-node-private-community:attempt",
      "problem_id": "vibemathed:klopp-zadik-node-private-community",
      "model": "ChatGPT 5.5 Plus",
      "provider": "OpenAI",
      "attempted_at": "2026-07-10T00:00:00.000Z",
      "human_collaborators": [
        "Laurentiu Marchis",
        "Olga Klopp",
        "Po-Ling Loh",
        "Ilias Zadik"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The AI declaration says the paper was written with the model's help and that it played a critical role in brainstorming the initial idea for a polynomial-time algorithm and in providing proof outlines for the main results. Two of the authors are the pair who posed the question.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2607.09441 - Near-optimal node-private community estimation in polynomial-time",
          "url": "https://arxiv.org/abs/2607.09441",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Klopp-Zadik Question on Polynomial-Time Node-Private Recovery",
          "url": "https://vibemathed.com/problem/klopp-zadik-node-private-community",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:klopp-zadik-node-private-community:verification",
      "problem_id": "vibemathed:klopp-zadik-node-private-community",
      "solution_event_id": "vibemathed:klopp-zadik-node-private-community:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Klopp-Zadik Question on Polynomial-Time Node-Private Recovery",
          "url": "https://vibemathed.com/problem/klopp-zadik-node-private-community",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2607.09441 - Near-optimal node-private community estimation in polynomial-time",
          "url": "https://arxiv.org/abs/2607.09441",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2607.09441 - Near-optimal node-private community estimation in polynomial-time",
      "url": "https://arxiv.org/abs/2607.09441",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Klopp-Zadik Question on Polynomial-Time Node-Private Recovery",
      "url": "https://vibemathed.com/problem/klopp-zadik-node-private-community",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:klopp-zadik-node-private-community:signal:watch_only",
      "problem_id": "vibemathed:klopp-zadik-node-private-community",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "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"
}