{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question",
  "title": "Johnson-Freyd-Ostrik-Yu Question on Categorical Cocycles",
  "canonical_statement": "Twisted Deligne products categorify the tensor product of two Grothendieck rings. Classifying them leads to categorical $n$-cocycles, and Johnson-Freyd, Ostrik and Yu asked whether these are always pullbacks of ordinary group cocycles on the universal grading group of the underlying based ring. For $3$-cocycles they are.",
  "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:johnson-freyd-ostrik-yu-cocycle-question:event",
      "problem_id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-07-21T00:00:00.000Z",
      "title": "arXiv:2607.19560 - Twisted Deligne products of semisimple tensor categories",
      "summary": "answered for 3-cocycles, inside a broader partial classification of twisted Deligne products",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:johnson-freyd-ostrik-yu-cocycle-question:attempt"
      ],
      "method_family_ids": [
        "vibemathed:johnson-freyd-ostrik-yu-cocycle-question:method"
      ],
      "source_assertion_ids": [
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      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question:attempt",
      "problem_id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question",
      "model": "ChatGPT 5.5 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-07-21T00:00:00.000Z",
      "human_collaborators": [
        "Pavel Etingof",
        "Dmitri Nikshych",
        "Victor Ostrik"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement says only that the authors collaborated with the model in this paper, especially in the Appendix, which is where the cocycle question is answered. No step is attributed, so the lowest tier applies.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2607.19560 - Twisted Deligne products of semisimple tensor categories",
          "url": "https://arxiv.org/abs/2607.19560",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Johnson-Freyd-Ostrik-Yu Question on Categorical Cocycles",
          "url": "https://vibemathed.com/problem/johnson-freyd-ostrik-yu-cocycle-question",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
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      "cost_usd": null,
      "independence": "unknown"
    }
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  "verifications": [
    {
      "id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question:verification",
      "problem_id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question",
      "solution_event_id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question: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: Johnson-Freyd-Ostrik-Yu Question on Categorical Cocycles",
          "url": "https://vibemathed.com/problem/johnson-freyd-ostrik-yu-cocycle-question",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2607.19560 - Twisted Deligne products of semisimple tensor categories",
          "url": "https://arxiv.org/abs/2607.19560",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2607.19560 - Twisted Deligne products of semisimple tensor categories",
      "url": "https://arxiv.org/abs/2607.19560",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Johnson-Freyd-Ostrik-Yu Question on Categorical Cocycles",
      "url": "https://vibemathed.com/problem/johnson-freyd-ostrik-yu-cocycle-question",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question:signal:recent_partial_result",
      "problem_id": "vibemathed:johnson-freyd-ostrik-yu-cocycle-question",
      "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"
}