{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:cycle-double-cover-conjecture",
  "title": "Cycle Double Cover Conjecture",
  "canonical_statement": "Conjectures that every bridgeless graph has a collection of cycles covering each edge exactly twice.",
  "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:cycle-double-cover-conjecture:event",
      "problem_id": "vibemathed:cycle-double-cover-conjecture",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-10T00:00:00.000Z",
      "title": "Scientific American",
      "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_discovered",
      "attempt_ids": [
        "vibemathed:cycle-double-cover-conjecture:attempt"
      ],
      "method_family_ids": [
        "vibemathed:cycle-double-cover-conjecture:method"
      ],
      "source_assertion_ids": [
        "vibemathed:cycle-double-cover-conjecture:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:cycle-double-cover-conjecture:attempt",
      "problem_id": "vibemathed:cycle-double-cover-conjecture",
      "model": "GPT-5.6 Sol Ultra",
      "provider": "OpenAI",
      "attempted_at": "2026-07-10T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Running in Ultra mode with 64 parallel subagents, GPT-5.6 Sol produced a claimed proof of the full Cycle Double Cover Conjecture in under an hour. OpenAI released both the proof manuscript and the task prompt; a public Lean formalization was added afterwards.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Independent Codex-assisted proof claim the same week (Kintali), unreviewed, arXiv:2607.14140",
          "url": "https://arxiv.org/abs/2607.14140",
          "kind": "independent",
          "license": null
        },
        {
          "label": "Lean-checked proof",
          "url": "https://github.com/openai/cdc-lean",
          "kind": "lean-proof",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "Scientific American",
          "url": "https://www.scientificamerican.com/article/chatgpt-just-proved-another-50-year-old-math-conjecture/",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Cycle Double Cover Conjecture",
          "url": "https://vibemathed.com/problem/cycle-double-cover-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:cycle-double-cover-conjecture:verification",
      "problem_id": "vibemathed:cycle-double-cover-conjecture",
      "solution_event_id": "vibemathed:cycle-double-cover-conjecture:event",
      "level": "lean_checked_statement_unaudited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Announced by OpenAI researcher Ethan Knight on 10 July 2026, timed to the GPT-5.6 Sol Ultra release. Not peer-reviewed; the Cycle Double Cover Conjecture has a history of claimed proofs later found to have gaps, so mathematicians are treating it cautiously pending independent review. Lean released here: https://github.com/openai/cdc-lean",
      "sources": [
        {
          "label": "VibeMathed: Cycle Double Cover Conjecture",
          "url": "https://vibemathed.com/problem/cycle-double-cover-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Scientific American",
          "url": "https://www.scientificamerican.com/article/chatgpt-just-proved-another-50-year-old-math-conjecture/",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "Scientific American",
      "url": "https://www.scientificamerican.com/article/chatgpt-just-proved-another-50-year-old-math-conjecture/",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Cycle Double Cover Conjecture",
      "url": "https://vibemathed.com/problem/cycle-double-cover-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:cycle-double-cover-conjecture:signal:replay_ready",
      "problem_id": "vibemathed:cycle-double-cover-conjecture",
      "kind": "replay_ready",
      "reason": "A public source and a non-unreviewed verification label support replay triage.",
      "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"
}