{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:chen-lawrencenko-conjectures",
  "title": "The Chen-Lawrencenko Conjectures on Cyclic Colorations",
  "canonical_statement": "A cyclic coloration of a triangulation of a closed 2-manifold gives the faces around every vertex distinct colors. Chen and Lawrencenko made two conjectures about the cyclic chromatic number of minimal triangulations in 1999. Their second is proved here and their first disproved.",
  "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:chen-lawrencenko-conjectures:event",
      "problem_id": "vibemathed:chen-lawrencenko-conjectures",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-08-07T00:00:00.000Z",
      "title": "arXiv",
      "summary": "One conjecture each way: the second proved, the first disproved. Two further Chen-Lawrencenko conjectures remain open and are flagged as such in the paper.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:chen-lawrencenko-conjectures:attempt"
      ],
      "method_family_ids": [
        "vibemathed:chen-lawrencenko-conjectures:method"
      ],
      "source_assertion_ids": [
        "vibemathed:chen-lawrencenko-conjectures:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:chen-lawrencenko-conjectures:attempt",
      "problem_id": "vibemathed:chen-lawrencenko-conjectures",
      "model": "GPT-5.6 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-08-07T00:00:00.000Z",
      "human_collaborators": [
        "John M. Campbell"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "\"We succeed, based on our extensive interactions with GPT-5.6 Pro, in proving and disproving, respectively, Chen and Lawrencenko's second and first conjectures.\" The acknowledgement places the model in the exploratory and proof-development stages, with all suggestions substantially revised, corrected and independently verified by the author.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.06863",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Chen-Lawrencenko Conjectures on Cyclic Colorations",
          "url": "https://vibemathed.com/problem/chen-lawrencenko-conjectures",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:chen-lawrencenko-conjectures:verification",
      "problem_id": "vibemathed:chen-lawrencenko-conjectures",
      "solution_event_id": "vibemathed:chen-lawrencenko-conjectures: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, with no independent review.",
      "sources": [
        {
          "label": "VibeMathed: The Chen-Lawrencenko Conjectures on Cyclic Colorations",
          "url": "https://vibemathed.com/problem/chen-lawrencenko-conjectures",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.06863",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2608.06863",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Chen-Lawrencenko Conjectures on Cyclic Colorations",
      "url": "https://vibemathed.com/problem/chen-lawrencenko-conjectures",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:chen-lawrencenko-conjectures:signal:watch_only",
      "problem_id": "vibemathed:chen-lawrencenko-conjectures",
      "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"
}