{
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  "source": "vibemath",
  "problem_id": "vibemathed:erdos-1032",
  "title": "Erdős Problem #1032",
  "canonical_statement": "Do arbitrarily large 4-chromatic edge-critical graphs exist with minimum degree bounded below by a positive constant times the number of vertices?",
  "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:erdos-1032:event",
      "problem_id": "vibemathed:erdos-1032",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-05-07T00:00:00.000Z",
      "title": "erdosproblems.com/1032",
      "summary": "a new density-degree inequality gives δ(G) ≤ (3/10 + o(1))|V(G)|, improving 0.328; existence of a linear construction remains open",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
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  "attempts": [
    {
      "id": "vibemathed:erdos-1032:attempt",
      "problem_id": "vibemathed:erdos-1032",
      "model": "GPT-5.5 Pro, Codex",
      "provider": "OpenAI",
      "attempted_at": "2026-05-07T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": null,
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "erdosproblems.com/1032",
          "url": "https://www.erdosproblems.com/1032",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Erdős Problem #1032",
          "url": "https://vibemathed.com/problem/erdos-1032",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
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      "id": "vibemathed:erdos-1032:verification",
      "problem_id": "vibemathed:erdos-1032",
      "solution_event_id": "vibemathed:erdos-1032:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Lean-checked with expert screening.",
      "sources": [
        {
          "label": "VibeMathed: Erdős Problem #1032",
          "url": "https://vibemathed.com/problem/erdos-1032",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "erdosproblems.com/1032",
          "url": "https://www.erdosproblems.com/1032",
          "kind": "primary-mathematical-source",
          "license": null
        }
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  "sources": [
    {
      "label": "erdosproblems.com/1032",
      "url": "https://www.erdosproblems.com/1032",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Erdős Problem #1032",
      "url": "https://vibemathed.com/problem/erdos-1032",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "replay",
  "recommended_exposure": "method_aware",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-1032:signal:recent_partial_result",
      "problem_id": "vibemathed:erdos-1032",
      "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"
}