{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:erdos-768",
  "title": "Erdős Problem #768",
  "canonical_statement": "If $A(x)$ counts integers satisfying the Sylow divisor condition, determine the constant $c$ in $A(x)/x = \\exp(-(c + o(1)) \\sqrt{\\log x} \\log\\log x)$. The claimed exact value is $c = 1/(2\\sqrt{\\log 2})$.",
  "plain_summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "candidate",
  "solution_events": [
    {
      "id": "vibemathed:erdos-768:event",
      "problem_id": "vibemathed:erdos-768",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-07-25T00:00:00.000Z",
      "title": "erdosproblems.com/768",
      "summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
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    }
  ],
  "attempts": [
    {
      "id": "vibemathed:erdos-768:attempt",
      "problem_id": "vibemathed:erdos-768",
      "model": "ChatGPT + Aristotle",
      "provider": "OpenAI / Harmonic",
      "attempted_at": "2026-07-25T00:00:00.000Z",
      "human_collaborators": [
        "Eric Li"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": null,
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "erdosproblems.com/768",
          "url": "https://www.erdosproblems.com/768",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Erdős Problem #768",
          "url": "https://vibemathed.com/problem/erdos-768",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
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      "cost_usd": null,
      "independence": "unknown"
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  "verifications": [
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      "id": "vibemathed:erdos-768:verification",
      "problem_id": "vibemathed:erdos-768",
      "solution_event_id": "vibemathed:erdos-768:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Three clean Lean checks; the community tracker update is pending.",
      "sources": [
        {
          "label": "VibeMathed: Erdős Problem #768",
          "url": "https://vibemathed.com/problem/erdos-768",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
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          "label": "erdosproblems.com/768",
          "url": "https://www.erdosproblems.com/768",
          "kind": "primary-mathematical-source",
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    {
      "label": "erdosproblems.com/768",
      "url": "https://www.erdosproblems.com/768",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Erdős Problem #768",
      "url": "https://vibemathed.com/problem/erdos-768",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-768:signal:verify_now",
      "problem_id": "vibemathed:erdos-768",
      "kind": "verify_now",
      "reason": "The source labels this result as a candidate; verification should precede reuse.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "The source status is candidate and must not be represented as solved.",
    "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"
}