{
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  "source": "vibemath",
  "problem_id": "vibemathed:erdos-997",
  "title": "Erdős Problem #997",
  "canonical_statement": "Statement not supplied by the source.",
  "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": [
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      "status": "resolved",
      "occurred_at": "2026-03-31T00:00:00.000Z",
      "title": "erdosproblems.com",
      "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:erdos-997:attempt"
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      "method_family_ids": [
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      "id": "vibemathed:erdos-997:attempt",
      "problem_id": "vibemathed:erdos-997",
      "model": "OpenAI internal model",
      "provider": null,
      "attempted_at": "2026-03-31T00:00:00.000Z",
      "human_collaborators": [
        "Boris Alexeev",
        "Moe Putterman",
        "Mehtaab Sawhney",
        "Mark Sellke",
        "Gregory Valiant"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "From \"Short proofs in combinatorics and number theory\": \"In each case, the proof is due entirely to an internal model at OpenAI. The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance.\" This entry's solve is that paper's Theorem 4.1, proving that for every real alpha the sequence of fractional parts of alpha times the primes is not well-distributed.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Short proofs in combinatorics and number theory (Section 4)",
          "url": "https://arxiv.org/abs/2603.29961",
          "kind": "paper",
          "license": null
        }
      ],
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          "url": "https://www.erdosproblems.com/997",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Erdős Problem #997",
          "url": "https://vibemathed.com/problem/erdos-997",
          "kind": "source-assertion",
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      "independence": "unknown"
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      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Listed as solved on erdosproblems.com and the proof is verified in Lean. Solve credited via Terence Tao's AI-contributions wiki.",
      "sources": [
        {
          "label": "VibeMathed: Erdős Problem #997",
          "url": "https://vibemathed.com/problem/erdos-997",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
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      "url": "https://www.erdosproblems.com/997",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Erdős Problem #997",
      "url": "https://vibemathed.com/problem/erdos-997",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-997:signal:watch_only",
      "problem_id": "vibemathed:erdos-997",
      "kind": "watch_only",
      "reason": "The source statement is missing; retrieve it before constructing a replay task.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "The source did not supply a mathematical statement; retrieve it before replay or verification. VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}