{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:erdos-741",
  "title": "Erdős Problem #741",
  "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": [
    {
      "id": "vibemathed:erdos-741:event",
      "problem_id": "vibemathed:erdos-741",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-04-16T00:00:00.000Z",
      "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-741:attempt"
      ],
      "method_family_ids": [
        "vibemathed:erdos-741:method"
      ],
      "source_assertion_ids": [
        "vibemathed:erdos-741:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:erdos-741:attempt",
      "problem_id": "vibemathed:erdos-741",
      "model": "DeepMind prover agent",
      "provider": null,
      "attempted_at": "2026-04-16T00:00:00.000Z",
      "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.\" Priority note: this paper (31 March 2026) constructs the basis of order two with no syndetic split that Burr and Erdos asked for, which is this problem. The solve recorded here is dated 16 April 2026 and credited to a DeepMind prover agent, so the Lean-verified resolution appears to follow the earlier OpenAI-model proof rather than to be independent of it. Both are linked; the priority has not been adjudicated here.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Short proofs in combinatorics and number theory (Section 3), 31 March 2026",
          "url": "https://arxiv.org/abs/2603.29961",
          "kind": "paper",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "erdosproblems.com",
          "url": "https://www.erdosproblems.com/741",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Erdős Problem #741",
          "url": "https://vibemathed.com/problem/erdos-741",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:erdos-741:verification",
      "problem_id": "vibemathed:erdos-741",
      "solution_event_id": "vibemathed:erdos-741:event",
      "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 #741",
          "url": "https://vibemathed.com/problem/erdos-741",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "erdosproblems.com",
          "url": "https://www.erdosproblems.com/741",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "erdosproblems.com",
      "url": "https://www.erdosproblems.com/741",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Erdős Problem #741",
      "url": "https://vibemathed.com/problem/erdos-741",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-741:signal:watch_only",
      "problem_id": "vibemathed:erdos-741",
      "kind": "watch_only",
      "reason": "The source statement is missing; retrieve it before constructing a replay task.",
      "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.",
    "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"
}