{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1573",
  "content_hash": null,
  "slug": "grahl-sequence-infinitely-many-ones-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: The MathOverflow thread remains open with zero answers, and the checked OEIS records still present the infinitude of ones as an unresolved question. No later proof or counterexample was located. Exact unresolved remainder: Prove that for every integer N there exists m>N with a_m=1, or prove that a_m is never 1 beyond an explicit index. Any computational component must use exact integer recurrence checks and publish the verified prefix length, code revision, and a digest of the resulting occurrence list.",
  "relevance": "For Infinitely many ones in the greedy three-term-progression-free sequence, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: The MathOverflow thread remains open with zero answers, and the checked OEIS records still present the infinitude of ones as an unresolved question. No later proof or counterexample was located.\n\nExact unresolved remainder: Prove that for every integer N there exists m>N with a_m=1, or prove that a_m is never 1 beyond an explicit index. Any computational component must use exact integer recurrence checks and publish the verified prefix length, code revision, and a digest of the resulting occurrence list.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/338415/on-the-first-sequence-without-triple-in-arithmetic-progression",
      "locator": "Full question, answers, and visible comments concerning Infinitely many ones in the greedy three-term-progression-free sequence; checked 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/338415/on-the-first-sequence-without-triple-in-arithmetic-progression",
    "locator": "Full question, answers, and visible comments concerning Infinitely many ones in the greedy three-term-progression-free sequence; checked 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1315",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "grahl-sequence-infinitely-many-ones",
      "title": "grahl sequence infinitely many ones",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}