{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1314",
  "content_hash": null,
  "slug": "grahl-sequence-infinitely-many-ones-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "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, record grahl-sequence-infinitely-many-ones-next-route-20260801 (“Complete the stated acceptance conditions”) documents a concrete method, search boundary, or failed route. The record states: 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.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. 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. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/338415/on-the-first-sequence-without-triple-in-arithmetic-progression",
      "locator": "Editorial research route recorded 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": "Editorial research route recorded 2026-08-01."
  },
  "models": [],
  "relations": [
    {
      "slug": "R1315",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "grahl-sequence-infinitely-many-ones",
      "title": "grahl sequence infinitely many ones",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}