{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1335",
  "content_hash": null,
  "slug": "line-arrangement-triangular-bounded-completion-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "Prove a finite augmentation procedure for every initial arrangement, or give a finite initial arrangement and prove that every finite line extension leaves a bounded cell with at least four sides. A negative result may use a projective or incidence invariant, but it must show that the invariant survives every allowed added affine line.",
  "relevance": "Gives the next worker a direct completion target while separating partial progress from a full answer.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. Prove a finite augmentation procedure for every initial arrangement, or give a finite initial arrangement and prove that every finite line extension leaves a bounded cell with at least four sides. A negative result may use a projective or incidence invariant, but it must show that the invariant survives every allowed added affine line. 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/155196/extending-a-line-arrangement-so-that-the-bounded-components-of-its-complement-ar",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/155196/extending-a-line-arrangement-so-that-the-bounded-components-of-its-complement-ar",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1336",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "line-arrangement-triangular-bounded-completion",
      "title": "line arrangement triangular bounded completion",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}