{
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  "ref": "R1630",
  "content_hash": null,
  "slug": "line-arrangement-triangular-bounded-completion-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 page has zero answers and records several partial constructions. Current literature searches on simplicial arrangements and arrangement extension did not locate a proof or counterexample for the affine bounded-cell completion problem. Exact unresolved remainder: 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": "For Completing a line arrangement to triangular bounded cells, 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 page has zero answers and records several partial constructions. Current literature searches on simplicial arrangements and arrangement extension did not locate a proof or counterexample for the affine bounded-cell completion problem.\n\nExact unresolved remainder: 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.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1108.3000",
      "locator": "abstract and exhaustive classification of real-projective simplicial arrangements with at most 27 lines"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1108.3000",
    "locator": "abstract and exhaustive classification of real-projective simplicial arrangements with at most 27 lines"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1336",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "line-arrangement-triangular-bounded-completion",
      "title": "line arrangement triangular bounded completion",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}