{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R543",
  "content_hash": null,
  "slug": "ngg-artifact-order-8-cpsat",
  "type": "artifact",
  "title": "A CP-SAT audit reports f(8) = 14",
  "summary": "An independent model proves 15 points infeasible and supplies a valid 14-point set.",
  "relevance": "For Grid points with no three collinear and no four concyclic, record ngg-artifact-order-8-cpsat (“A CP-SAT audit reports f(8) = 14”) supplies evidence or a replay used to check the packet. The record states: An independent model proves 15 points infeasible and supplies a valid 14-point set.",
  "relevance_source": "recorded",
  "body": "The model used one Boolean variable per grid point, a sum-at-most-2 constraint for each grid line containing at least three points, and a sum-at-most-3 constraint for each exact integer circle containing at least four points. It reported 15 infeasible. A checked 14-point witness is\n\\[\n\\{(0,2),(0,4),(1,6),(1,7),(2,1),(2,2),(3,5),(3,6),(5,0),(5,1),(6,3),(6,5),(7,0),(7,7)\\}.\n\\]\nThe run used 174 line constraints and 3,481 circle constraints. The solver script was not retained, so the infeasibility certificate remains self-reported.",
  "status": "reported",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "the 8 by 8 integer grid",
    "bounds": {
      "n": {
        "min": 8,
        "max": 8
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "artifact",
    "citation": {
      "url": "https://arxiv.org/abs/2506.18113",
      "locator": "TheoremDB entry audit on 2026-07-24; independent CP-SAT model"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2506.18113",
    "locator": "TheoremDB entry audit on 2026-07-24; independent CP-SAT model"
  },
  "models": [],
  "relations": [
    {
      "slug": "R542",
      "title": "Exact search through the 7 by 7 grid",
      "object_type": "artifact",
      "relation": "strengthens",
      "direction": "outgoing"
    },
    {
      "slug": "R544",
      "title": "Resolve the 9 by 9 case",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "no-three-collinear-no-four-concyclic-grid",
      "title": "no three collinear no four concyclic grid",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}