{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R542",
  "content_hash": null,
  "slug": "ngg-artifact-exact-through-7",
  "type": "artifact",
  "title": "Exact search through the 7 by 7 grid",
  "summary": "Exact backtracking gives \\(f(2),\\ldots,f(7)=3,5,6,8,10,12\\).",
  "relevance": "For Grid points with no three collinear and no four concyclic, record ngg-artifact-exact-through-7 (“Exact search through the 7 by 7 grid”) supplies evidence or a replay used to check the packet. The record states: Exact backtracking gives \\(f(2),\\ldots,f(7)=3,5,6,8,10,12\\).",
  "relevance_source": "recorded",
  "body": "The search adds grid points one at a time. Exact integer determinants reject a third point on any occupied line and a fourth point on any occupied circle. Branch-and-bound proves the optimum at each order from 2 through 7. The values agree with \\(2n-2\\) for \\(4\\leq n\\leq7\\).",
  "status": "available",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "every square grid order from 2 through 7",
    "bounds": {
      "n": {
        "min": 2,
        "max": 7
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_computation",
    "source": "research/candidate-screening/multi3.py",
    "citation": {
      "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/multi3.py",
      "locator": "research/candidate-screening/multi3.py, grid search section"
    },
    "missing": [
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/multi3.py",
    "locator": "research/candidate-screening/multi3.py, grid search section"
  },
  "models": [],
  "relations": [
    {
      "slug": "R545",
      "title": "The published bounds leave a wide gap",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "R543",
      "title": "A CP-SAT audit reports f(8) = 14",
      "object_type": "artifact",
      "relation": "strengthens",
      "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"
    }
  ]
}