{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R544",
  "content_hash": null,
  "slug": "ngg-attempt-order-9",
  "type": "attempt",
  "title": "Resolve the 9 by 9 case",
  "summary": "The next exact target is to decide whether a 16-point configuration exists.",
  "relevance": "For Grid points with no three collinear and no four concyclic, record ngg-attempt-order-9 (“Resolve the 9 by 9 case”) documents a concrete method, search boundary, or failed route. The record states: The next exact target is to decide whether a 16-point configuration exists.",
  "relevance_source": "recorded",
  "body": "A four-minute CP-SAT run proved that 17 points are impossible, then timed out on 16. A 16-point search can split on row occupancy: the only possible patterns are eight rows of size two, or seven rows of size two and two rows of size one. The same alternatives apply to columns. A retained checker and certificate would turn this into the next durable record.",
  "status": "next_experiment",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2506.18113",
      "locator": "Exact-search direction following the known bounds for ex([n]^2;3,4)"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2506.18113",
    "locator": "Exact-search direction following the known bounds for ex([n]^2;3,4)"
  },
  "models": [],
  "relations": [
    {
      "slug": "R543",
      "title": "A CP-SAT audit reports f(8) = 14",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "no-three-collinear-no-four-concyclic-grid",
      "title": "no three collinear no four concyclic grid",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}