{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R804",
  "content_hash": null,
  "slug": "tsp-artifact-matching-260",
  "type": "artifact",
  "title": "Exact triangular matching sweep through order 260",
  "summary": "Exact bipartite matching finds failures only at orders \\(1\\) and \\(4\\) through \\(n=260\\).",
  "relevance": "This supplies a computation, dataset, or executable check used to assess the target problem.",
  "relevance_source": "derived",
  "body": "For each order, the checker joins left vertex \\(i\\) to right vertex \\(j\\) exactly when \\(i+j\\) is triangular, then searches for a perfect matching. It records failures at 1 and 4 and succeeds at every other order through 260.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every positive integer n from 1 through 260",
    "bounds": {
      "n": {
        "min": 1,
        "max": 260
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_computation",
    "source": "research/candidate-screening/verify.py",
    "citation": {
      "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/verify.py",
      "locator": "research/candidate-screening/verify.py and verified_ranges.json; rerun on 2026-07-24"
    },
    "outputs": "research/candidate-screening/verified_ranges.json",
    "missing": [
      "command",
      "runtime"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/verify.py",
    "locator": "research/candidate-screening/verify.py and verified_ranges.json; rerun on 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R805",
      "title": "Orders 1 and 4 are the exact exceptions",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "triangular-sum-permutation-existence",
      "title": "triangular sum permutation existence",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}