{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R117",
  "content_hash": null,
  "slug": "cd1685-claim-current-interval",
  "type": "claim",
  "title": "The current table interval is 104 through 115",
  "summary": "The live LJCR record gives 104 <= C(16,8,5) <= 115; the exact covering number remains unresolved.",
  "relevance": "For Covering every five-set with eight-sets on sixteen points, record cd1685-claim-current-interval (“The current table interval is 104 through 115”) records a bound, answer, status fact, or structural consequence. The record states: The live LJCR record gives 104 <= C(16,8,5) <= 115; the exact covering number remains unresolved.",
  "relevance_source": "recorded",
  "body": "A \\((16,8,5)\\) covering is a family of 8-subsets of a 16-point set such that every 5-subset lies in at least one block. The covering number \\(C(16,8,5)\\) is the smallest possible family size.\n\nThe La Jolla Covering Repository page accessed on 2026-07-24 reports\n\\[\n104\\le C(16,8,5)\\le115.\n\\]\nIt credits the displayed 115-block cover to Alessandro Jurcovich and labels the lower-bound method `Schonheim`. The companion replay verifies every block and all \\(\\binom{16}{5}=4368\\) coverage requirements. The lower-bound record spells out the recursive calculation. Together they certify the interval. They leave an eleven-block gap, so the candidate's request for a single exact value is still open.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the live La Jolla Covering Repository record for C(16,8,5), checked on 2026-07-24",
    "bounds": {
      "v": {
        "min": 16,
        "max": 16
      },
      "k": {
        "min": 8,
        "max": 8
      },
      "t": {
        "min": 5,
        "max": 5
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://ljcr.dmgordon.org/cover/show_cover.php?k=8&t=5&v=16",
      "locator": "La Jolla Covering Repository, C(16,8,5) record, heading, creator credit, lower-bound label, and complete block list; accessed 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://ljcr.dmgordon.org/cover/show_cover.php?k=8&t=5&v=16",
    "locator": "La Jolla Covering Repository, C(16,8,5) record, heading, creator credit, lower-bound label, and complete block list; accessed 2026-07-24"
  },
  "relations": [
    {
      "slug": "R118",
      "title": "Jurcovich's 115 blocks form a covering",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R119",
      "title": "The recursive lower bound is 104",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "covering-design-16-8-5",
      "title": "covering design 16 8 5",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}