{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R118",
  "content_hash": null,
  "slug": "cd1685-claim-jurcovich-cover",
  "type": "claim",
  "title": "Jurcovich's 115 blocks form a covering",
  "summary": "Exhaustive enumeration confirms that the published family contains every 5-subset in at least one of its 115 distinct 8-blocks.",
  "relevance": "For Covering every five-set with eight-sets on sixteen points, record cd1685-claim-jurcovich-cover (“Jurcovich's 115 blocks form a covering”) records a bound, answer, status fact, or structural consequence. The record states: Exhaustive enumeration confirms that the published family contains every 5-subset in at least one of its 115 distinct 8-blocks.",
  "relevance_source": "recorded",
  "body": "The repository supplies 115 distinct, increasing 8-subsets of \\(\\{1,\\ldots,16\\}\\). Exhaustive enumeration gives coverage multiplicities\n\\[\n1:3124,\\quad2:768,\\quad3:224,\\quad4:192,\\quad5:32,\\quad6:16,\\quad7:12.\n\\]\nTheir sum is 6440, agreeing with the independent incidence check \\(115\\binom85=6440\\). Every requirement has positive multiplicity, which proves \\(C(16,8,5)\\le115\\).\n\nEach block contains between 12 and 32 private 5-subsets, meaning requirements covered by that block alone within this family. All 115 blocks are therefore essential to this particular cover. This local irredundancy makes no minimum-size claim. The canonical newline-delimited block family has SHA-256 digest `52698bf4869691120b55da7419b340005acc8b8a807aafbdeabc3377f4b73664`.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "all 5-subsets of the 16-point ground set against the 115 displayed Jurcovich blocks",
    "bounds": {
      "ground_set_size": {
        "min": 16,
        "max": 16
      },
      "block_size": {
        "min": 8,
        "max": 8
      },
      "block_count": {
        "min": 115,
        "max": 115
      },
      "requirements": {
        "min": 4368,
        "max": 4368
      }
    },
    "exhaustive": true
  },
  "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": "Complete 115-block list credited to Alessandro Jurcovich; independently replayed in cd1685-artifact-exhaustive-cover"
    },
    "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": "Complete 115-block list credited to Alessandro Jurcovich; independently replayed in cd1685-artifact-exhaustive-cover"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R117",
      "title": "The current table interval is 104 through 115",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R116",
      "title": "Exhaustive replay of the 115-block covering",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "covering-design-16-8-5",
      "title": "covering design 16 8 5",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}