{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R790",
  "content_hash": null,
  "slug": "tlef15-claim-explicit-33-point-construction",
  "type": "claim",
  "title": "A 33-point equilateral-triangle-free set",
  "summary": "Exact coordinate arithmetic verifies that none of the 2,380 equilateral triangles is contained in the set.",
  "relevance": "For Largest equilateral-triangle-free subset of the fifteen-row triangular lattice, record tlef15-claim-explicit-33-point-construction (“A 33-point equilateral-triangle-free set”) records a bound, answer, status fact, or structural consequence. The record states: Exact coordinate arithmetic verifies that none of the 2,380 equilateral triangles is contained in the set.",
  "relevance_source": "recorded",
  "body": "A certified construction is\n\\[\n\\begin{aligned}\n\\{&(0,4),(0,6),(0,7),(0,10),(0,11),(0,14),\\\\\n&(1,4),(1,5),(1,7),(1,9),(1,11),(1,13),\\\\\n&(2,7),(2,8),(2,11),(2,12),(3,2),(3,3),(4,1),(5,0),(6,0),\\\\\n&(7,0),(7,1),(7,2),(8,2),(9,1),(10,0),\\\\\n&(11,0),(11,1),(11,2),(12,2),(13,1),(14,0)\\}.\n\\end{aligned}\n\\]\nThe verifier generates every third vertex by applying both 60-degree rotations to each lattice displacement. Deduplication produces 2,380 unordered triples, and none lies wholly in this set.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "the stated 33 lattice points, checked against every equilateral triangle among the 120 vertices of T_15",
    "bounds": {
      "selected_points": {
        "min": 33,
        "max": 33
      },
      "checked_triangles": {
        "min": 2380,
        "max": 2380
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2405.12321",
      "locator": "Exact integer-coordinate verification in tlef15-artifact-construction-and-upper-bound"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2405.12321",
    "locator": "Exact integer-coordinate verification in tlef15-artifact-construction-and-upper-bound"
  },
  "models": [],
  "relations": [
    {
      "slug": "R789",
      "title": "The current certified interval is 33 through 56",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R787",
      "title": "Executable construction and parity upper-bound certificate",
      "object_type": "artifact",
      "relation": "reproduces",
      "direction": "incoming"
    },
    {
      "slug": "triangular-lattice-15-equilateral-free",
      "title": "triangular lattice 15 equilateral free",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}