{
  "schema": 1,
  "status": "PASS",
  "checks": 19700,
  "by_kind": {
    "terminal fractional certificate": 1,
    "all N5 allocations enumerated": 1,
    "integer D optimum": 1,
    "integer G optimum differs": 1,
    "integer D sensitivity exceeds G optimum": 1,
    "terminal two distinct c-optimal certificates": 2,
    "singular estimable certificate": 1,
    "singular inestimable is not pseudoinverse zero": 1,
    "terminal transformed target and dual": 1,
    "coordinate change versus changed target": 1,
    "trace budget and maximum lower bound": 814,
    "AMGM efficiency bound for every sampled competitor": 11440,
    "rank-one determinant path exact identity": 3702,
    "analytic improving step": 1929,
    "separate primal basis and dual vertex enumeration agree": 200,
    "LP unbiasedness": 200,
    "LP all-candidate dual feasibility": 200,
    "LP weights attain squared norm even if singular": 196,
    "LP complementarity signs": 196,
    "full rank candidate variance upper bound": 200,
    "normal equation variance equals direct estimator sum": 200,
    "target scaling square": 400,
    "support-only sensitivity trap": 1,
    "D versus c external target": 1,
    "body intercept versus slope estimability": 1,
    "invalid exact contract rejected": 9
  },
  "rational_designs": 814,
  "LP_target_cases": 200,
  "terminal": {
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      [
        "1",
        "0"
      ],
      [
        "0",
        "1"
      ],
      [
        "1",
        "1"
      ],
      [
        "1/2",
        "-1/2"
      ]
    ],
    "fractional": {
      "w": [
        "1/3",
        "1/3",
        "1/3",
        "0"
      ],
      "M": [
        [
          "2/3",
          "1/3"
        ],
        [
          "1/3",
          "2/3"
        ]
      ],
      "sensitivity": [
        "2",
        "2",
        "2",
        "3/2"
      ],
      "det": "1/3"
    },
    "N5_all_allocations": [
      {
        "n": [
          0,
          0,
          0,
          5
        ],
        "det": "0",
        "sensitivity": null
      },
      {
        "n": [
          0,
          0,
          1,
          4
        ],
        "det": "4/25",
        "sensitivity": [
          "5/2",
          "5/2",
          "5",
          "5/4"
        ]
      },
      {
        "n": [
          0,
          0,
          2,
          3
        ],
        "det": "6/25",
        "sensitivity": [
          "55/24",
          "55/24",
          "5/2",
          "5/3"
        ]
      },
      {
        "n": [
          0,
          0,
          3,
          2
        ],
        "det": "6/25",
        "sensitivity": [
          "35/12",
          "35/12",
          "5/3",
          "5/2"
        ]
      },
      {
        "n": [
          0,
          0,
          4,
          1
        ],
        "det": "4/25",
        "sensitivity": [
          "85/16",
          "85/16",
          "5/4",
          "5"
        ]
      },
      {
        "n": [
          0,
          0,
          5,
          0
        ],
        "det": "0",
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      },
      {
        "n": [
          0,
          1,
          0,
          4
        ],
        "det": "1/25",
        "sensitivity": [
          "10",
          "5",
          "25",
          "5/4"
        ]
      },
      {
        "n": [
          0,
          1,
          1,
          3
        ],
        "det": "19/100",
        "sensitivity": [
          "55/19",
          "35/19",
          "80/19",
          "25/19"
        ]
      },
      {
        "n": [
          0,
          1,
          2,
          2
        ],
        "det": "13/50",
        "sensitivity": [
          "35/13",
          "25/13",
          "30/13",
          "45/26"
        ]
      },
      {
        "n": [
          0,
          1,
          3,
          1
        ],
        "det": "1/4",
        "sensitivity": [
          "17/5",
          "13/5",
          "8/5",
          "13/5"
        ]
      },
      {
        "n": [
          0,
          1,
          4,
          0
        ],
        "det": "4/25",
        "sensitivity": [
          "25/4",
          "5",
          "5/4",
          "85/16"
        ]
      },
      {
        "n": [
          0,
          2,
          0,
          3
        ],
        "det": "3/50",
        "sensitivity": [
          "55/6",
          "5/2",
          "50/3",
          "5/3"
        ]
      },
      {
        "n": [
          0,
          2,
          1,
          2
        ],
        "det": "1/5",
        "sensitivity": [
          "7/2",
          "3/2",
          "4",
          "3/2"
        ]
      },
      {
        "n": [
          0,
          2,
          2,
          1
        ],
        "det": "13/50",
        "sensitivity": [
          "85/26",
          "45/26",
          "30/13",
          "25/13"
        ]
      },
      {
        "n": [
          0,
          2,
          3,
          0
        ],
        "det": "6/25",
        "sensitivity": [
          "25/6",
          "5/2",
          "5/3",
          "35/12"
        ]
      },
      {
        "n": [
          0,
          3,
          0,
          2
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        "det": "3/50",
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          "35/3",
          "5/3",
          "50/3",
          "5/2"
        ]
      },
      {
        "n": [
          0,
          3,
          1,
          1
        ],
        "det": "19/100",
        "sensitivity": [
          "85/19",
          "25/19",
          "80/19",
          "35/19"
        ]
      },
      {
        "n": [
          0,
          3,
          2,
          0
        ],
        "det": "6/25",
        "sensitivity": [
          "25/6",
          "5/3",
          "5/2",
          "55/24"
        ]
      },
      {
        "n": [
          0,
          4,
          0,
          1
        ],
        "det": "1/25",
        "sensitivity": [
          "85/4",
          "5/4",
          "25",
          "5"
        ]
      },
      {
        "n": [
          0,
          4,
          1,
          0
        ],
        "det": "4/25",
        "sensitivity": [
          "25/4",
          "5/4",
          "5",
          "5/2"
        ]
      },
      {
        "n": [
          0,
          5,
          0,
          0
        ],
        "det": "0",
        "sensitivity": null
      },
      {
        "n": [
          1,
          0,
          0,
          4
        ],
        "det": "1/25",
        "sensitivity": [
          "5",
          "10",
          "25",
          "5/4"
        ]
      },
      {
        "n": [
          1,
          0,
          1,
          3
        ],
        "det": "19/100",
        "sensitivity": [
          "35/19",
          "55/19",
          "80/19",
          "25/19"
        ]
      },
      {
        "n": [
          1,
          0,
          2,
          2
        ],
        "det": "13/50",
        "sensitivity": [
          "25/13",
          "35/13",
          "30/13",
          "45/26"
        ]
      },
      {
        "n": [
          1,
          0,
          3,
          1
        ],
        "det": "1/4",
        "sensitivity": [
          "13/5",
          "17/5",
          "8/5",
          "13/5"
        ]
      },
      {
        "n": [
          1,
          0,
          4,
          0
        ],
        "det": "4/25",
        "sensitivity": [
          "5",
          "25/4",
          "5/4",
          "85/16"
        ]
      },
      {
        "n": [
          1,
          1,
          0,
          3
        ],
        "det": "1/10",
        "sensitivity": [
          "7/2",
          "7/2",
          "10",
          "1"
        ]
      },
      {
        "n": [
          1,
          1,
          1,
          2
        ],
        "det": "6/25",
        "sensitivity": [
          "25/12",
          "25/12",
          "10/3",
          "5/4"
        ]
      },
      {
        "n": [
          1,
          1,
          2,
          1
        ],
        "det": "3/10",
        "sensitivity": [
          "13/6",
          "13/6",
          "2",
          "5/3"
        ]
      },
      {
        "n": [
          1,
          1,
          3,
          0
        ],
        "det": "7/25",
        "sensitivity": [
          "20/7",
          "20/7",
          "10/7",
          "5/2"
        ]
      },
      {
        "n": [
          1,
          2,
          0,
          2
        ],
        "det": "7/50",
        "sensitivity": [
          "25/7",
          "15/7",
          "50/7",
          "15/14"
        ]
      },
      {
        "n": [
          1,
          2,
          1,
          1
        ],
        "det": "27/100",
        "sensitivity": [
          "65/27",
          "5/3",
          "80/27",
          "35/27"
        ]
      },
      {
        "n": [
          1,
          2,
          2,
          0
        ],
        "det": "8/25",
        "sensitivity": [
          "5/2",
          "15/8",
          "15/8",
          "55/32"
        ]
      },
      {
        "n": [
          1,
          3,
          0,
          1
        ],
        "det": "4/25",
        "sensitivity": [
          "65/16",
          "25/16",
          "25/4",
          "5/4"
        ]
      },
      {
        "n": [
          1,
          3,
          1,
          0
        ],
        "det": "7/25",
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          "20/7",
          "10/7",
          "20/7",
          "10/7"
        ]
      },
      {
        "n": [
          1,
          4,
          0,
          0
        ],
        "det": "4/25",
        "sensitivity": [
          "5",
          "5/4",
          "25/4",
          "25/16"
        ]
      },
      {
        "n": [
          2,
          0,
          0,
          3
        ],
        "det": "3/50",
        "sensitivity": [
          "5/2",
          "55/6",
          "50/3",
          "5/3"
        ]
      },
      {
        "n": [
          2,
          0,
          1,
          2
        ],
        "det": "1/5",
        "sensitivity": [
          "3/2",
          "7/2",
          "4",
          "3/2"
        ]
      },
      {
        "n": [
          2,
          0,
          2,
          1
        ],
        "det": "13/50",
        "sensitivity": [
          "45/26",
          "85/26",
          "30/13",
          "25/13"
        ]
      },
      {
        "n": [
          2,
          0,
          3,
          0
        ],
        "det": "6/25",
        "sensitivity": [
          "5/2",
          "25/6",
          "5/3",
          "35/12"
        ]
      },
      {
        "n": [
          2,
          1,
          0,
          2
        ],
        "det": "7/50",
        "sensitivity": [
          "15/7",
          "25/7",
          "50/7",
          "15/14"
        ]
      },
      {
        "n": [
          2,
          1,
          1,
          1
        ],
        "det": "27/100",
        "sensitivity": [
          "5/3",
          "65/27",
          "80/27",
          "35/27"
        ]
      },
      {
        "n": [
          2,
          1,
          2,
          0
        ],
        "det": "8/25",
        "sensitivity": [
          "15/8",
          "5/2",
          "15/8",
          "55/32"
        ]
      },
      {
        "n": [
          2,
          2,
          0,
          1
        ],
        "det": "1/5",
        "sensitivity": [
          "9/4",
          "9/4",
          "5",
          "1"
        ]
      },
      {
        "n": [
          2,
          2,
          1,
          0
        ],
        "det": "8/25",
        "sensitivity": [
          "15/8",
          "15/8",
          "5/2",
          "5/4"
        ]
      },
      {
        "n": [
          2,
          3,
          0,
          0
        ],
        "det": "6/25",
        "sensitivity": [
          "5/2",
          "5/3",
          "25/6",
          "25/24"
        ]
      },
      {
        "n": [
          3,
          0,
          0,
          2
        ],
        "det": "3/50",
        "sensitivity": [
          "5/3",
          "35/3",
          "50/3",
          "5/2"
        ]
      },
      {
        "n": [
          3,
          0,
          1,
          1
        ],
        "det": "19/100",
        "sensitivity": [
          "25/19",
          "85/19",
          "80/19",
          "35/19"
        ]
      },
      {
        "n": [
          3,
          0,
          2,
          0
        ],
        "det": "6/25",
        "sensitivity": [
          "5/3",
          "25/6",
          "5/2",
          "55/24"
        ]
      },
      {
        "n": [
          3,
          1,
          0,
          1
        ],
        "det": "4/25",
        "sensitivity": [
          "25/16",
          "65/16",
          "25/4",
          "5/4"
        ]
      },
      {
        "n": [
          3,
          1,
          1,
          0
        ],
        "det": "7/25",
        "sensitivity": [
          "10/7",
          "20/7",
          "20/7",
          "10/7"
        ]
      },
      {
        "n": [
          3,
          2,
          0,
          0
        ],
        "det": "6/25",
        "sensitivity": [
          "5/3",
          "5/2",
          "25/6",
          "25/24"
        ]
      },
      {
        "n": [
          4,
          0,
          0,
          1
        ],
        "det": "1/25",
        "sensitivity": [
          "5/4",
          "85/4",
          "25",
          "5"
        ]
      },
      {
        "n": [
          4,
          0,
          1,
          0
        ],
        "det": "4/25",
        "sensitivity": [
          "5/4",
          "25/4",
          "5",
          "5/2"
        ]
      },
      {
        "n": [
          4,
          1,
          0,
          0
        ],
        "det": "4/25",
        "sensitivity": [
          "5/4",
          "5",
          "25/4",
          "25/16"
        ]
      },
      {
        "n": [
          5,
          0,
          0,
          0
        ],
        "det": "0",
        "sensitivity": null
      }
    ],
    "integer_D_optima": [
      {
        "n": [
          1,
          2,
          2,
          0
        ],
        "det": "8/25",
        "sensitivity": [
          "5/2",
          "15/8",
          "15/8",
          "55/32"
        ]
      },
      {
        "n": [
          2,
          1,
          2,
          0
        ],
        "det": "8/25",
        "sensitivity": [
          "15/8",
          "5/2",
          "15/8",
          "55/32"
        ]
      },
      {
        "n": [
          2,
          2,
          1,
          0
        ],
        "det": "8/25",
        "sensitivity": [
          "15/8",
          "15/8",
          "5/2",
          "5/4"
        ]
      }
    ],
    "integer_G_optima": [
      {
        "n": [
          1,
          1,
          2,
          1
        ],
        "det": "3/10",
        "sensitivity": [
          "13/6",
          "13/6",
          "2",
          "5/3"
        ]
      }
    ],
    "c_target": [
      "2",
      "-1"
    ],
    "c_designs": [
      {
        "b": [
          "2",
          "-1",
          "0",
          "0"
        ],
        "w": [
          "2/3",
          "1/3",
          "0",
          "0"
        ],
        "M": [
          [
            "2/3",
            "0"
          ],
          [
            "0",
            "1/3"
          ]
        ],
        "variance": "9"
      },
      {
        "b": [
          "1",
          "0",
          "0",
          "2"
        ],
        "w": [
          "1/3",
          "0",
          "0",
          "2/3"
        ],
        "M": [
          [
            "1/2",
            "-1/6"
          ],
          [
            "-1/6",
            "1/6"
          ]
        ],
        "variance": "9"
      }
    ],
    "singular": {
      "target": [
        "1",
        "-1"
      ],
      "M": [
        [
          "1/4",
          "-1/4"
        ],
        [
          "-1/4",
          "1/4"
        ]
      ],
      "variance": 4,
      "T": [
        [
          "1",
          "1"
        ],
        [
          "0",
          "2"
        ]
      ],
      "transformed_candidates": [
        [
          "1",
          "0"
        ],
        [
          "1",
          "2"
        ],
        [
          "2",
          "2"
        ],
        [
          "0",
          "-1"
        ]
      ],
      "transformed_target": [
        "0",
        "-2"
      ],
      "transformed_dual": [
        "1",
        "-1"
      ]
    }
  },
  "scope": "Exact finite arithmetic certificates; rational weight grids and explicitly listed target families, not a numerical optimizer or a proof by sampling."
}