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    "leaves": [
      {
        "edge": 0,
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        "depth": 1,
        "status": "CERTIFIED",
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        ],
        "end_value": [
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        ],
        "length_upper": "1",
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      },
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      },
      {
        "edge": 1,
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        "status": "BOUNDARY_ZERO",
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        ],
        "end_value": [
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        ],
        "length_upper": "1",
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      },
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    ],
    "winding": null
  },
  "cluster_polynomial": [
    [
      "0",
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    ],
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      "-1",
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    ],
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    ],
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    ],
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    ]
  ],
  "coefficient_errors": [
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    "1/1000",
    "1/1000",
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    "1/1000"
  ],
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    {
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        "1",
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      ],
      "radius": "1/4",
      "count": 3,
      "shifted_coefficients": [
        [
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        ],
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        ],
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        ],
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        ],
        [
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        ],
        [
          "1",
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        ]
      ],
      "dominant_lower": "1/8",
      "other_upper": "285/4096",
      "coefficient_error": "61741/4096000",
      "margin": "165259/4096000",
      "status": "CERTIFIED"
    },
    {
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        "-1",
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      ],
      "radius": "1/4",
      "count": 2,
      "shifted_coefficients": [
        [
          "0",
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        ],
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        ],
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          "8",
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        ],
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          "-20",
          "-24"
        ],
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          "18",
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        ],
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          "-7",
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        ],
        [
          "1",
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        ]
      ],
      "dominant_lower": "1",
      "other_upper": "3333/4096",
      "coefficient_error": "61741/4096000",
      "margin": "701259/4096000",
      "status": "CERTIFIED"
    },
    {
      "center": [
        "0",
        "2"
      ],
      "radius": "1/4",
      "count": 1,
      "shifted_coefficients": [
        [
          "0",
          "0"
        ],
        [
          "-25",
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        ],
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          "105",
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        ],
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          "26",
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        ],
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          "-42",
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        ],
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          "-1",
          "10"
        ],
        [
          "1",
          "0"
        ]
      ],
      "dominant_lower": "25/2",
      "other_upper": "45517/4096",
      "coefficient_error": "953317/4096000",
      "margin": "4729683/4096000",
      "status": "CERTIFIED"
    }
  ],
  "concrete_perturbations": [
    {
      "coefficients": [
        [
          "-1/2000",
          "3999/2000"
        ],
        [
          "-1",
          "-3999/2000"
        ],
        [
          "2001/2000",
          "-4"
        ],
        [
          "3999/2000",
          "7999/2000"
        ],
        [
          "-2",
          "4001/2000"
        ],
        [
          "-1999/2000",
          "-2"
        ],
        [
          "1999/2000",
          "-1/2000"
        ]
      ],
      "counts": [
        3,
        2,
        1
      ]
    },
    {
      "coefficients": [
        [
          "0",
          "2"
        ],
        [
          "-1999/2000",
          "-4001/2000"
        ],
        [
          "1999/2000",
          "-7999/2000"
        ],
        [
          "2",
          "4"
        ],
        [
          "-3999/2000",
          "3999/2000"
        ],
        [
          "-2001/2000",
          "-3999/2000"
        ],
        [
          "1",
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        ]
      ],
      "counts": [
        3,
        2,
        1
      ]
    },
    {
      "coefficients": [
        [
          "1/2000",
          "4001/2000"
        ],
        [
          "-2001/2000",
          "-2"
        ],
        [
          "1",
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        ],
        [
          "4001/2000",
          "8001/2000"
        ],
        [
          "-4001/2000",
          "2"
        ],
        [
          "-1",
          "-4001/2000"
        ],
        [
          "2001/2000",
          "1/2000"
        ]
      ],
      "counts": [
        3,
        2,
        1
      ]
    },
    {
      "coefficients": [
        [
          "-1/2000",
          "3999/2000"
        ],
        [
          "-1",
          "-3999/2000"
        ],
        [
          "2001/2000",
          "-4"
        ],
        [
          "3999/2000",
          "7999/2000"
        ],
        [
          "-2",
          "4001/2000"
        ],
        [
          "-1999/2000",
          "-2"
        ],
        [
          "1999/2000",
          "-1/2000"
        ]
      ],
      "counts": [
        3,
        2,
        1
      ]
    },
    {
      "coefficients": [
        [
          "0",
          "2"
        ],
        [
          "-1999/2000",
          "-4001/2000"
        ],
        [
          "1999/2000",
          "-7999/2000"
        ],
        [
          "2",
          "4"
        ],
        [
          "-3999/2000",
          "3999/2000"
        ],
        [
          "-2001/2000",
          "-3999/2000"
        ],
        [
          "1",
          "0"
        ]
      ],
      "counts": [
        3,
        2,
        1
      ]
    },
    {
      "coefficients": [
        [
          "1/2000",
          "4001/2000"
        ],
        [
          "-2001/2000",
          "-2"
        ],
        [
          "1",
          "-8001/2000"
        ],
        [
          "4001/2000",
          "8001/2000"
        ],
        [
          "-4001/2000",
          "2"
        ],
        [
          "-1",
          "-4001/2000"
        ],
        [
          "2001/2000",
          "1/2000"
        ]
      ],
      "counts": [
        3,
        2,
        1
      ]
    }
  ],
  "meromorphic_counts": {
    "zeros": 2,
    "poles": 2,
    "net": 0
  },
  "mutation_tests": [
    "missing_leaf",
    "altered_margin",
    "altered_value",
    "altered_winding",
    "invalid_edge",
    "edge_order",
    "gap",
    "unresolved_marked_safe",
    "missing_cluster",
    "wrong_count",
    "wrong_shift",
    "wrong_error"
  ],
  "scope": "Exact finite certificate checks, not a black-box complete root isolator; no floating arithmetic, automatic precision oracle, or imported solver. General proofs are in the accompanying pages."
}