{
  "status": "PASS",
  "arithmetic": "Python fractions.Fraction; exact, standard library only",
  "coefficients_increasing_degree": {
    "F": [
      "2",
      "-2",
      "-3",
      "1",
      "5",
      "-2",
      "-2",
      "1"
    ],
    "squarefree_part": [
      "-2",
      "0",
      "3",
      "2",
      "-3",
      "-1",
      "1"
    ]
  },
  "sturm_cubic_chain": [
    [
      "-1",
      "-1",
      "0",
      "1"
    ],
    [
      "-1",
      "0",
      "3"
    ],
    [
      "1",
      "2/3"
    ],
    [
      "-23/4"
    ]
  ],
  "weighted_cubic_chain": [
    [
      "-1",
      "-1",
      "0",
      "1"
    ],
    [
      "2",
      "3",
      "-4"
    ],
    [
      "5/8",
      "-1/16"
    ],
    [
      "368"
    ]
  ],
  "manual_isolating_intervals": [
    [
      "-3/2",
      "-11/8"
    ],
    [
      "3/4",
      "5/4"
    ],
    [
      "5/4",
      "4/3"
    ],
    [
      "11/8",
      "3/2"
    ]
  ],
  "distinct_real_roots": 4,
  "real_roots_counting_multiplicity": 5,
  "multiplicities": [
    1,
    2,
    1,
    1
  ],
  "q_sign_by_interval": [
    0,
    -1,
    -1,
    0
  ],
  "aggregate_queries_N_U_W": [
    4,
    -2,
    2
  ],
  "positive_negative_zero_counts": [
    0,
    2,
    2
  ],
  "cubic_hermite_matrices": [
    [
      [
        "3",
        "0",
        "2"
      ],
      [
        "0",
        "2",
        "3"
      ],
      [
        "2",
        "3",
        "2"
      ]
    ],
    [
      [
        "-4",
        "3",
        "-2"
      ],
      [
        "3",
        "-2",
        "-1"
      ],
      [
        "-2",
        "-1",
        "1"
      ]
    ],
    [
      [
        "6",
        "-7",
        "5"
      ],
      [
        "-7",
        "5",
        "-1"
      ],
      [
        "5",
        "-1",
        "-2"
      ]
    ]
  ],
  "cubic_hermite_signatures": [
    1,
    -1,
    1
  ],
  "automatic_isolating_intervals": [
    [
      "-23/16",
      "-11/8"
    ],
    [
      "31/32",
      "259/256"
    ],
    [
      "21/16",
      "347/256"
    ],
    [
      "179/128",
      "369/256"
    ]
  ],
  "rational_midpoint_guard_test": {
    "intervals": [
      [
        "-57/40",
        "-87/64"
      ],
      [
        "-3/64",
        "3/40"
      ],
      [
        "207/160",
        "453/320"
      ]
    ],
    "fallbacks": 1
  },
  "known_root_query_crosschecks": 125,
  "mutation_checks": [
    "negative remainder sign",
    "empty proposed isolator",
    "root endpoint",
    "zero input"
  ],
  "scope": "mathematical certificate check; not proof-assistant or site-build validation"
}