{
  "raw_polynomial": "u**3 - u**2 - u + 1",
  "degree": 3,
  "isolating_intervals": [
    {
      "lower": "-1",
      "upper": "-1",
      "multiplicity": 1
    },
    {
      "lower": "1",
      "upper": "1",
      "multiplicity": 2
    }
  ],
  "candidates": [
    {
      "ratio": "-1",
      "ratio_numerical": -1.0,
      "multiplicity": 1,
      "status": "rejected_nonpositive_ratio"
    },
    {
      "ratio": "1",
      "ratio_numerical": 1.0,
      "multiplicity": 2,
      "status": "exceptional_ratio_checked_separately"
    }
  ],
  "exceptional": {
    "status": "positive_exceptional_equilibrium",
    "ratio": "1",
    "free_substrate": "-1/2 + sqrt(5)/2",
    "state": [
      "-1/2 + sqrt(5)/2",
      "-1/2 + sqrt(5)/2",
      "1/(1/2 + sqrt(5)/2)",
      "1/(1/2 + sqrt(5)/2)",
      "(-1/2 + sqrt(5)/2)/(1/2 + sqrt(5)/2)",
      "(-1/2 + sqrt(5)/2)/(1/2 + sqrt(5)/2)"
    ]
  },
  "positive_count": 1
}