[
  {
    "assignment": [
      null,
      null,
      null,
      null
    ],
    "species": [],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      null,
      0
    ],
    "species": [
      3
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      null,
      3
    ],
    "species": [
      3
    ],
    "padded_coefficients": [
      "a + b + c + 2*d",
      "a*b + a*c + 2*a*d + b*c + 2*b*d + 2*c*d",
      "a*b*c + 2*a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + 2*a**3*b**2*d + a**3*b*c**2 + 4*a**3*b*c*d + 4*a**3*b*d**2 + 2*a**3*c**2*d + 4*a**3*c*d**2 + a**2*b**3*c + 2*a**2*b**3*d + 2*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 8*a**2*b**2*d**2 + a**2*b*c**3 + 8*a**2*b*c**2*d + 16*a**2*b*c*d**2 + 8*a**2*b*d**3 + 2*a**2*c**3*d + 8*a**2*c**2*d**2 + 8*a**2*c*d**3 + a*b**3*c**2 + 4*a*b**3*c*d + 4*a*b**3*d**2 + a*b**2*c**3 + 8*a*b**2*c**2*d + 16*a*b**2*c*d**2 + 8*a*b**2*d**3 + 4*a*b*c**3*d + 16*a*b*c**2*d**2 + 16*a*b*c*d**3 + 4*a*c**3*d**2 + 8*a*c**2*d**3 + 2*b**3*c**2*d + 4*b**3*c*d**2 + 2*b**2*c**3*d + 8*b**2*c**2*d**2 + 8*b**2*c*d**3 + 4*b*c**3*d**2 + 8*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      1,
      null
    ],
    "species": [
      2
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      1,
      0
    ],
    "species": [
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      1,
      3
    ],
    "species": [
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + c + 2*d",
      "a*b + a*c + 2*a*d + b*c + 2*b*d + 2*c*d",
      "a*b*c + 2*a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + 2*a**3*b**2*d + a**3*b*c**2 + 4*a**3*b*c*d + 4*a**3*b*d**2 + 2*a**3*c**2*d + 4*a**3*c*d**2 + a**2*b**3*c + 2*a**2*b**3*d + 2*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 8*a**2*b**2*d**2 + a**2*b*c**3 + 8*a**2*b*c**2*d + 16*a**2*b*c*d**2 + 8*a**2*b*d**3 + 2*a**2*c**3*d + 8*a**2*c**2*d**2 + 8*a**2*c*d**3 + a*b**3*c**2 + 4*a*b**3*c*d + 4*a*b**3*d**2 + a*b**2*c**3 + 8*a*b**2*c**2*d + 16*a*b**2*c*d**2 + 8*a*b**2*d**3 + 4*a*b*c**3*d + 16*a*b*c**2*d**2 + 16*a*b*c*d**3 + 4*a*c**3*d**2 + 8*a*c**2*d**3 + 2*b**3*c**2*d + 4*b**3*c*d**2 + 2*b**2*c**3*d + 8*b**2*c**2*d**2 + 8*b**2*c*d**3 + 4*b*c**3*d**2 + 8*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      2,
      null
    ],
    "species": [
      2
    ],
    "padded_coefficients": [
      "a + b + 2*c + d",
      "a*b + 2*a*c + a*d + 2*b*c + b*d + 2*c*d",
      "2*a*b*c + a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + a**3*b*d**2 + 4*a**3*c**2*d + 2*a**3*c*d**2 + 2*a**2*b**3*c + a**2*b**3*d + 8*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 2*a**2*b**2*d**2 + 8*a**2*b*c**3 + 16*a**2*b*c**2*d + 8*a**2*b*c*d**2 + a**2*b*d**3 + 8*a**2*c**3*d + 8*a**2*c**2*d**2 + 2*a**2*c*d**3 + 4*a*b**3*c**2 + 4*a*b**3*c*d + a*b**3*d**2 + 8*a*b**2*c**3 + 16*a*b**2*c**2*d + 8*a*b**2*c*d**2 + a*b**2*d**3 + 16*a*b*c**3*d + 16*a*b*c**2*d**2 + 4*a*b*c*d**3 + 8*a*c**3*d**2 + 4*a*c**2*d**3 + 4*b**3*c**2*d + 2*b**3*c*d**2 + 8*b**2*c**3*d + 8*b**2*c**2*d**2 + 2*b**2*c*d**3 + 8*b*c**3*d**2 + 4*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "4"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      2,
      0
    ],
    "species": [
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + 2*c + d",
      "a*b + 2*a*c + a*d + 2*b*c + b*d",
      "a*b*(2*c + d)",
      "0"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + a**3*b*d**2 + 2*a**2*b**3*c + a**2*b**3*d + 8*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 2*a**2*b**2*d**2 + 8*a**2*b*c**3 + 12*a**2*b*c**2*d + 6*a**2*b*c*d**2 + a**2*b*d**3 + 4*a*b**3*c**2 + 4*a*b**3*c*d + a*b**3*d**2 + 8*a*b**2*c**3 + 12*a*b**2*c**2*d + 6*a*b**2*c*d**2 + a*b**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": true,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      null,
      2,
      3
    ],
    "species": [
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + 2*c + 2*d",
      "a*b + 2*a*c + 2*a*d + 2*b*c + 2*b*d",
      "2*a*b*(c + d)",
      "0"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + 2*a**3*b**2*d + 4*a**3*b*c**2 + 8*a**3*b*c*d + 4*a**3*b*d**2 + 2*a**2*b**3*c + 2*a**2*b**3*d + 8*a**2*b**2*c**2 + 16*a**2*b**2*c*d + 8*a**2*b**2*d**2 + 8*a**2*b*c**3 + 24*a**2*b*c**2*d + 24*a**2*b*c*d**2 + 8*a**2*b*d**3 + 4*a*b**3*c**2 + 8*a*b**3*c*d + 4*a*b**3*d**2 + 8*a*b**2*c**3 + 24*a*b**2*c**2*d + 24*a*b**2*c*d**2 + 8*a*b**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": true,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      1,
      null,
      null
    ],
    "species": [
      1
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      1,
      null,
      0
    ],
    "species": [
      1,
      3
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      1,
      null,
      3
    ],
    "species": [
      1,
      3
    ],
    "padded_coefficients": [
      "a + b + c + 2*d",
      "a*b + a*c + 2*a*d + b*c + 2*b*d + 2*c*d",
      "a*b*c + 2*a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + 2*a**3*b**2*d + a**3*b*c**2 + 4*a**3*b*c*d + 4*a**3*b*d**2 + 2*a**3*c**2*d + 4*a**3*c*d**2 + a**2*b**3*c + 2*a**2*b**3*d + 2*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 8*a**2*b**2*d**2 + a**2*b*c**3 + 8*a**2*b*c**2*d + 16*a**2*b*c*d**2 + 8*a**2*b*d**3 + 2*a**2*c**3*d + 8*a**2*c**2*d**2 + 8*a**2*c*d**3 + a*b**3*c**2 + 4*a*b**3*c*d + 4*a*b**3*d**2 + a*b**2*c**3 + 8*a*b**2*c**2*d + 16*a*b**2*c*d**2 + 8*a*b**2*d**3 + 4*a*b*c**3*d + 16*a*b*c**2*d**2 + 16*a*b*c*d**3 + 4*a*c**3*d**2 + 8*a*c**2*d**3 + 2*b**3*c**2*d + 4*b**3*c*d**2 + 2*b**2*c**3*d + 8*b**2*c**2*d**2 + 8*b**2*c*d**3 + 4*b*c**3*d**2 + 8*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      1,
      2,
      null
    ],
    "species": [
      1,
      2
    ],
    "padded_coefficients": [
      "a + b + 2*c + d",
      "a*b + 2*a*c + a*d + 2*b*c + b*d + 2*c*d",
      "2*a*b*c + a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + a**3*b*d**2 + 4*a**3*c**2*d + 2*a**3*c*d**2 + 2*a**2*b**3*c + a**2*b**3*d + 8*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 2*a**2*b**2*d**2 + 8*a**2*b*c**3 + 16*a**2*b*c**2*d + 8*a**2*b*c*d**2 + a**2*b*d**3 + 8*a**2*c**3*d + 8*a**2*c**2*d**2 + 2*a**2*c*d**3 + 4*a*b**3*c**2 + 4*a*b**3*c*d + a*b**3*d**2 + 8*a*b**2*c**3 + 16*a*b**2*c**2*d + 8*a*b**2*c*d**2 + a*b**2*d**3 + 16*a*b*c**3*d + 16*a*b*c**2*d**2 + 4*a*b*c*d**3 + 8*a*c**3*d**2 + 4*a*c**2*d**3 + 4*b**3*c**2*d + 2*b**3*c*d**2 + 8*b**2*c**3*d + 8*b**2*c**2*d**2 + 2*b**2*c*d**3 + 8*b*c**3*d**2 + 4*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "4"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      1,
      2,
      0
    ],
    "species": [
      1,
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + 2*c + d",
      "a*b + 2*a*c + a*d + 2*b*c + b*d",
      "a*b*(2*c + d)",
      "0"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + a**3*b*d**2 + 2*a**2*b**3*c + a**2*b**3*d + 8*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 2*a**2*b**2*d**2 + 8*a**2*b*c**3 + 12*a**2*b*c**2*d + 6*a**2*b*c*d**2 + a**2*b*d**3 + 4*a*b**3*c**2 + 4*a*b**3*c*d + a*b**3*d**2 + 8*a*b**2*c**3 + 12*a*b**2*c**2*d + 6*a*b**2*c*d**2 + a*b**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": true,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      null,
      1,
      2,
      3
    ],
    "species": [
      1,
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + 2*c + 2*d",
      "a*b + 2*a*c + 2*a*d + 2*b*c + 2*b*d",
      "2*b*(a*c + a*d + 2*c*d)",
      "4*a*b*c*d"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + 2*a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + 4*a**3*b*d**2 + 2*a**2*b**3*c + 2*a**2*b**3*d + 8*a**2*b**2*c**2 + 12*a**2*b**2*c*d + 8*a**2*b**2*d**2 + 8*a**2*b*c**3 + 16*a**2*b*c**2*d + 16*a**2*b*c*d**2 + 8*a**2*b*d**3 + 4*a*b**3*c**2 + 8*a*b**3*c*d + 4*a*b**3*d**2 + 8*a*b**2*c**3 + 16*a*b**2*c**2*d + 16*a*b**2*c*d**2 + 8*a*b**2*d**3 + 8*b**3*c**2*d + 8*b**3*c*d**2 + 16*b**2*c**3*d + 16*b**2*c**2*d**2 + 16*b**2*c*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "16"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      null,
      null,
      null
    ],
    "species": [
      0
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      null,
      null,
      3
    ],
    "species": [
      0,
      3
    ],
    "padded_coefficients": [
      "a + b + c + 2*d",
      "a*b + a*c + 3*a*d + b*c + 2*b*d + 2*c*d",
      "a*b*c + 3*a*b*d + 3*a*c*d + 2*b*c*d",
      "3*a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + 3*a**3*b**2*d + a**3*b*c**2 + 6*a**3*b*c*d + 9*a**3*b*d**2 + 3*a**3*c**2*d + 9*a**3*c*d**2 + a**2*b**3*c + 3*a**2*b**3*d + 2*a**2*b**2*c**2 + 9*a**2*b**2*c*d + 12*a**2*b**2*d**2 + a**2*b*c**3 + 9*a**2*b*c**2*d + 24*a**2*b*c*d**2 + 18*a**2*b*d**3 + 3*a**2*c**3*d + 12*a**2*c**2*d**2 + 18*a**2*c*d**3 + a*b**3*c**2 + 4*a*b**3*c*d + 6*a*b**3*d**2 + a*b**2*c**3 + 8*a*b**2*c**2*d + 18*a*b**2*c*d**2 + 12*a*b**2*d**3 + 4*a*b*c**3*d + 18*a*b*c**2*d**2 + 24*a*b*c*d**3 + 6*a*c**3*d**2 + 12*a*c**2*d**3 + 2*b**3*c**2*d + 4*b**3*c*d**2 + 2*b**2*c**3*d + 8*b**2*c**2*d**2 + 8*b**2*c*d**3 + 4*b*c**3*d**2 + 8*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      null,
      1,
      null
    ],
    "species": [
      0,
      2
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      null,
      1,
      3
    ],
    "species": [
      0,
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + c + 2*d",
      "a*b + a*c + 3*a*d + b*c + 2*b*d + 2*c*d",
      "a*b*c + 3*a*b*d + 3*a*c*d + 2*b*c*d",
      "3*a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + 3*a**3*b**2*d + a**3*b*c**2 + 6*a**3*b*c*d + 9*a**3*b*d**2 + 3*a**3*c**2*d + 9*a**3*c*d**2 + a**2*b**3*c + 3*a**2*b**3*d + 2*a**2*b**2*c**2 + 9*a**2*b**2*c*d + 12*a**2*b**2*d**2 + a**2*b*c**3 + 9*a**2*b*c**2*d + 24*a**2*b*c*d**2 + 18*a**2*b*d**3 + 3*a**2*c**3*d + 12*a**2*c**2*d**2 + 18*a**2*c*d**3 + a*b**3*c**2 + 4*a*b**3*c*d + 6*a*b**3*d**2 + a*b**2*c**3 + 8*a*b**2*c**2*d + 18*a*b**2*c*d**2 + 12*a*b**2*d**3 + 4*a*b*c**3*d + 18*a*b*c**2*d**2 + 24*a*b*c*d**3 + 6*a*c**3*d**2 + 12*a*c**2*d**3 + 2*b**3*c**2*d + 4*b**3*c*d**2 + 2*b**2*c**3*d + 8*b**2*c**2*d**2 + 8*b**2*c*d**3 + 4*b*c**3*d**2 + 8*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      null,
      2,
      null
    ],
    "species": [
      0,
      2
    ],
    "padded_coefficients": [
      "a + b + 2*c + d",
      "a*b + 2*a*c + a*d + 2*b*c + b*d + 2*c*d",
      "2*a*b*c + a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + a**3*b*d**2 + 4*a**3*c**2*d + 2*a**3*c*d**2 + 2*a**2*b**3*c + a**2*b**3*d + 8*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 2*a**2*b**2*d**2 + 8*a**2*b*c**3 + 16*a**2*b*c**2*d + 8*a**2*b*c*d**2 + a**2*b*d**3 + 8*a**2*c**3*d + 8*a**2*c**2*d**2 + 2*a**2*c*d**3 + 4*a*b**3*c**2 + 4*a*b**3*c*d + a*b**3*d**2 + 8*a*b**2*c**3 + 16*a*b**2*c**2*d + 8*a*b**2*c*d**2 + a*b**2*d**3 + 16*a*b*c**3*d + 16*a*b*c**2*d**2 + 4*a*b*c*d**3 + 8*a*c**3*d**2 + 4*a*c**2*d**3 + 4*b**3*c**2*d + 2*b**3*c*d**2 + 8*b**2*c**3*d + 8*b**2*c**2*d**2 + 2*b**2*c*d**3 + 8*b*c**3*d**2 + 4*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "4"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      null,
      2,
      3
    ],
    "species": [
      0,
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + 2*c + 2*d",
      "a*b + 2*a*c + 3*a*d + 2*b*c + 2*b*d",
      "a*b*(2*c + 3*d)",
      "0"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + 3*a**3*b**2*d + 4*a**3*b*c**2 + 12*a**3*b*c*d + 9*a**3*b*d**2 + 2*a**2*b**3*c + 3*a**2*b**3*d + 8*a**2*b**2*c**2 + 20*a**2*b**2*c*d + 12*a**2*b**2*d**2 + 8*a**2*b*c**3 + 32*a**2*b*c**2*d + 42*a**2*b*c*d**2 + 18*a**2*b*d**3 + 4*a*b**3*c**2 + 10*a*b**3*c*d + 6*a*b**3*d**2 + 8*a*b**2*c**3 + 28*a*b**2*c**2*d + 32*a*b**2*c*d**2 + 12*a*b**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "20"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "32"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "42"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "10"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "28"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "32"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "12"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": true,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      1,
      null,
      null
    ],
    "species": [
      0,
      1
    ],
    "padded_coefficients": [
      "a + b + c + d",
      "a*b + a*c + a*d + b*c + b*d + c*d",
      "a*b*c + a*b*d + a*c*d + b*c*d",
      "a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + a**3*b**2*d + a**3*b*c**2 + 2*a**3*b*c*d + a**3*b*d**2 + a**3*c**2*d + a**3*c*d**2 + a**2*b**3*c + a**2*b**3*d + 2*a**2*b**2*c**2 + 4*a**2*b**2*c*d + 2*a**2*b**2*d**2 + a**2*b*c**3 + 4*a**2*b*c**2*d + 4*a**2*b*c*d**2 + a**2*b*d**3 + a**2*c**3*d + 2*a**2*c**2*d**2 + a**2*c*d**3 + a*b**3*c**2 + 2*a*b**3*c*d + a*b**3*d**2 + a*b**2*c**3 + 4*a*b**2*c**2*d + 4*a*b**2*c*d**2 + a*b**2*d**3 + 2*a*b*c**3*d + 4*a*b*c**2*d**2 + 2*a*b*c*d**3 + a*c**3*d**2 + a*c**2*d**3 + b**3*c**2*d + b**3*c*d**2 + b**2*c**3*d + 2*b**2*c**2*d**2 + b**2*c*d**3 + b*c**3*d**2 + b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "1"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      1,
      null,
      3
    ],
    "species": [
      0,
      1,
      3
    ],
    "padded_coefficients": [
      "a + b + c + 2*d",
      "a*b + a*c + 3*a*d + b*c + 2*b*d + 2*c*d",
      "a*b*c + 3*a*b*d + 3*a*c*d + 2*b*c*d",
      "3*a*b*c*d"
    ],
    "hurwitz_polynomial": "a**3*b**2*c + 3*a**3*b**2*d + a**3*b*c**2 + 6*a**3*b*c*d + 9*a**3*b*d**2 + 3*a**3*c**2*d + 9*a**3*c*d**2 + a**2*b**3*c + 3*a**2*b**3*d + 2*a**2*b**2*c**2 + 9*a**2*b**2*c*d + 12*a**2*b**2*d**2 + a**2*b*c**3 + 9*a**2*b*c**2*d + 24*a**2*b*c*d**2 + 18*a**2*b*d**3 + 3*a**2*c**3*d + 12*a**2*c**2*d**2 + 18*a**2*c*d**3 + a*b**3*c**2 + 4*a*b**3*c*d + 6*a*b**3*d**2 + a*b**2*c**3 + 8*a*b**2*c**2*d + 18*a*b**2*c*d**2 + 12*a*b**2*d**3 + 4*a*b*c**3*d + 18*a*b*c**2*d**2 + 24*a*b*c*d**3 + 6*a*c**3*d**2 + 12*a*c**2*d**3 + 2*b**3*c**2*d + 4*b**3*c*d**2 + 2*b**2*c**3*d + 8*b**2*c**2*d**2 + 8*b**2*c*d**3 + 4*b*c**3*d**2 + 8*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "8"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      1,
      2,
      null
    ],
    "species": [
      0,
      1,
      2
    ],
    "padded_coefficients": [
      "a + b + 2*c + d",
      "a*b + 2*a*c + a*d + 2*b*c + b*d + 2*c*d",
      "2*a*b*c + a*b*d + 2*a*c*d + 2*b*c*d",
      "2*a*b*c*d"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + a**3*b**2*d + 4*a**3*b*c**2 + 4*a**3*b*c*d + a**3*b*d**2 + 4*a**3*c**2*d + 2*a**3*c*d**2 + 2*a**2*b**3*c + a**2*b**3*d + 8*a**2*b**2*c**2 + 8*a**2*b**2*c*d + 2*a**2*b**2*d**2 + 8*a**2*b*c**3 + 16*a**2*b*c**2*d + 8*a**2*b*c*d**2 + a**2*b*d**3 + 8*a**2*c**3*d + 8*a**2*c**2*d**2 + 2*a**2*c*d**3 + 4*a*b**3*c**2 + 4*a*b**3*c*d + a*b**3*d**2 + 8*a*b**2*c**3 + 16*a*b**2*c**2*d + 8*a*b**2*c*d**2 + a*b**2*d**3 + 16*a*b*c**3*d + 16*a*b*c**2*d**2 + 4*a*b*c*d**3 + 8*a*c**3*d**2 + 4*a*c**2*d**3 + 4*b**3*c**2*d + 2*b**3*c*d**2 + 8*b**2*c**3*d + 8*b**2*c**2*d**2 + 2*b**2*c*d**3 + 8*b*c**3*d**2 + 4*b*c**2*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          3,
          0,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          0,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          2,
          0,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          0,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "1"
      },
      {
        "exponents": [
          1,
          1,
          3,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          0,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          0,
          2,
          3
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          0,
          1,
          3,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          1,
          2,
          3
        ],
        "coefficient": "4"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  },
  {
    "assignment": [
      0,
      1,
      2,
      3
    ],
    "species": [
      0,
      1,
      2,
      3
    ],
    "padded_coefficients": [
      "a + b + 2*c + 2*d",
      "a*b + 2*a*c + 3*a*d + 2*b*c + 2*b*d",
      "b*(2*a*c + 3*a*d + 4*c*d)",
      "4*a*b*c*d"
    ],
    "hurwitz_polynomial": "2*a**3*b**2*c + 3*a**3*b**2*d + 4*a**3*b*c**2 + 8*a**3*b*c*d + 9*a**3*b*d**2 + 2*a**2*b**3*c + 3*a**2*b**3*d + 8*a**2*b**2*c**2 + 16*a**2*b**2*c*d + 12*a**2*b**2*d**2 + 8*a**2*b*c**3 + 24*a**2*b*c**2*d + 38*a**2*b*c*d**2 + 18*a**2*b*d**3 + 4*a*b**3*c**2 + 10*a*b**3*c*d + 6*a*b**3*d**2 + 8*a*b**2*c**3 + 20*a*b**2*c**2*d + 20*a*b**2*c*d**2 + 12*a*b**2*d**3 + 8*a*b*c**2*d**2 + 8*a*b*c*d**3 + 8*b**3*c**2*d + 8*b**3*c*d**2 + 16*b**2*c**3*d + 16*b**2*c**2*d**2 + 16*b**2*c*d**3",
    "hurwitz_monomials": [
      {
        "exponents": [
          3,
          2,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          3,
          2,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          3,
          1,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          3,
          1,
          1,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          3,
          1,
          0,
          2
        ],
        "coefficient": "9"
      },
      {
        "exponents": [
          2,
          3,
          1,
          0
        ],
        "coefficient": "2"
      },
      {
        "exponents": [
          2,
          3,
          0,
          1
        ],
        "coefficient": "3"
      },
      {
        "exponents": [
          2,
          2,
          2,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          2,
          1,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          2,
          2,
          0,
          2
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          2,
          1,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          2,
          1,
          2,
          1
        ],
        "coefficient": "24"
      },
      {
        "exponents": [
          2,
          1,
          1,
          2
        ],
        "coefficient": "38"
      },
      {
        "exponents": [
          2,
          1,
          0,
          3
        ],
        "coefficient": "18"
      },
      {
        "exponents": [
          1,
          3,
          2,
          0
        ],
        "coefficient": "4"
      },
      {
        "exponents": [
          1,
          3,
          1,
          1
        ],
        "coefficient": "10"
      },
      {
        "exponents": [
          1,
          3,
          0,
          2
        ],
        "coefficient": "6"
      },
      {
        "exponents": [
          1,
          2,
          3,
          0
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          2,
          2,
          1
        ],
        "coefficient": "20"
      },
      {
        "exponents": [
          1,
          2,
          1,
          2
        ],
        "coefficient": "20"
      },
      {
        "exponents": [
          1,
          2,
          0,
          3
        ],
        "coefficient": "12"
      },
      {
        "exponents": [
          1,
          1,
          2,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          1,
          1,
          1,
          3
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          2,
          1
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          3,
          1,
          2
        ],
        "coefficient": "8"
      },
      {
        "exponents": [
          0,
          2,
          3,
          1
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          0,
          2,
          2,
          2
        ],
        "coefficient": "16"
      },
      {
        "exponents": [
          0,
          2,
          1,
          3
        ],
        "coefficient": "16"
      }
    ],
    "certified_D_nonunstable": true,
    "singular": false,
    "scope": "All positive diagonal column scalings, by polynomial nonnegativity and the quartic exclusion lemma."
  }
]