files / problems / hilbert16-limit-cycles / compute / q3 / qq-t2-radial / certs / section6_degree.json

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{
  "paper": "arXiv:2604.12883v1 \u00a76, m=2",
  "rho2": [
    1,
    4
  ],
  "T2": "2*t**2 - 1",
  "T2_prime": "4*t",
  "X": {
    "P": "-x*(x**2 + y**2 - 1/4) + y",
    "Q": "-x - y*(x**2 + y**2 - 1/4)",
    "deg": 3
  },
  "Y": {
    "u_dot": "T2'(v) * P(T2(u), T2(v))",
    "v_dot": "T2'(u) * Q(T2(u), T2(v))",
    "deg_u": 7,
    "deg_v": 7,
    "deg": 7,
    "n_terms_u": 8,
    "n_terms_v": 8,
    "monomials_u": [
      {
        "u": 0,
        "v": 1,
        "num": 3,
        "den": 1
      },
      {
        "u": 0,
        "v": 3,
        "num": -8,
        "den": 1
      },
      {
        "u": 2,
        "v": 1,
        "num": -30,
        "den": 1
      },
      {
        "u": 0,
        "v": 5,
        "num": 16,
        "den": 1
      },
      {
        "u": 2,
        "v": 3,
        "num": 32,
        "den": 1
      },
      {
        "u": 4,
        "v": 1,
        "num": 48,
        "den": 1
      },
      {
        "u": 2,
        "v": 5,
        "num": -32,
        "den": 1
      },
      {
        "u": 6,
        "v": 1,
        "num": -32,
        "den": 1
      }
    ],
    "monomials_v": [
      {
        "u": 1,
        "v": 0,
        "num": 11,
        "den": 1
      },
      {
        "u": 1,
        "v": 2,
        "num": -30,
        "den": 1
      },
      {
        "u": 3,
        "v": 0,
        "num": -24,
        "den": 1
      },
      {
        "u": 1,
        "v": 4,
        "num": 48,
        "den": 1
      },
      {
        "u": 3,
        "v": 2,
        "num": 32,
        "den": 1
      },
      {
        "u": 5,
        "v": 0,
        "num": 16,
        "den": 1
      },
      {
        "u": 1,
        "v": 6,
        "num": -32,
        "den": 1
      },
      {
        "u": 5,
        "v": 2,
        "num": -32,
        "den": 1
      }
    ],
    "leading_u": "-32 u^2 v (u^4 + v^4)",
    "leading_v": "-32 u v^2 (u^4 + v^4)"
  },
  "integer_time_rescale_4X": {
    "P": "-4*x**3 - 4*x*y**2 + x + 4*y",
    "Q": "-4*x**2*y - 4*x - 4*y**3 + y",
    "deg_Y": 7
  },
  "conjugacy": true,
  "expected_deg": 7,
  "H7_from_this_field": 4,
  "beats_PT_74": false,
  "same_4_sheets_as_CL_at_N7": true,
  "beats_CL": false,
  "CL_beats_this": false
}