{
  "probeA": [
    {
      "m": 1,
      "result": [
        {
          "tag": "m=1,q0free",
          "branch": 0,
          "c": "0",
          "free": [
            "P0",
            "P1",
            "P2"
          ],
          "samples": [
            {
              "vals": "{P0: 1/2, P1: -1, P2: 1}",
              "verdict": "c=0 not Keller"
            },
            {
              "vals": "{P0: 3, P1: 1/2, P2: 1/2}",
              "verdict": "c=0 not Keller"
            },
            {
              "vals": "{P0: 2, P1: 2, P2: -1}",
              "verdict": "c=0 not Keller"
            }
          ]
        }
      ]
    },
    {
      "m": 2,
      "result": [
        {
          "tag": "m=2,q0free",
          "branch": 0,
          "c": "0",
          "free": [],
          "samples": [
            {
              "vals": "{}",
              "verdict": "c=0 not Keller"
            }
          ]
        }
      ]
    },
    {
      "m": 3,
      "result": [
        {
          "tag": "m=3,q0free",
          "branch": 0,
          "c": "0",
          "free": [
            "R0"
          ],
          "samples": [
            {
              "vals": "{R0: 3}",
              "verdict": "c=0 not Keller"
            },
            {
              "vals": "{R0: 1/2}",
              "verdict": "c=0 not Keller"
            },
            {
              "vals": "{R0: 1}",
              "verdict": "c=0 not Keller"
            }
          ]
        },
        {
          "tag": "m=3,q0free",
          "branch": 1,
          "c": "-R0**2/2",
          "free": [
            "R0"
          ],
          "samples": [
            {
              "vals": {
                "R0": "1/2"
              },
              "coeffs": {
                "P0": "1",
                "P1": "7/4",
                "P2": "3/4",
                "Q0": "1/4",
                "Q1": "3",
                "Q2": "9/4",
                "R0": "1/2",
                "R1": "-3/4"
              },
              "verdict": "SPECIMEN deg{3}"
            },
            {
              "vals": {
                "R0": "-1"
              },
              "coeffs": {
                "P0": "-2",
                "P1": "-7/2",
                "P2": "-3/2",
                "Q0": "-1/2",
                "Q1": "-6",
                "Q2": "-9/2",
                "R0": "-1",
                "R1": "3/2"
              },
              "verdict": "SPECIMEN deg{3}"
            },
            {
              "vals": {
                "R0": "-1"
              },
              "coeffs": {
                "P0": "-2",
                "P1": "-7/2",
                "P2": "-3/2",
                "Q0": "-1/2",
                "Q1": "-6",
                "Q2": "-9/2",
                "R0": "-1",
                "R1": "3/2"
              },
              "verdict": "SPECIMEN deg{3}"
            }
          ]
        }
      ]
    },
    {
      "m": 4,
      "result": [
        {
          "tag": "m=4,q0free",
          "branch": 0,
          "c": "0",
          "free": [],
          "samples": [
            {
              "vals": "{}",
              "verdict": "c=0 not Keller"
            }
          ]
        }
      ]
    },
    {
      "m": 5,
      "result": [
        {
          "tag": "m=5,q0free",
          "branch": 0,
          "c": "0",
          "free": [],
          "samples": [
            {
              "vals": "{}",
              "verdict": "c=0 not Keller"
            }
          ]
        }
      ]
    }
  ],
  "probeB": [
    {
      "k": 1,
      "integrability_branches": [
        {
          "psi": "g0 + g1*x*y + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g0",
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 2, g1: -1, g2: -1}",
              "result": [
                {
                  "tag": "k=1 slope(-x**2*y**2 - x*y + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: 2, Q0: 1, Q1: 1, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 1/2, Q0: -1, Q1: 1/2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 3, P2: 1/2, Q0: 1/2, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 1, g1: 2, g2: 1}",
              "result": [
                {
                  "tag": "k=1 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: -1, P2: 2, Q0: -1, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 2, P2: 1, Q0: 3, Q1: -1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1, P2: 1, Q0: 3, Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                },
                {
                  "tag": "k=1 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 1,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: -1, Q0: 2, Q1: 1/2, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1/2, Q0: 2, Q1: -1, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 3, Q0: 1, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                },
                {
                  "tag": "k=1 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 2,
                  "c": "0",
                  "free": [
                    "P0",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, Q0: 1/2, Q1: 3, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, Q0: 2, Q1: 2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, Q0: 3, Q1: -1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                },
                {
                  "tag": "k=1 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 3,
                  "c": "0",
                  "free": [
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{Q0: 1, Q1: -1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{Q0: 3, Q1: 1/2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{Q0: -1, Q1: -1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                },
                {
                  "tag": "k=1 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 4,
                  "c": "0",
                  "free": [
                    "Q2",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{Q2: 2, R1: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{Q2: 2, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{Q2: -1, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                },
                {
                  "tag": "k=1 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 5,
                  "c": "0",
                  "free": [
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{Q1: 1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{Q1: 2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "0",
          "chi": "h0 + h1*x*y",
          "free": [
            "h0",
            "h1"
          ],
          "keller": [
            {
              "slope_vals": "{h0: 2, h1: -1}",
              "result": [
                {
                  "tag": "k=1 slope(0;-x*y + 2)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: 3, P2: -1, R0: -1, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1, P2: 3, R0: 2, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1/2, P2: -1, R0: 2, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{h0: 1, h1: 2}",
              "result": [
                {
                  "tag": "k=1 slope(0;2*x*y + 1)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: 3, P2: -1, R0: -1, R1: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1/2, P2: 1/2, R0: -1, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1, P2: -1, R0: 2, R1: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g0*x*y + g0",
          "chi": "h0*x*y + h0",
          "free": [
            "g0",
            "h0"
          ],
          "keller": [
            {
              "slope_vals": "{g0: -1, h0: 2}",
              "result": [
                {
                  "tag": "k=1 slope(-x*y - 1;2*x*y + 2)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "R0"
                  ],
                  "samples": [
                    {
                      "vals": "{R0: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 1, h0: -1}",
              "result": [
                {
                  "tag": "k=1 slope(x*y + 1;-x*y - 1)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "R0"
                  ],
                  "samples": [
                    {
                      "vals": "{R0: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        }
      ]
    },
    {
      "k": 2,
      "integrability_branches": [
        {
          "psi": "g0 + g1*x*y + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g0",
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 1, g1: 2, g2: -1}",
              "result": [
                {
                  "tag": "k=2 slope(-x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 1/2, P2: -1, Q0: -1, Q1: -1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: -1, Q0: 2, Q1: 1/2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 3, P2: -1, Q0: -1, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 1, g1: -1, g2: -1}",
              "result": [
                {
                  "tag": "k=2 slope(-x**2*y**2 - x*y + 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, P1: -1, P2: 1/2, Q0: 1, Q1: 1/2, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 1, Q0: 1, Q1: -1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: -1, P2: -1, Q0: 3, Q1: 1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "0",
          "chi": "h0 + h1*x*y",
          "free": [
            "h0",
            "h1"
          ],
          "keller": [
            {
              "slope_vals": "{h0: 2, h1: 2}",
              "result": [
                {
                  "tag": "k=2 slope(0;2*x*y + 2)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: -1, R0: 3, R1: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1, P2: 3, R0: 1/2, R1: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1, P2: 1, R0: -1, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{h0: -1, h1: 1}",
              "result": [
                {
                  "tag": "k=2 slope(0;x*y - 1)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: 2, P2: 2, R0: 2, R1: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 2, R0: 3, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 1/2, R0: 1, R1: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g1*x*y + 3*g1/4 + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g1: -1, g2: 2}",
              "result": [
                {
                  "tag": "k=2 slope(2*x**2*y**2 - x*y - 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 1, P2: 2, Q0: 2, Q1: -1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 1, Q0: 2, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 2, P2: -1, Q0: -1, Q1: 1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g1: -1, g2: 1}",
              "result": [
                {
                  "tag": "k=2 slope(x**2*y**2 - x*y - 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 2, P2: 1/2, Q0: 1, Q1: 1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1, P2: 1/2, Q0: 1, Q1: -1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: -1, P2: 3, Q0: -1, Q1: 1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g1*x*y + 3*g1/4",
          "chi": "0",
          "free": [
            "g1"
          ],
          "keller": [
            {
              "slope_vals": "{g1: 1}",
              "result": [
                {
                  "tag": "k=2 slope(x*y + 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 2, P2: 1, Q0: 1, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1, P2: 3, Q0: 1, Q1: -1, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: 3, Q0: 1/2, Q1: 2, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g1: -1}",
              "result": [
                {
                  "tag": "k=2 slope(-x*y - 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 1, P2: 3, Q0: -1, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1/2, P2: -1, Q0: -1, Q1: 2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 2, P2: 1, Q0: 3, Q1: 2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g0",
          "chi": "0",
          "free": [
            "g0"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 1}",
              "result": [
                {
                  "tag": "k=2 slope(1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: 2, Q0: 3, Q1: 2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 3, P2: 1, Q0: 1/2, Q1: 1, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1, P2: 3, Q0: 2, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: -1}",
              "result": [
                {
                  "tag": "k=2 slope(-1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 1, P2: 1/2, Q0: -1, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: -1, Q0: 1/2, Q1: 1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 1/2, Q0: 1/2, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "4*g0*x*y/3 + g0",
          "chi": "0",
          "free": [
            "g0"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 2}",
              "result": [
                {
                  "tag": "k=2 slope(8*x*y/3 + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 1, Q0: 2, Q1: 1, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 3, Q0: 2, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 3, P2: 1, Q0: -1, Q1: 2, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 2}",
              "result": [
                {
                  "tag": "k=2 slope(8*x*y/3 + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: 3, P2: 1/2, Q0: 2, Q1: 1/2, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 3, P2: 1, Q0: 2, Q1: 1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1/2, P2: 1/2, Q0: 2, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        }
      ]
    },
    {
      "k": 3,
      "integrability_branches": [
        {
          "psi": "g0 + g1*x*y + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g0",
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 2, g1: -1, g2: 1}",
              "result": [
                {
                  "tag": "k=3 slope(x**2*y**2 - x*y + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, P1: 1, P2: 1/2, Q0: 1, Q1: 1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1/2, P2: -1, Q0: 2, Q1: -1, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1, P2: -1, Q0: 1, Q1: -1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 2, g1: 2, g2: -1}",
              "result": [
                {
                  "tag": "k=3 slope(-x**2*y**2 + 2*x*y + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: 2, P2: 3, Q0: 2, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: -1, Q0: 3, Q1: 1/2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: -1, P2: 3, Q0: 2, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "0",
          "chi": "h0 + h1*x*y",
          "free": [
            "h0",
            "h1"
          ],
          "keller": [
            {
              "slope_vals": "{h0: -1, h1: 2}",
              "result": [
                {
                  "tag": "k=3 slope(0;2*x*y - 1)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: -1, P2: 3, R0: 2, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 1, R0: 1, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: -1, P2: 1/2, R0: 2, R1: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{h0: 1, h1: 1}",
              "result": [
                {
                  "tag": "k=3 slope(0;x*y + 1)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: 1, P2: -1, R0: 3, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: 1, R0: 3, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 3, P2: 3, R0: 1/2, R1: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g1*x*y + g1/2 + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g1: 2, g2: 1}",
              "result": [
                {
                  "tag": "k=3 slope(x**2*y**2 + 2*x*y + 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 2, P2: 1, Q0: 2, Q1: 3, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: 2, Q0: 1/2, Q1: 1/2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 2, P2: 3, Q0: 3, Q1: 1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g1: -1, g2: 2}",
              "result": [
                {
                  "tag": "k=3 slope(2*x**2*y**2 - x*y - 1/2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, P1: 1, P2: 1, Q0: 1, Q1: 1, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 2, P2: -1, Q0: 1, Q1: 1/2, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: -1, P2: 1, Q0: 1/2, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g2*x**2*y**2 + 2*g2*x*y + g2",
          "chi": "h0",
          "free": [
            "g2",
            "h0"
          ],
          "keller": [
            {
              "slope_vals": "{g2: -1, h0: 1}",
              "result": [
                {
                  "tag": "k=3 slope(-x**2*y**2 - 2*x*y - 1;1)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "R0"
                  ],
                  "samples": [
                    {
                      "vals": "{R0: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                },
                {
                  "tag": "k=3 slope(-x**2*y**2 - 2*x*y - 1;1)",
                  "branch": 1,
                  "c": "-R0**2/6",
                  "free": [
                    "R0"
                  ],
                  "samples": [
                    {
                      "vals": {
                        "R0": "2"
                      },
                      "coeffs": {
                        "P0": "-4",
                        "P1": "-7",
                        "P2": "-3",
                        "Q0": "1/3",
                        "Q1": "4",
                        "Q2": "3",
                        "R0": "2",
                        "R1": "-3"
                      },
                      "verdict": "SPECIMEN deg{3}"
                    },
                    {
                      "vals": {
                        "R0": "-1"
                      },
                      "coeffs": {
                        "P0": "2",
                        "P1": "7/2",
                        "P2": "3/2",
                        "Q0": "-1/6",
                        "Q1": "-2",
                        "Q2": "-3/2",
                        "R0": "-1",
                        "R1": "3/2"
                      },
                      "verdict": "SPECIMEN deg{3}"
                    },
                    {
                      "vals": {
                        "R0": "-1"
                      },
                      "coeffs": {
                        "P0": "2",
                        "P1": "7/2",
                        "P2": "3/2",
                        "Q0": "-1/6",
                        "Q1": "-2",
                        "Q2": "-3/2",
                        "R0": "-1",
                        "R1": "3/2"
                      },
                      "verdict": "SPECIMEN deg{3}"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g2: 2, h0: 2}",
              "result": [
                {
                  "tag": "k=3 slope(2*x**2*y**2 + 4*x*y + 2;2)",
                  "branch": 0,
                  "c": "R0**2/6",
                  "free": [
                    "R0"
                  ],
                  "samples": [
                    {
                      "vals": {
                        "R0": "3"
                      },
                      "coeffs": {
                        "P0": "-3",
                        "P1": "-21/4",
                        "P2": "-9/4",
                        "Q0": "-1/2",
                        "Q1": "-6",
                        "Q2": "-9/2",
                        "R0": "3",
                        "R1": "-9/2"
                      },
                      "verdict": "SPECIMEN deg{3}"
                    },
                    {
                      "vals": {
                        "R0": "1/2"
                      },
                      "coeffs": {
                        "P0": "-1/2",
                        "P1": "-7/8",
                        "P2": "-3/8",
                        "Q0": "-1/12",
                        "Q1": "-1",
                        "Q2": "-3/4",
                        "R0": "1/2",
                        "R1": "-3/4"
                      },
                      "verdict": "SPECIMEN deg{3}"
                    },
                    {
                      "vals": {
                        "R0": "1"
                      },
                      "coeffs": {
                        "P0": "-1",
                        "P1": "-7/4",
                        "P2": "-3/4",
                        "Q0": "-1/6",
                        "Q1": "-2",
                        "Q2": "-3/2",
                        "R0": "1",
                        "R1": "-3/2"
                      },
                      "verdict": "SPECIMEN deg{3}"
                    }
                  ]
                },
                {
                  "tag": "k=3 slope(2*x**2*y**2 + 4*x*y + 2;2)",
                  "branch": 1,
                  "c": "0",
                  "free": [
                    "R0"
                  ],
                  "samples": [
                    {
                      "vals": "{R0: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{R0: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g0 + g1*x*y",
          "chi": "0",
          "free": [
            "g0",
            "g1"
          ],
          "keller": [
            {
              "slope_vals": "{g0: -1, g1: 1}",
              "result": [
                {
                  "tag": "k=3 slope(x*y - 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: -1, P2: 3, Q0: 3, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1/2, P2: 1/2, Q0: 3, Q1: 2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 3, Q0: 2, Q1: 3, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 1, g1: -1}",
              "result": [
                {
                  "tag": "k=3 slope(-x*y + 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: 3, P2: 1, Q0: 2, Q1: 3, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 3, Q0: 1/2, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 2, P2: 1, Q0: 1, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "0",
          "chi": "h1*x*y - h1/6",
          "free": [
            "h1"
          ],
          "keller": [
            {
              "slope_vals": "{h1: 2}",
              "result": [
                {
                  "tag": "k=3 slope(0;2*x*y - 1/3)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 1, P2: 1/2, R0: 1, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1, P2: 1/2, R0: 1, R1: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: -1, P2: 3, R0: 1, R1: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{h1: 1}",
              "result": [
                {
                  "tag": "k=3 slope(0;x*y - 1/6)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 2, P2: 1/2, R0: 1, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1, P2: 1/2, R0: 2, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 2, P2: 2, R0: 3, R1: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g1*x*y + g1/2",
          "chi": "0",
          "free": [
            "g1"
          ],
          "keller": [
            {
              "slope_vals": "{g1: -1}",
              "result": [
                {
                  "tag": "k=3 slope(-x*y - 1/2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: -1, P2: 1, Q0: -1, Q1: 3, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1/2, P2: 1/2, Q0: -1, Q1: 3, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1, P2: 1/2, Q0: 3, Q1: -1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g1: 2}",
              "result": [
                {
                  "tag": "k=3 slope(2*x*y + 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, P1: -1, P2: -1, Q0: 2, Q1: -1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: -1, P2: 3, Q0: 1, Q1: 2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 2, P2: 3, Q0: 3, Q1: -1, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g0",
          "chi": "0",
          "free": [
            "g0"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 1}",
              "result": [
                {
                  "tag": "k=3 slope(1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: 3, P2: -1, Q0: 1, Q1: 1/2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 1, P2: 1, Q0: 2, Q1: 1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1/2, P2: 2, Q0: 1, Q1: 1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 1}",
              "result": [
                {
                  "tag": "k=3 slope(1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 3, P2: 2, Q0: 3, Q1: 1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1/2, P2: 3, Q0: 1, Q1: 3, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 3, P2: 1/2, Q0: -1, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        }
      ]
    },
    {
      "k": 4,
      "integrability_branches": [
        {
          "psi": "g0 + g1*x*y + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g0",
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 2, g1: -1, g2: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-x**2*y**2 - x*y + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: -1, P2: 2, Q0: 2, Q1: 2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: 2, Q0: 2, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 3, P2: 1/2, Q0: 1/2, Q1: 1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: 2, g1: 1, g2: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-x**2*y**2 + x*y + 2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 3, P2: 1/2, Q0: 1, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 3, P2: 1/2, Q0: 3, Q1: 3, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: -1, Q0: 1, Q1: 3, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "0",
          "chi": "h0 + h1*x*y",
          "free": [
            "h0",
            "h1"
          ],
          "keller": [
            {
              "slope_vals": "{h0: 2, h1: 2}",
              "result": [
                {
                  "tag": "k=4 slope(0;2*x*y + 2)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: -1, P1: 1, P2: 1, R0: -1, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1/2, P2: -1, R0: 2, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 3, P2: -1, R0: 1, R1: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{h0: 2, h1: 1}",
              "result": [
                {
                  "tag": "k=4 slope(0;x*y + 2)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "R0",
                    "R1"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 3, P1: 1, P2: 1/2, R0: 1/2, R1: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 2, P2: 2, R0: -1, R1: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: -1, P2: 1, R0: -1, R1: -1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g1*x*y + 3*g1/8 + g2*x**2*y**2",
          "chi": "0",
          "free": [
            "g1",
            "g2"
          ],
          "keller": [
            {
              "slope_vals": "{g1: 2, g2: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-x**2*y**2 + 2*x*y + 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: -1, P2: -1, Q0: -1, Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 3, P2: -1, Q0: 2, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 1, Q0: 1, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g1: 2, g2: 1}",
              "result": [
                {
                  "tag": "k=4 slope(x**2*y**2 + 2*x*y + 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: 2, Q0: 3, Q1: -1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: 3, Q0: 1, Q1: -1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 2, P2: 1/2, Q0: 2, Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g1*x*y + 3*g1/8",
          "chi": "0",
          "free": [
            "g1"
          ],
          "keller": [
            {
              "slope_vals": "{g1: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-x*y - 3/8;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: 3, P2: 1, Q0: 1/2, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 3, P2: 2, Q0: 3, Q1: 2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 2, P2: 3, Q0: 1/2, Q1: 3, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g1: 2}",
              "result": [
                {
                  "tag": "k=4 slope(2*x*y + 3/4;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, P1: 3, P2: -1, Q0: 2, Q1: 2, Q2: -1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: -1, P2: -1, Q0: -1, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 2, P2: 1/2, Q0: 1, Q1: 2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "g0",
          "chi": "0",
          "free": [
            "g0"
          ],
          "keller": [
            {
              "slope_vals": "{g0: 2}",
              "result": [
                {
                  "tag": "k=4 slope(2;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 2, P2: 1/2, Q0: 3, Q1: 1, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1, P1: 1/2, P2: 1/2, Q0: -1, Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 2, P1: 1/2, P2: 3, Q0: 2, Q1: 1, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1, P1: 3, P2: 2, Q0: 1, Q1: 1, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: -1, P1: 1/2, P2: -1, Q0: 1, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 3, P2: 1, Q0: -1, Q1: 2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "psi": "8*g0*x*y/3 + g0",
          "chi": "0",
          "free": [
            "g0"
          ],
          "keller": [
            {
              "slope_vals": "{g0: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-8*x*y/3 - 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 2, P1: 3, P2: -1, Q0: 1, Q1: 1/2, Q2: 2}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1, P2: 1, Q0: 3, Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1/2, P2: -1, Q0: 1, Q1: 1, Q2: 1/2}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            },
            {
              "slope_vals": "{g0: -1}",
              "result": [
                {
                  "tag": "k=4 slope(-8*x*y/3 - 1;0)",
                  "branch": 0,
                  "c": "0",
                  "free": [
                    "P0",
                    "P1",
                    "P2",
                    "Q0",
                    "Q1",
                    "Q2"
                  ],
                  "samples": [
                    {
                      "vals": "{P0: 1/2, P1: -1, P2: -1, Q0: 1/2, Q1: 1/2, Q2: 3}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 1/2, P1: 1/2, P2: 3, Q0: 1, Q1: 3, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    },
                    {
                      "vals": "{P0: 3, P1: 1, P2: -1, Q0: -1, Q1: 1/2, Q2: 1}",
                      "verdict": "c=0 not Keller"
                    }
                  ]
                }
              ]
            }
          ]
        }
      ]
    }
  ]
}