{
  "schema": 1,
  "provenance": {
    "date": "2026-09-11",
    "node": "v24.14.0",
    "platform": "darwin",
    "arch": "arm64",
    "jsSha256": "42a8ee86f67255259de87cc87c08e47b2dca65177564dcb74506233e86fd6c40"
  },
  "atomic": {
    "schema": 1,
    "parameters": {
      "mode": "atomic",
      "a": "1",
      "x": "0",
      "b": "0.35,0.65",
      "y": "-2,2",
      "thirdMass": "0.5,0.5",
      "thirdX": "0,4",
      "weights": "0.25,0.25,0.5",
      "candidateMass": "1",
      "candidateX": "1",
      "s": "0.25",
      "t": "0.5",
      "sourcePoints": "-1,0;1,0",
      "targetPoints": "0,-1;0,1",
      "pairing": "direct",
      "sourceMean": "0,0",
      "targetMean": "1,-1",
      "sourceCov": "4,1;1,1",
      "targetCov": "1,-0.5;-0.5,2"
    },
    "result": {
      "source": [
        {
          "position": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        }
      ],
      "target": [
        {
          "position": {
            "numerator": "-2",
            "denominator": "1",
            "value": -2
          },
          "mass": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          }
        },
        {
          "position": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "mass": {
            "numerator": "13",
            "denominator": "20",
            "value": 0.65
          }
        }
      ],
      "quantiles": [
        {
          "k": 0,
          "left": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "right": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          },
          "mass": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          },
          "x": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "y": {
            "numerator": "-2",
            "denominator": "1",
            "value": -2
          },
          "velocity": {
            "numerator": "-2",
            "denominator": "1",
            "value": -2
          },
          "atS": {
            "numerator": "-1",
            "denominator": "2",
            "value": -0.5
          },
          "atT": {
            "numerator": "-1",
            "denominator": "1",
            "value": -1
          },
          "cost": {
            "numerator": "7",
            "denominator": "5",
            "value": 1.4
          }
        },
        {
          "k": 1,
          "left": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          },
          "right": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "mass": {
            "numerator": "13",
            "denominator": "20",
            "value": 0.65
          },
          "x": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "y": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "velocity": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "atS": {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          },
          "atT": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "cost": {
            "numerator": "13",
            "denominator": "5",
            "value": 2.6
          }
        }
      ],
      "distanceSquared": {
        "numerator": "4",
        "denominator": "1",
        "value": 4
      },
      "distanceApproximation": 2,
      "atS": [
        {
          "position": {
            "numerator": "-1",
            "denominator": "2",
            "value": -0.5
          },
          "mass": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          }
        },
        {
          "position": {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          },
          "mass": {
            "numerator": "13",
            "denominator": "20",
            "value": 0.65
          }
        }
      ],
      "displacement": [
        {
          "position": {
            "numerator": "-1",
            "denominator": "1",
            "value": -1
          },
          "mass": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          }
        },
        {
          "position": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "mass": {
            "numerator": "13",
            "denominator": "20",
            "value": 0.65
          }
        }
      ],
      "mixture": [
        {
          "position": {
            "numerator": "-2",
            "denominator": "1",
            "value": -2
          },
          "mass": {
            "numerator": "7",
            "denominator": "40",
            "value": 0.175
          }
        },
        {
          "position": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "mass": {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          }
        },
        {
          "position": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "mass": {
            "numerator": "13",
            "denominator": "40",
            "value": 0.325
          }
        }
      ],
      "betweenSquared": {
        "numerator": "1",
        "denominator": "4",
        "value": 0.25
      },
      "expectedBetweenSquared": {
        "numerator": "1",
        "denominator": "4",
        "value": 0.25
      },
      "sameDistribution": false,
      "timeRows": [
        {
          "time": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "displacement": [
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              }
            }
          ],
          "startSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "endSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "expectedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "expectedEndSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "mixtureStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "mixtureEndSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            "secondMoment": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            "variance": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            "secondMoment": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            "variance": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "20",
            "value": 0.05
          },
          "displacement": [
            {
              "position": {
                "numerator": "-1",
                "denominator": "10",
                "value": -0.1
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "1",
                "denominator": "10",
                "value": 0.1
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "400",
                "value": 0.0175
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "19",
                "denominator": "20",
                "value": 0.95
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "400",
                "value": 0.0325
              }
            }
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "endSquared": {
            "numerator": "361",
            "denominator": "100",
            "value": 3.61
          },
          "expectedStartSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "expectedEndSquared": {
            "numerator": "361",
            "denominator": "100",
            "value": 3.61
          },
          "mixtureStartSquared": {
            "numerator": "1",
            "denominator": "5",
            "value": 0.2
          },
          "mixtureEndSquared": {
            "numerator": "19",
            "denominator": "5",
            "value": 3.8
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "100",
              "value": 0.03
            },
            "secondMoment": {
              "numerator": "1",
              "denominator": "100",
              "value": 0.01
            },
            "variance": {
              "numerator": "91",
              "denominator": "10000",
              "value": 0.0091
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "100",
              "value": 0.03
            },
            "secondMoment": {
              "numerator": "1",
              "denominator": "5",
              "value": 0.2
            },
            "variance": {
              "numerator": "1991",
              "denominator": "10000",
              "value": 0.1991
            }
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "10",
            "value": 0.1
          },
          "displacement": [
            {
              "position": {
                "numerator": "-1",
                "denominator": "5",
                "value": -0.2
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "1",
                "denominator": "5",
                "value": 0.2
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "200",
                "value": 0.035
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "9",
                "denominator": "10",
                "value": 0.9
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "200",
                "value": 0.065
              }
            }
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "endSquared": {
            "numerator": "81",
            "denominator": "25",
            "value": 3.24
          },
          "expectedStartSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "expectedEndSquared": {
            "numerator": "81",
            "denominator": "25",
            "value": 3.24
          },
          "mixtureStartSquared": {
            "numerator": "2",
            "denominator": "5",
            "value": 0.4
          },
          "mixtureEndSquared": {
            "numerator": "18",
            "denominator": "5",
            "value": 3.6
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "50",
              "value": 0.06
            },
            "secondMoment": {
              "numerator": "1",
              "denominator": "25",
              "value": 0.04
            },
            "variance": {
              "numerator": "91",
              "denominator": "2500",
              "value": 0.0364
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "50",
              "value": 0.06
            },
            "secondMoment": {
              "numerator": "2",
              "denominator": "5",
              "value": 0.4
            },
            "variance": {
              "numerator": "991",
              "denominator": "2500",
              "value": 0.3964
            }
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "20",
            "value": 0.15
          },
          "displacement": [
            {
              "position": {
                "numerator": "-3",
                "denominator": "10",
                "value": -0.3
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "3",
                "denominator": "10",
                "value": 0.3
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "21",
                "denominator": "400",
                "value": 0.0525
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "17",
                "denominator": "20",
                "value": 0.85
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "39",
                "denominator": "400",
                "value": 0.0975
              }
            }
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "endSquared": {
            "numerator": "289",
            "denominator": "100",
            "value": 2.89
          },
          "expectedStartSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "expectedEndSquared": {
            "numerator": "289",
            "denominator": "100",
            "value": 2.89
          },
          "mixtureStartSquared": {
            "numerator": "3",
            "denominator": "5",
            "value": 0.6
          },
          "mixtureEndSquared": {
            "numerator": "17",
            "denominator": "5",
            "value": 3.4
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "100",
              "value": 0.09
            },
            "secondMoment": {
              "numerator": "9",
              "denominator": "100",
              "value": 0.09
            },
            "variance": {
              "numerator": "819",
              "denominator": "10000",
              "value": 0.0819
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "100",
              "value": 0.09
            },
            "secondMoment": {
              "numerator": "3",
              "denominator": "5",
              "value": 0.6
            },
            "variance": {
              "numerator": "5919",
              "denominator": "10000",
              "value": 0.5919
            }
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "5",
            "value": 0.2
          },
          "displacement": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "5",
                "value": -0.4
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "5",
                "value": 0.4
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "100",
                "value": 0.07
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "4",
                "denominator": "5",
                "value": 0.8
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "100",
                "value": 0.13
              }
            }
          ],
          "startSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "endSquared": {
            "numerator": "64",
            "denominator": "25",
            "value": 2.56
          },
          "expectedStartSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "expectedEndSquared": {
            "numerator": "64",
            "denominator": "25",
            "value": 2.56
          },
          "mixtureStartSquared": {
            "numerator": "4",
            "denominator": "5",
            "value": 0.8
          },
          "mixtureEndSquared": {
            "numerator": "16",
            "denominator": "5",
            "value": 3.2
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "25",
              "value": 0.12
            },
            "secondMoment": {
              "numerator": "4",
              "denominator": "25",
              "value": 0.16
            },
            "variance": {
              "numerator": "91",
              "denominator": "625",
              "value": 0.1456
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "25",
              "value": 0.12
            },
            "secondMoment": {
              "numerator": "4",
              "denominator": "5",
              "value": 0.8
            },
            "variance": {
              "numerator": "491",
              "denominator": "625",
              "value": 0.7856
            }
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "displacement": [
            {
              "position": {
                "numerator": "-1",
                "denominator": "2",
                "value": -0.5
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "1",
                "denominator": "2",
                "value": 0.5
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "80",
                "value": 0.0875
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "3",
                "denominator": "4",
                "value": 0.75
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "80",
                "value": 0.1625
              }
            }
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          },
          "expectedStartSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "expectedEndSquared": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          },
          "mixtureStartSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "mixtureEndSquared": {
            "numerator": "3",
            "denominator": "1",
            "value": 3
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "20",
              "value": 0.15
            },
            "secondMoment": {
              "numerator": "1",
              "denominator": "4",
              "value": 0.25
            },
            "variance": {
              "numerator": "91",
              "denominator": "400",
              "value": 0.2275
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "20",
              "value": 0.15
            },
            "secondMoment": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "variance": {
              "numerator": "391",
              "denominator": "400",
              "value": 0.9775
            }
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "10",
            "value": 0.3
          },
          "displacement": [
            {
              "position": {
                "numerator": "-3",
                "denominator": "5",
                "value": -0.6
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "3",
                "denominator": "5",
                "value": 0.6
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "21",
                "denominator": "200",
                "value": 0.105
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "7",
                "denominator": "10",
                "value": 0.7
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "39",
                "denominator": "200",
                "value": 0.195
              }
            }
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "endSquared": {
            "numerator": "49",
            "denominator": "25",
            "value": 1.96
          },
          "expectedStartSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "expectedEndSquared": {
            "numerator": "49",
            "denominator": "25",
            "value": 1.96
          },
          "mixtureStartSquared": {
            "numerator": "6",
            "denominator": "5",
            "value": 1.2
          },
          "mixtureEndSquared": {
            "numerator": "14",
            "denominator": "5",
            "value": 2.8
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "50",
              "value": 0.18
            },
            "secondMoment": {
              "numerator": "9",
              "denominator": "25",
              "value": 0.36
            },
            "variance": {
              "numerator": "819",
              "denominator": "2500",
              "value": 0.3276
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "50",
              "value": 0.18
            },
            "secondMoment": {
              "numerator": "6",
              "denominator": "5",
              "value": 1.2
            },
            "variance": {
              "numerator": "2919",
              "denominator": "2500",
              "value": 1.1676
            }
          }
        },
        {
          "time": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          },
          "displacement": [
            {
              "position": {
                "numerator": "-7",
                "denominator": "10",
                "value": -0.7
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "7",
                "denominator": "10",
                "value": 0.7
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "49",
                "denominator": "400",
                "value": 0.1225
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "91",
                "denominator": "400",
                "value": 0.2275
              }
            }
          ],
          "startSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "endSquared": {
            "numerator": "169",
            "denominator": "100",
            "value": 1.69
          },
          "expectedStartSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "expectedEndSquared": {
            "numerator": "169",
            "denominator": "100",
            "value": 1.69
          },
          "mixtureStartSquared": {
            "numerator": "7",
            "denominator": "5",
            "value": 1.4
          },
          "mixtureEndSquared": {
            "numerator": "13",
            "denominator": "5",
            "value": 2.6
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "21",
              "denominator": "100",
              "value": 0.21
            },
            "secondMoment": {
              "numerator": "49",
              "denominator": "100",
              "value": 0.49
            },
            "variance": {
              "numerator": "4459",
              "denominator": "10000",
              "value": 0.4459
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "21",
              "denominator": "100",
              "value": 0.21
            },
            "secondMoment": {
              "numerator": "7",
              "denominator": "5",
              "value": 1.4
            },
            "variance": {
              "numerator": "13559",
              "denominator": "10000",
              "value": 1.3559
            }
          }
        },
        {
          "time": {
            "numerator": "2",
            "denominator": "5",
            "value": 0.4
          },
          "displacement": [
            {
              "position": {
                "numerator": "-4",
                "denominator": "5",
                "value": -0.8
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "4",
                "denominator": "5",
                "value": 0.8
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "50",
                "value": 0.14
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "3",
                "denominator": "5",
                "value": 0.6
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "50",
                "value": 0.26
              }
            }
          ],
          "startSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "endSquared": {
            "numerator": "36",
            "denominator": "25",
            "value": 1.44
          },
          "expectedStartSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "expectedEndSquared": {
            "numerator": "36",
            "denominator": "25",
            "value": 1.44
          },
          "mixtureStartSquared": {
            "numerator": "8",
            "denominator": "5",
            "value": 1.6
          },
          "mixtureEndSquared": {
            "numerator": "12",
            "denominator": "5",
            "value": 2.4
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "6",
              "denominator": "25",
              "value": 0.24
            },
            "secondMoment": {
              "numerator": "16",
              "denominator": "25",
              "value": 0.64
            },
            "variance": {
              "numerator": "364",
              "denominator": "625",
              "value": 0.5824
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "6",
              "denominator": "25",
              "value": 0.24
            },
            "secondMoment": {
              "numerator": "8",
              "denominator": "5",
              "value": 1.6
            },
            "variance": {
              "numerator": "964",
              "denominator": "625",
              "value": 1.5424
            }
          }
        },
        {
          "time": {
            "numerator": "9",
            "denominator": "20",
            "value": 0.45
          },
          "displacement": [
            {
              "position": {
                "numerator": "-9",
                "denominator": "10",
                "value": -0.9
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "9",
                "denominator": "10",
                "value": 0.9
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "63",
                "denominator": "400",
                "value": 0.1575
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "11",
                "denominator": "20",
                "value": 0.55
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "117",
                "denominator": "400",
                "value": 0.2925
              }
            }
          ],
          "startSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "endSquared": {
            "numerator": "121",
            "denominator": "100",
            "value": 1.21
          },
          "expectedStartSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "expectedEndSquared": {
            "numerator": "121",
            "denominator": "100",
            "value": 1.21
          },
          "mixtureStartSquared": {
            "numerator": "9",
            "denominator": "5",
            "value": 1.8
          },
          "mixtureEndSquared": {
            "numerator": "11",
            "denominator": "5",
            "value": 2.2
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "27",
              "denominator": "100",
              "value": 0.27
            },
            "secondMoment": {
              "numerator": "81",
              "denominator": "100",
              "value": 0.81
            },
            "variance": {
              "numerator": "7371",
              "denominator": "10000",
              "value": 0.7371
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "27",
              "denominator": "100",
              "value": 0.27
            },
            "secondMoment": {
              "numerator": "9",
              "denominator": "5",
              "value": 1.8
            },
            "variance": {
              "numerator": "17271",
              "denominator": "10000",
              "value": 1.7271
            }
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          },
          "displacement": [
            {
              "position": {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "40",
                "value": 0.175
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "2",
                "value": 0.5
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "40",
                "value": 0.325
              }
            }
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "expectedStartSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "expectedEndSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "mixtureStartSquared": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "mixtureEndSquared": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "10",
              "value": 0.3
            },
            "secondMoment": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "variance": {
              "numerator": "91",
              "denominator": "100",
              "value": 0.91
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "10",
              "value": 0.3
            },
            "secondMoment": {
              "numerator": "2",
              "denominator": "1",
              "value": 2
            },
            "variance": {
              "numerator": "191",
              "denominator": "100",
              "value": 1.91
            }
          }
        },
        {
          "time": {
            "numerator": "11",
            "denominator": "20",
            "value": 0.55
          },
          "displacement": [
            {
              "position": {
                "numerator": "-11",
                "denominator": "10",
                "value": -1.1
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "11",
                "denominator": "10",
                "value": 1.1
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "77",
                "denominator": "400",
                "value": 0.1925
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "9",
                "denominator": "20",
                "value": 0.45
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "143",
                "denominator": "400",
                "value": 0.3575
              }
            }
          ],
          "startSquared": {
            "numerator": "121",
            "denominator": "100",
            "value": 1.21
          },
          "endSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "expectedStartSquared": {
            "numerator": "121",
            "denominator": "100",
            "value": 1.21
          },
          "expectedEndSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "mixtureStartSquared": {
            "numerator": "11",
            "denominator": "5",
            "value": 2.2
          },
          "mixtureEndSquared": {
            "numerator": "9",
            "denominator": "5",
            "value": 1.8
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "33",
              "denominator": "100",
              "value": 0.33
            },
            "secondMoment": {
              "numerator": "121",
              "denominator": "100",
              "value": 1.21
            },
            "variance": {
              "numerator": "11011",
              "denominator": "10000",
              "value": 1.1011
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "33",
              "denominator": "100",
              "value": 0.33
            },
            "secondMoment": {
              "numerator": "11",
              "denominator": "5",
              "value": 2.2
            },
            "variance": {
              "numerator": "20911",
              "denominator": "10000",
              "value": 2.0911
            }
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "5",
            "value": 0.6
          },
          "displacement": [
            {
              "position": {
                "numerator": "-6",
                "denominator": "5",
                "value": -1.2
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "6",
                "denominator": "5",
                "value": 1.2
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "21",
                "denominator": "100",
                "value": 0.21
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "2",
                "denominator": "5",
                "value": 0.4
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "39",
                "denominator": "100",
                "value": 0.39
              }
            }
          ],
          "startSquared": {
            "numerator": "36",
            "denominator": "25",
            "value": 1.44
          },
          "endSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "expectedStartSquared": {
            "numerator": "36",
            "denominator": "25",
            "value": 1.44
          },
          "expectedEndSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "mixtureStartSquared": {
            "numerator": "12",
            "denominator": "5",
            "value": 2.4
          },
          "mixtureEndSquared": {
            "numerator": "8",
            "denominator": "5",
            "value": 1.6
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "25",
              "value": 0.36
            },
            "secondMoment": {
              "numerator": "36",
              "denominator": "25",
              "value": 1.44
            },
            "variance": {
              "numerator": "819",
              "denominator": "625",
              "value": 1.3104
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "25",
              "value": 0.36
            },
            "secondMoment": {
              "numerator": "12",
              "denominator": "5",
              "value": 2.4
            },
            "variance": {
              "numerator": "1419",
              "denominator": "625",
              "value": 2.2704
            }
          }
        },
        {
          "time": {
            "numerator": "13",
            "denominator": "20",
            "value": 0.65
          },
          "displacement": [
            {
              "position": {
                "numerator": "-13",
                "denominator": "10",
                "value": -1.3
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "13",
                "denominator": "10",
                "value": 1.3
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "91",
                "denominator": "400",
                "value": 0.2275
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "169",
                "denominator": "400",
                "value": 0.4225
              }
            }
          ],
          "startSquared": {
            "numerator": "169",
            "denominator": "100",
            "value": 1.69
          },
          "endSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "expectedStartSquared": {
            "numerator": "169",
            "denominator": "100",
            "value": 1.69
          },
          "expectedEndSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "mixtureStartSquared": {
            "numerator": "13",
            "denominator": "5",
            "value": 2.6
          },
          "mixtureEndSquared": {
            "numerator": "7",
            "denominator": "5",
            "value": 1.4
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "39",
              "denominator": "100",
              "value": 0.39
            },
            "secondMoment": {
              "numerator": "169",
              "denominator": "100",
              "value": 1.69
            },
            "variance": {
              "numerator": "15379",
              "denominator": "10000",
              "value": 1.5379
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "39",
              "denominator": "100",
              "value": 0.39
            },
            "secondMoment": {
              "numerator": "13",
              "denominator": "5",
              "value": 2.6
            },
            "variance": {
              "numerator": "24479",
              "denominator": "10000",
              "value": 2.4479
            }
          }
        },
        {
          "time": {
            "numerator": "7",
            "denominator": "10",
            "value": 0.7
          },
          "displacement": [
            {
              "position": {
                "numerator": "-7",
                "denominator": "5",
                "value": -1.4
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "7",
                "denominator": "5",
                "value": 1.4
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "49",
                "denominator": "200",
                "value": 0.245
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "3",
                "denominator": "10",
                "value": 0.3
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "91",
                "denominator": "200",
                "value": 0.455
              }
            }
          ],
          "startSquared": {
            "numerator": "49",
            "denominator": "25",
            "value": 1.96
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "expectedStartSquared": {
            "numerator": "49",
            "denominator": "25",
            "value": 1.96
          },
          "expectedEndSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "mixtureStartSquared": {
            "numerator": "14",
            "denominator": "5",
            "value": 2.8
          },
          "mixtureEndSquared": {
            "numerator": "6",
            "denominator": "5",
            "value": 1.2
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "21",
              "denominator": "50",
              "value": 0.42
            },
            "secondMoment": {
              "numerator": "49",
              "denominator": "25",
              "value": 1.96
            },
            "variance": {
              "numerator": "4459",
              "denominator": "2500",
              "value": 1.7836
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "21",
              "denominator": "50",
              "value": 0.42
            },
            "secondMoment": {
              "numerator": "14",
              "denominator": "5",
              "value": 2.8
            },
            "variance": {
              "numerator": "6559",
              "denominator": "2500",
              "value": 2.6236
            }
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "4",
            "value": 0.75
          },
          "displacement": [
            {
              "position": {
                "numerator": "-3",
                "denominator": "2",
                "value": -1.5
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "3",
                "denominator": "2",
                "value": 1.5
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "21",
                "denominator": "80",
                "value": 0.2625
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "39",
                "denominator": "80",
                "value": 0.4875
              }
            }
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "expectedStartSquared": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          },
          "expectedEndSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "mixtureStartSquared": {
            "numerator": "3",
            "denominator": "1",
            "value": 3
          },
          "mixtureEndSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "20",
              "value": 0.45
            },
            "secondMoment": {
              "numerator": "9",
              "denominator": "4",
              "value": 2.25
            },
            "variance": {
              "numerator": "819",
              "denominator": "400",
              "value": 2.0475
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "9",
              "denominator": "20",
              "value": 0.45
            },
            "secondMoment": {
              "numerator": "3",
              "denominator": "1",
              "value": 3
            },
            "variance": {
              "numerator": "1119",
              "denominator": "400",
              "value": 2.7975
            }
          }
        },
        {
          "time": {
            "numerator": "4",
            "denominator": "5",
            "value": 0.8
          },
          "displacement": [
            {
              "position": {
                "numerator": "-8",
                "denominator": "5",
                "value": -1.6
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "8",
                "denominator": "5",
                "value": 1.6
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "25",
                "value": 0.28
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "5",
                "value": 0.2
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "25",
                "value": 0.52
              }
            }
          ],
          "startSquared": {
            "numerator": "64",
            "denominator": "25",
            "value": 2.56
          },
          "endSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "expectedStartSquared": {
            "numerator": "64",
            "denominator": "25",
            "value": 2.56
          },
          "expectedEndSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "mixtureStartSquared": {
            "numerator": "16",
            "denominator": "5",
            "value": 3.2
          },
          "mixtureEndSquared": {
            "numerator": "4",
            "denominator": "5",
            "value": 0.8
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "12",
              "denominator": "25",
              "value": 0.48
            },
            "secondMoment": {
              "numerator": "64",
              "denominator": "25",
              "value": 2.56
            },
            "variance": {
              "numerator": "1456",
              "denominator": "625",
              "value": 2.3296
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "12",
              "denominator": "25",
              "value": 0.48
            },
            "secondMoment": {
              "numerator": "16",
              "denominator": "5",
              "value": 3.2
            },
            "variance": {
              "numerator": "1856",
              "denominator": "625",
              "value": 2.9696
            }
          }
        },
        {
          "time": {
            "numerator": "17",
            "denominator": "20",
            "value": 0.85
          },
          "displacement": [
            {
              "position": {
                "numerator": "-17",
                "denominator": "10",
                "value": -1.7
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "17",
                "denominator": "10",
                "value": 1.7
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "119",
                "denominator": "400",
                "value": 0.2975
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "3",
                "denominator": "20",
                "value": 0.15
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "221",
                "denominator": "400",
                "value": 0.5525
              }
            }
          ],
          "startSquared": {
            "numerator": "289",
            "denominator": "100",
            "value": 2.89
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "expectedStartSquared": {
            "numerator": "289",
            "denominator": "100",
            "value": 2.89
          },
          "expectedEndSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "mixtureStartSquared": {
            "numerator": "17",
            "denominator": "5",
            "value": 3.4
          },
          "mixtureEndSquared": {
            "numerator": "3",
            "denominator": "5",
            "value": 0.6
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "51",
              "denominator": "100",
              "value": 0.51
            },
            "secondMoment": {
              "numerator": "289",
              "denominator": "100",
              "value": 2.89
            },
            "variance": {
              "numerator": "26299",
              "denominator": "10000",
              "value": 2.6299
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "51",
              "denominator": "100",
              "value": 0.51
            },
            "secondMoment": {
              "numerator": "17",
              "denominator": "5",
              "value": 3.4
            },
            "variance": {
              "numerator": "31399",
              "denominator": "10000",
              "value": 3.1399
            }
          }
        },
        {
          "time": {
            "numerator": "9",
            "denominator": "10",
            "value": 0.9
          },
          "displacement": [
            {
              "position": {
                "numerator": "-9",
                "denominator": "5",
                "value": -1.8
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "9",
                "denominator": "5",
                "value": 1.8
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "63",
                "denominator": "200",
                "value": 0.315
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "10",
                "value": 0.1
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "117",
                "denominator": "200",
                "value": 0.585
              }
            }
          ],
          "startSquared": {
            "numerator": "81",
            "denominator": "25",
            "value": 3.24
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "expectedStartSquared": {
            "numerator": "81",
            "denominator": "25",
            "value": 3.24
          },
          "expectedEndSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "mixtureStartSquared": {
            "numerator": "18",
            "denominator": "5",
            "value": 3.6
          },
          "mixtureEndSquared": {
            "numerator": "2",
            "denominator": "5",
            "value": 0.4
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "27",
              "denominator": "50",
              "value": 0.54
            },
            "secondMoment": {
              "numerator": "81",
              "denominator": "25",
              "value": 3.24
            },
            "variance": {
              "numerator": "7371",
              "denominator": "2500",
              "value": 2.9484
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "27",
              "denominator": "50",
              "value": 0.54
            },
            "secondMoment": {
              "numerator": "18",
              "denominator": "5",
              "value": 3.6
            },
            "variance": {
              "numerator": "8271",
              "denominator": "2500",
              "value": 3.3084
            }
          }
        },
        {
          "time": {
            "numerator": "19",
            "denominator": "20",
            "value": 0.95
          },
          "displacement": [
            {
              "position": {
                "numerator": "-19",
                "denominator": "10",
                "value": -1.9
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "19",
                "denominator": "10",
                "value": 1.9
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "133",
                "denominator": "400",
                "value": 0.3325
              }
            },
            {
              "position": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              "mass": {
                "numerator": "1",
                "denominator": "20",
                "value": 0.05
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "247",
                "denominator": "400",
                "value": 0.6175
              }
            }
          ],
          "startSquared": {
            "numerator": "361",
            "denominator": "100",
            "value": 3.61
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "expectedStartSquared": {
            "numerator": "361",
            "denominator": "100",
            "value": 3.61
          },
          "expectedEndSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "mixtureStartSquared": {
            "numerator": "19",
            "denominator": "5",
            "value": 3.8
          },
          "mixtureEndSquared": {
            "numerator": "1",
            "denominator": "5",
            "value": 0.2
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "57",
              "denominator": "100",
              "value": 0.57
            },
            "secondMoment": {
              "numerator": "361",
              "denominator": "100",
              "value": 3.61
            },
            "variance": {
              "numerator": "32851",
              "denominator": "10000",
              "value": 3.2851
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "57",
              "denominator": "100",
              "value": 0.57
            },
            "secondMoment": {
              "numerator": "19",
              "denominator": "5",
              "value": 3.8
            },
            "variance": {
              "numerator": "34751",
              "denominator": "10000",
              "value": 3.4751
            }
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "displacement": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "mixture": [
            {
              "position": {
                "numerator": "-2",
                "denominator": "1",
                "value": -2
              },
              "mass": {
                "numerator": "7",
                "denominator": "20",
                "value": 0.35
              }
            },
            {
              "position": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "mass": {
                "numerator": "13",
                "denominator": "20",
                "value": 0.65
              }
            }
          ],
          "startSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "endSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "expectedStartSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "expectedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "mixtureStartSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "mixtureEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "displacementStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "5",
              "value": 0.6
            },
            "secondMoment": {
              "numerator": "4",
              "denominator": "1",
              "value": 4
            },
            "variance": {
              "numerator": "91",
              "denominator": "25",
              "value": 3.64
            }
          },
          "mixtureStats": {
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "mean": {
              "numerator": "3",
              "denominator": "5",
              "value": 0.6
            },
            "secondMoment": {
              "numerator": "4",
              "denominator": "1",
              "value": 4
            },
            "variance": {
              "numerator": "91",
              "denominator": "25",
              "value": 3.64
            }
          }
        }
      ]
    }
  },
  "barycenter": {
    "schema": 1,
    "parameters": {
      "mode": "barycenter",
      "a": "1",
      "x": "0",
      "b": "1",
      "y": "2",
      "thirdMass": "1",
      "thirdX": "4",
      "weights": "0.25,0.25,0.5",
      "candidateMass": "1",
      "candidateX": "2",
      "s": "0.25",
      "t": "0.5",
      "sourcePoints": "-1,0;1,0",
      "targetPoints": "0,-1;0,1",
      "pairing": "direct",
      "sourceMean": "0,0",
      "targetMean": "1,-1",
      "sourceCov": "4,1;1,1",
      "targetCov": "1,-0.5;-0.5,2"
    },
    "result": {
      "distributions": [
        [
          {
            "position": {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            }
          }
        ],
        [
          {
            "position": {
              "numerator": "2",
              "denominator": "1",
              "value": 2
            },
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            }
          }
        ],
        [
          {
            "position": {
              "numerator": "4",
              "denominator": "1",
              "value": 4
            },
            "mass": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            }
          }
        ]
      ],
      "weights": [
        {
          "numerator": "1",
          "denominator": "4",
          "value": 0.25
        },
        {
          "numerator": "1",
          "denominator": "4",
          "value": 0.25
        },
        {
          "numerator": "1",
          "denominator": "2",
          "value": 0.5
        }
      ],
      "candidate": [
        {
          "position": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        }
      ],
      "barycenter": [
        {
          "position": {
            "numerator": "5",
            "denominator": "2",
            "value": 2.5
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        }
      ],
      "quantiles": [
        {
          "k": 0,
          "left": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "right": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "positions": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "2",
              "denominator": "1",
              "value": 2
            },
            {
              "numerator": "4",
              "denominator": "1",
              "value": 4
            }
          ],
          "barycenterPosition": {
            "numerator": "5",
            "denominator": "2",
            "value": 2.5
          },
          "weightedVariance": {
            "numerator": "11",
            "denominator": "4",
            "value": 2.75
          }
        }
      ],
      "costRows": [
        {
          "k": 0,
          "weight": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "optimalCost": {
            "numerator": "25",
            "denominator": "4",
            "value": 6.25
          },
          "candidateCost": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "optimalContribution": {
            "numerator": "25",
            "denominator": "16",
            "value": 1.5625
          },
          "candidateContribution": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 1,
          "weight": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "optimalCost": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "candidateCost": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalContribution": {
            "numerator": "1",
            "denominator": "16",
            "value": 0.0625
          },
          "candidateContribution": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        },
        {
          "k": 2,
          "weight": {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          },
          "optimalCost": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          },
          "candidateCost": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "optimalContribution": {
            "numerator": "9",
            "denominator": "8",
            "value": 1.125
          },
          "candidateContribution": {
            "numerator": "2",
            "denominator": "1",
            "value": 2
          }
        }
      ],
      "objective": {
        "numerator": "11",
        "denominator": "4",
        "value": 2.75
      },
      "candidateObjective": {
        "numerator": "3",
        "denominator": "1",
        "value": 3
      },
      "gap": {
        "numerator": "1",
        "denominator": "4",
        "value": 0.25
      },
      "candidateDistanceSquared": {
        "numerator": "1",
        "denominator": "4",
        "value": 0.25
      },
      "certifiedOptimal": false,
      "barycenterStats": {
        "mass": {
          "numerator": "1",
          "denominator": "1",
          "value": 1
        },
        "mean": {
          "numerator": "5",
          "denominator": "2",
          "value": 2.5
        },
        "secondMoment": {
          "numerator": "25",
          "denominator": "4",
          "value": 6.25
        },
        "variance": {
          "numerator": "0",
          "denominator": "1",
          "value": 0
        }
      },
      "candidateStats": {
        "mass": {
          "numerator": "1",
          "denominator": "1",
          "value": 1
        },
        "mean": {
          "numerator": "2",
          "denominator": "1",
          "value": 2
        },
        "secondMoment": {
          "numerator": "4",
          "denominator": "1",
          "value": 4
        },
        "variance": {
          "numerator": "0",
          "denominator": "1",
          "value": 0
        }
      }
    }
  },
  "plane": {
    "schema": 1,
    "parameters": {
      "mode": "plane",
      "a": "1",
      "x": "0",
      "b": "0.35,0.65",
      "y": "-2,2",
      "thirdMass": "0.5,0.5",
      "thirdX": "0,4",
      "weights": "0.25,0.25,0.5",
      "candidateMass": "1",
      "candidateX": "1",
      "s": "0.25",
      "t": "0.5",
      "sourcePoints": "-1,0;1,0",
      "targetPoints": "-1,0;1,0",
      "pairing": "cross",
      "sourceMean": "0,0",
      "targetMean": "1,-1",
      "sourceCov": "4,1;1,1",
      "targetCov": "1,-0.5;-0.5,2"
    },
    "result": {
      "source": [
        [
          {
            "numerator": "-1",
            "denominator": "1",
            "value": -1
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ],
        [
          {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ]
      ],
      "target": [
        [
          {
            "numerator": "-1",
            "denominator": "1",
            "value": -1
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ],
        [
          {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ]
      ],
      "massPerLabel": {
        "numerator": "1",
        "denominator": "2",
        "value": 0.5
      },
      "assignments": [
        {
          "k": 0,
          "permutation": [
            0,
            1
          ],
          "cost": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimal": true
        },
        {
          "k": 1,
          "permutation": [
            1,
            0
          ],
          "cost": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "optimal": false
        }
      ],
      "selected": 1,
      "optimalAssignments": 1,
      "selectedOptimal": false,
      "distanceSquared": {
        "numerator": "0",
        "denominator": "1",
        "value": 0
      },
      "selectedCost": {
        "numerator": "4",
        "denominator": "1",
        "value": 4
      },
      "excessCost": {
        "numerator": "4",
        "denominator": "1",
        "value": 4
      },
      "atS": [
        [
          {
            "numerator": "-1",
            "denominator": "2",
            "value": -0.5
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ],
        [
          {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ]
      ],
      "atT": [
        [
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ],
        [
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ]
      ],
      "alternativeAtT": [
        [
          {
            "numerator": "-1",
            "denominator": "1",
            "value": -1
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ],
        [
          {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        ]
      ],
      "betweenSquared": {
        "numerator": "1",
        "denominator": "4",
        "value": 0.25
      },
      "particleBoundSquared": {
        "numerator": "1",
        "denominator": "4",
        "value": 0.25
      },
      "timeRows": [
        {
          "time": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "positions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "endSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleEndBoundSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "20",
            "value": 0.05
          },
          "positions": [
            [
              {
                "numerator": "-9",
                "denominator": "10",
                "value": -0.9
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "9",
                "denominator": "10",
                "value": 0.9
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "particleEndBoundSquared": {
            "numerator": "361",
            "denominator": "100",
            "value": 3.61
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "10",
            "value": 0.1
          },
          "positions": [
            [
              {
                "numerator": "-4",
                "denominator": "5",
                "value": -0.8
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "4",
                "denominator": "5",
                "value": 0.8
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "particleEndBoundSquared": {
            "numerator": "81",
            "denominator": "25",
            "value": 3.24
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "20",
            "value": 0.15
          },
          "positions": [
            [
              {
                "numerator": "-7",
                "denominator": "10",
                "value": -0.7
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "7",
                "denominator": "10",
                "value": 0.7
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "particleEndBoundSquared": {
            "numerator": "289",
            "denominator": "100",
            "value": 2.89
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "5",
            "value": 0.2
          },
          "positions": [
            [
              {
                "numerator": "-3",
                "denominator": "5",
                "value": -0.6
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "3",
                "denominator": "5",
                "value": 0.6
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "endSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "particleEndBoundSquared": {
            "numerator": "64",
            "denominator": "25",
            "value": 2.56
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "positions": [
            [
              {
                "numerator": "-1",
                "denominator": "2",
                "value": -0.5
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "2",
                "value": 0.5
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "particleEndBoundSquared": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "10",
            "value": 0.3
          },
          "positions": [
            [
              {
                "numerator": "-2",
                "denominator": "5",
                "value": -0.4
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "2",
                "denominator": "5",
                "value": 0.4
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "particleEndBoundSquared": {
            "numerator": "49",
            "denominator": "25",
            "value": 1.96
          }
        },
        {
          "time": {
            "numerator": "7",
            "denominator": "20",
            "value": 0.35
          },
          "positions": [
            [
              {
                "numerator": "-3",
                "denominator": "10",
                "value": -0.3
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "3",
                "denominator": "10",
                "value": 0.3
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "endSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "particleEndBoundSquared": {
            "numerator": "169",
            "denominator": "100",
            "value": 1.69
          }
        },
        {
          "time": {
            "numerator": "2",
            "denominator": "5",
            "value": 0.4
          },
          "positions": [
            [
              {
                "numerator": "-1",
                "denominator": "5",
                "value": -0.2
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "5",
                "value": 0.2
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "endSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "particleEndBoundSquared": {
            "numerator": "36",
            "denominator": "25",
            "value": 1.44
          }
        },
        {
          "time": {
            "numerator": "9",
            "denominator": "20",
            "value": 0.45
          },
          "positions": [
            [
              {
                "numerator": "-1",
                "denominator": "10",
                "value": -0.1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "10",
                "value": 0.1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "endSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "particleEndBoundSquared": {
            "numerator": "121",
            "denominator": "100",
            "value": 1.21
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "2",
            "value": 0.5
          },
          "positions": [
            [
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "particleEndBoundSquared": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "time": {
            "numerator": "11",
            "denominator": "20",
            "value": 0.55
          },
          "positions": [
            [
              {
                "numerator": "1",
                "denominator": "10",
                "value": 0.1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-1",
                "denominator": "10",
                "value": -0.1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "endSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "121",
            "denominator": "100",
            "value": 1.21
          },
          "particleEndBoundSquared": {
            "numerator": "81",
            "denominator": "100",
            "value": 0.81
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "5",
            "value": 0.6
          },
          "positions": [
            [
              {
                "numerator": "1",
                "denominator": "5",
                "value": 0.2
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-1",
                "denominator": "5",
                "value": -0.2
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "endSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "36",
            "denominator": "25",
            "value": 1.44
          },
          "particleEndBoundSquared": {
            "numerator": "16",
            "denominator": "25",
            "value": 0.64
          }
        },
        {
          "time": {
            "numerator": "13",
            "denominator": "20",
            "value": 0.65
          },
          "positions": [
            [
              {
                "numerator": "3",
                "denominator": "10",
                "value": 0.3
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-3",
                "denominator": "10",
                "value": -0.3
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "endSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "169",
            "denominator": "100",
            "value": 1.69
          },
          "particleEndBoundSquared": {
            "numerator": "49",
            "denominator": "100",
            "value": 0.49
          }
        },
        {
          "time": {
            "numerator": "7",
            "denominator": "10",
            "value": 0.7
          },
          "positions": [
            [
              {
                "numerator": "2",
                "denominator": "5",
                "value": 0.4
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-2",
                "denominator": "5",
                "value": -0.4
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "49",
            "denominator": "25",
            "value": 1.96
          },
          "particleEndBoundSquared": {
            "numerator": "9",
            "denominator": "25",
            "value": 0.36
          }
        },
        {
          "time": {
            "numerator": "3",
            "denominator": "4",
            "value": 0.75
          },
          "positions": [
            [
              {
                "numerator": "1",
                "denominator": "2",
                "value": 0.5
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-1",
                "denominator": "2",
                "value": -0.5
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "9",
            "denominator": "4",
            "value": 2.25
          },
          "particleEndBoundSquared": {
            "numerator": "1",
            "denominator": "4",
            "value": 0.25
          }
        },
        {
          "time": {
            "numerator": "4",
            "denominator": "5",
            "value": 0.8
          },
          "positions": [
            [
              {
                "numerator": "3",
                "denominator": "5",
                "value": 0.6
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-3",
                "denominator": "5",
                "value": -0.6
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "endSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "64",
            "denominator": "25",
            "value": 2.56
          },
          "particleEndBoundSquared": {
            "numerator": "4",
            "denominator": "25",
            "value": 0.16
          }
        },
        {
          "time": {
            "numerator": "17",
            "denominator": "20",
            "value": 0.85
          },
          "positions": [
            [
              {
                "numerator": "7",
                "denominator": "10",
                "value": 0.7
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-7",
                "denominator": "10",
                "value": -0.7
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "endSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "289",
            "denominator": "100",
            "value": 2.89
          },
          "particleEndBoundSquared": {
            "numerator": "9",
            "denominator": "100",
            "value": 0.09
          }
        },
        {
          "time": {
            "numerator": "9",
            "denominator": "10",
            "value": 0.9
          },
          "positions": [
            [
              {
                "numerator": "4",
                "denominator": "5",
                "value": 0.8
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-4",
                "denominator": "5",
                "value": -0.8
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "81",
            "denominator": "25",
            "value": 3.24
          },
          "particleEndBoundSquared": {
            "numerator": "1",
            "denominator": "25",
            "value": 0.04
          }
        },
        {
          "time": {
            "numerator": "19",
            "denominator": "20",
            "value": 0.95
          },
          "positions": [
            [
              {
                "numerator": "9",
                "denominator": "10",
                "value": 0.9
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-9",
                "denominator": "10",
                "value": -0.9
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "endSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "361",
            "denominator": "100",
            "value": 3.61
          },
          "particleEndBoundSquared": {
            "numerator": "1",
            "denominator": "100",
            "value": 0.01
          }
        },
        {
          "time": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "positions": [
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "alternativePositions": [
            [
              {
                "numerator": "-1",
                "denominator": "1",
                "value": -1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ],
            [
              {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            ]
          ],
          "startSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "endSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedStartSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "optimalSpeedEndSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "particleStartBoundSquared": {
            "numerator": "4",
            "denominator": "1",
            "value": 4
          },
          "particleEndBoundSquared": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          }
        }
      ]
    }
  },
  "gaussian": {
    "schema": 1,
    "parameters": {
      "mode": "gaussian",
      "a": "1",
      "x": "0",
      "b": "0.35,0.65",
      "y": "-2,2",
      "thirdMass": "0.5,0.5",
      "thirdX": "0,4",
      "weights": "0.25,0.25,0.5",
      "candidateMass": "1",
      "candidateX": "1",
      "s": "0.25",
      "t": "0.5",
      "sourcePoints": "-1,0;1,0",
      "targetPoints": "0,-1;0,1",
      "pairing": "direct",
      "sourceMean": "0,0",
      "targetMean": "0,0",
      "sourceCov": "1,0;0,4",
      "targetCov": "4,0;0,1"
    },
    "result": {
      "identicalCovariance": false,
      "sourceMean": [
        0,
        0
      ],
      "targetMean": [
        0,
        0
      ],
      "sourceCovariance": [
        [
          1,
          0
        ],
        [
          0,
          4
        ]
      ],
      "targetCovariance": [
        [
          4,
          0
        ],
        [
          0,
          1
        ]
      ],
      "sourceRoot": [
        [
          1,
          0
        ],
        [
          0,
          2
        ]
      ],
      "sourceInverseRoot": [
        [
          1,
          0
        ],
        [
          0,
          0.5
        ]
      ],
      "middle": [
        [
          4,
          0
        ],
        [
          0,
          4
        ]
      ],
      "middleRoot": [
        [
          2,
          0
        ],
        [
          0,
          2
        ]
      ],
      "map": [
        [
          2,
          0
        ],
        [
          0,
          0.5
        ]
      ],
      "mapOffset": [
        0,
        0
      ],
      "meanCost": 0,
      "covarianceCost": 2.0000000000000004,
      "distanceSquared": 2.0000000000000004,
      "distanceApproximation": 1.4142135623730951,
      "traceFormulaValue": 2,
      "atS": {
        "mean": [
          0,
          0
        ],
        "covariance": [
          [
            1.5625,
            0
          ],
          [
            0,
            3.0625
          ]
        ],
        "map": [
          [
            1.25,
            0
          ],
          [
            0,
            0.875
          ]
        ],
        "trace": 4.625,
        "determinant": 4.78515625
      },
      "atT": {
        "mean": [
          0,
          0
        ],
        "covariance": [
          [
            2.25,
            0
          ],
          [
            0,
            2.25
          ]
        ],
        "map": [
          [
            1.5,
            0
          ],
          [
            0,
            0.75
          ]
        ],
        "trace": 4.5,
        "determinant": 5.0625
      },
      "betweenSquared": 0.12500000000000003,
      "diagnostics": {
        "identityMapResidual": null,
        "mapSymmetry": 0,
        "pushforwardResidual": 0,
        "sourceRootResidual": 0,
        "middleRootResidual": 0,
        "traceCostResidual": -4.440892098500626e-16,
        "sourceDeterminant": 4,
        "targetDeterminant": 4,
        "sourceDetOverTrace": 0.8
      },
      "timeRows": [
        {
          "time": 0,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1,
              0
            ],
            [
              0,
              4
            ]
          ],
          "map": [
            [
              1,
              0
            ],
            [
              0,
              1
            ]
          ],
          "trace": 5,
          "determinant": 4,
          "startSquared": 0,
          "endSquared": 2.0000000000000004,
          "covarianceLinearBlend": [
            [
              1,
              0
            ],
            [
              0,
              4
            ]
          ]
        },
        {
          "time": 0.05,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.1025,
              0
            ],
            [
              0,
              3.8024999999999998
            ]
          ],
          "map": [
            [
              1.05,
              0
            ],
            [
              0,
              0.975
            ]
          ],
          "trace": 4.904999999999999,
          "determinant": 4.19225625,
          "startSquared": 0.005000000000000002,
          "endSquared": 1.8050000000000004,
          "covarianceLinearBlend": [
            [
              1.15,
              0
            ],
            [
              0,
              3.8499999999999996
            ]
          ]
        },
        {
          "time": 0.1,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.2100000000000002,
              0
            ],
            [
              0,
              3.6100000000000003
            ]
          ],
          "map": [
            [
              1.1,
              0
            ],
            [
              0,
              0.9500000000000001
            ]
          ],
          "trace": 4.82,
          "determinant": 4.368100000000001,
          "startSquared": 0.020000000000000007,
          "endSquared": 1.6200000000000006,
          "covarianceLinearBlend": [
            [
              1.3,
              0
            ],
            [
              0,
              3.7
            ]
          ]
        },
        {
          "time": 0.15,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.3224999999999998,
              0
            ],
            [
              0,
              3.4224999999999994
            ]
          ],
          "map": [
            [
              1.15,
              0
            ],
            [
              0,
              0.9249999999999999
            ]
          ],
          "trace": 4.744999999999999,
          "determinant": 4.5262562499999985,
          "startSquared": 0.045000000000000005,
          "endSquared": 1.445,
          "covarianceLinearBlend": [
            [
              1.45,
              0
            ],
            [
              0,
              3.55
            ]
          ]
        },
        {
          "time": 0.2,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.4400000000000004,
              0
            ],
            [
              0,
              3.24
            ]
          ],
          "map": [
            [
              1.2000000000000002,
              0
            ],
            [
              0,
              0.9
            ]
          ],
          "trace": 4.680000000000001,
          "determinant": 4.665600000000001,
          "startSquared": 0.08000000000000003,
          "endSquared": 1.2800000000000005,
          "covarianceLinearBlend": [
            [
              1.6,
              0
            ],
            [
              0,
              3.4000000000000004
            ]
          ]
        },
        {
          "time": 0.25,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.5625,
              0
            ],
            [
              0,
              3.0625
            ]
          ],
          "map": [
            [
              1.25,
              0
            ],
            [
              0,
              0.875
            ]
          ],
          "trace": 4.625,
          "determinant": 4.78515625,
          "startSquared": 0.12500000000000003,
          "endSquared": 1.1250000000000002,
          "covarianceLinearBlend": [
            [
              1.75,
              0
            ],
            [
              0,
              3.25
            ]
          ]
        },
        {
          "time": 0.3,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.6899999999999995,
              0
            ],
            [
              0,
              2.8899999999999997
            ]
          ],
          "map": [
            [
              1.2999999999999998,
              0
            ],
            [
              0,
              0.85
            ]
          ],
          "trace": 4.579999999999999,
          "determinant": 4.884099999999998,
          "startSquared": 0.18000000000000002,
          "endSquared": 0.9800000000000001,
          "covarianceLinearBlend": [
            [
              1.9,
              0
            ],
            [
              0,
              3.0999999999999996
            ]
          ]
        },
        {
          "time": 0.35,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.8225000000000002,
              0
            ],
            [
              0,
              2.7224999999999997
            ]
          ],
          "map": [
            [
              1.35,
              0
            ],
            [
              0,
              0.825
            ]
          ],
          "trace": 4.545,
          "determinant": 4.96175625,
          "startSquared": 0.24500000000000002,
          "endSquared": 0.8450000000000003,
          "covarianceLinearBlend": [
            [
              2.05,
              0
            ],
            [
              0,
              2.95
            ]
          ]
        },
        {
          "time": 0.4,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              1.9599999999999997,
              0
            ],
            [
              0,
              2.5600000000000005
            ]
          ],
          "map": [
            [
              1.4,
              0
            ],
            [
              0,
              0.8
            ]
          ],
          "trace": 4.5200000000000005,
          "determinant": 5.017600000000001,
          "startSquared": 0.3200000000000001,
          "endSquared": 0.7200000000000001,
          "covarianceLinearBlend": [
            [
              2.2,
              0
            ],
            [
              0,
              2.8
            ]
          ]
        },
        {
          "time": 0.45,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              2.1025000000000005,
              0
            ],
            [
              0,
              2.4025000000000003
            ]
          ],
          "map": [
            [
              1.4500000000000002,
              0
            ],
            [
              0,
              0.775
            ]
          ],
          "trace": 4.505000000000001,
          "determinant": 5.051256250000002,
          "startSquared": 0.40500000000000014,
          "endSquared": 0.6050000000000002,
          "covarianceLinearBlend": [
            [
              2.35,
              0
            ],
            [
              0,
              2.6500000000000004
            ]
          ]
        },
        {
          "time": 0.5,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              2.25,
              0
            ],
            [
              0,
              2.25
            ]
          ],
          "map": [
            [
              1.5,
              0
            ],
            [
              0,
              0.75
            ]
          ],
          "trace": 4.5,
          "determinant": 5.0625,
          "startSquared": 0.5000000000000001,
          "endSquared": 0.5000000000000001,
          "covarianceLinearBlend": [
            [
              2.5,
              0
            ],
            [
              0,
              2.5
            ]
          ]
        },
        {
          "time": 0.55,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              2.4025000000000003,
              0
            ],
            [
              0,
              2.1025
            ]
          ],
          "map": [
            [
              1.55,
              0
            ],
            [
              0,
              0.725
            ]
          ],
          "trace": 4.505000000000001,
          "determinant": 5.051256250000001,
          "startSquared": 0.6050000000000002,
          "endSquared": 0.405,
          "covarianceLinearBlend": [
            [
              2.6500000000000004,
              0
            ],
            [
              0,
              2.3499999999999996
            ]
          ]
        },
        {
          "time": 0.6,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              2.5600000000000005,
              0
            ],
            [
              0,
              1.9599999999999997
            ]
          ],
          "map": [
            [
              1.6,
              0
            ],
            [
              0,
              0.7
            ]
          ],
          "trace": 4.5200000000000005,
          "determinant": 5.017600000000001,
          "startSquared": 0.7200000000000001,
          "endSquared": 0.3200000000000001,
          "covarianceLinearBlend": [
            [
              2.8,
              0
            ],
            [
              0,
              2.2
            ]
          ]
        },
        {
          "time": 0.65,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              2.7224999999999997,
              0
            ],
            [
              0,
              1.8225000000000002
            ]
          ],
          "map": [
            [
              1.65,
              0
            ],
            [
              0,
              0.675
            ]
          ],
          "trace": 4.545,
          "determinant": 4.96175625,
          "startSquared": 0.8450000000000003,
          "endSquared": 0.24500000000000002,
          "covarianceLinearBlend": [
            [
              2.95,
              0
            ],
            [
              0,
              2.05
            ]
          ]
        },
        {
          "time": 0.7,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              2.8899999999999997,
              0
            ],
            [
              0,
              1.6900000000000002
            ]
          ],
          "map": [
            [
              1.7,
              0
            ],
            [
              0,
              0.65
            ]
          ],
          "trace": 4.58,
          "determinant": 4.8841,
          "startSquared": 0.9800000000000001,
          "endSquared": 0.18000000000000008,
          "covarianceLinearBlend": [
            [
              3.0999999999999996,
              0
            ],
            [
              0,
              1.9000000000000001
            ]
          ]
        },
        {
          "time": 0.75,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              3.0625,
              0
            ],
            [
              0,
              1.5625
            ]
          ],
          "map": [
            [
              1.75,
              0
            ],
            [
              0,
              0.625
            ]
          ],
          "trace": 4.625,
          "determinant": 4.78515625,
          "startSquared": 1.1250000000000002,
          "endSquared": 0.12500000000000003,
          "covarianceLinearBlend": [
            [
              3.25,
              0
            ],
            [
              0,
              1.75
            ]
          ]
        },
        {
          "time": 0.8,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              3.24,
              0
            ],
            [
              0,
              1.44
            ]
          ],
          "map": [
            [
              1.8,
              0
            ],
            [
              0,
              0.6
            ]
          ],
          "trace": 4.68,
          "determinant": 4.6656,
          "startSquared": 1.2800000000000005,
          "endSquared": 0.07999999999999997,
          "covarianceLinearBlend": [
            [
              3.4000000000000004,
              0
            ],
            [
              0,
              1.5999999999999999
            ]
          ]
        },
        {
          "time": 0.85,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              3.4225000000000003,
              0
            ],
            [
              0,
              1.3224999999999998
            ]
          ],
          "map": [
            [
              1.85,
              0
            ],
            [
              0,
              0.575
            ]
          ],
          "trace": 4.745,
          "determinant": 4.526256249999999,
          "startSquared": 1.445,
          "endSquared": 0.04500000000000002,
          "covarianceLinearBlend": [
            [
              3.55,
              0
            ],
            [
              0,
              1.4500000000000002
            ]
          ]
        },
        {
          "time": 0.9,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              3.61,
              0
            ],
            [
              0,
              1.2100000000000002
            ]
          ],
          "map": [
            [
              1.9,
              0
            ],
            [
              0,
              0.55
            ]
          ],
          "trace": 4.82,
          "determinant": 4.3681,
          "startSquared": 1.6200000000000006,
          "endSquared": 0.019999999999999993,
          "covarianceLinearBlend": [
            [
              3.7,
              0
            ],
            [
              0,
              1.2999999999999998
            ]
          ]
        },
        {
          "time": 0.95,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              3.8024999999999998,
              0
            ],
            [
              0,
              1.1025
            ]
          ],
          "map": [
            [
              1.95,
              0
            ],
            [
              0,
              0.525
            ]
          ],
          "trace": 4.904999999999999,
          "determinant": 4.19225625,
          "startSquared": 1.8050000000000004,
          "endSquared": 0.00500000000000001,
          "covarianceLinearBlend": [
            [
              3.8499999999999996,
              0
            ],
            [
              0,
              1.1500000000000001
            ]
          ]
        },
        {
          "time": 1,
          "mean": [
            0,
            0
          ],
          "covariance": [
            [
              4,
              0
            ],
            [
              0,
              1
            ]
          ],
          "map": [
            [
              2,
              0
            ],
            [
              0,
              0.5
            ]
          ],
          "trace": 5,
          "determinant": 4,
          "startSquared": 2.0000000000000004,
          "endSquared": 0,
          "covarianceLinearBlend": [
            [
              4,
              0
            ],
            [
              0,
              1
            ]
          ]
        }
      ]
    }
  }
}
