{
  "schema": 1,
  "provenance": {
    "date": "2026-09-11",
    "node": "v24.14.0",
    "platform": "darwin",
    "arch": "arm64",
    "jsSha256": "4f45ae70e1db579191ee4a2d153b45d2003e95f1d365fa8727c39870e764cf2e"
  },
  "cycle": {
    "parameters": {
      "mode": "cycle",
      "a": 2,
      "b": 1,
      "c": 1,
      "d": 2,
      "scaleExponent": 0,
      "x1": 1,
      "x2": 0.25,
      "x3": 0.5,
      "steps": 24,
      "w1": 2,
      "w2": 0.5,
      "w3": 1,
      "shift": 0,
      "network": "cycle",
      "alpha": 0.875,
      "lazy": 0,
      "teleport1": 0.5,
      "teleport2": 0.25,
      "mass1": 1,
      "mass2": 0
    },
    "result": {
      "mode": "cycle",
      "scale": 1,
      "A": [
        [
          0,
          0,
          1
        ],
        [
          2,
          0,
          0
        ],
        [
          0,
          0.5,
          0
        ]
      ],
      "N": [
        [
          0,
          0,
          1
        ],
        [
          2,
          0,
          0
        ],
        [
          0,
          0.5,
          0
        ]
      ],
      "diagonal": 0,
      "product": 1,
      "exactProduct": {
        "numerator": "1",
        "denominator": "1",
        "value": 1
      },
      "beta": 1,
      "rho": 1,
      "graph": {
        "edges": [
          {
            "from": 0,
            "to": 1,
            "weight": 2
          },
          {
            "from": 1,
            "to": 2,
            "weight": 0.5
          },
          {
            "from": 2,
            "to": 0,
            "weight": 1
          }
        ],
        "reach": [
          [
            true,
            true,
            true
          ],
          [
            true,
            true,
            true
          ],
          [
            true,
            true,
            true
          ]
        ],
        "classes": [
          {
            "vertices": [
              0,
              1,
              2
            ],
            "distances": [
              0,
              1,
              2
            ],
            "periodEdges": [
              {
                "from": 0,
                "to": 1,
                "weight": 2,
                "difference": 0
              },
              {
                "from": 1,
                "to": 2,
                "weight": 0.5,
                "difference": 0
              },
              {
                "from": 2,
                "to": 0,
                "weight": 1,
                "difference": 3
              }
            ],
            "period": 3,
            "closed": true,
            "matrix": [
              [
                0,
                0,
                1
              ],
              [
                2,
                0,
                0
              ],
              [
                0,
                0.5,
                0
              ]
            ]
          }
        ],
        "irreducible": true,
        "period": 3,
        "primitive": false,
        "positive": false
      },
      "eigen": [
        {
          "lambda": {
            "re": 1,
            "im": 0
          },
          "vector": [
            {
              "re": 0.4082482904638631,
              "im": 0
            },
            {
              "re": 0.8164965809277261,
              "im": 0
            },
            {
              "re": 0.4082482904638631,
              "im": 0
            }
          ],
          "av": [
            {
              "re": 0.4082482904638631,
              "im": 0
            },
            {
              "re": 0.8164965809277261,
              "im": 0
            },
            {
              "re": 0.4082482904638631,
              "im": 0
            }
          ],
          "residual": [
            {
              "re": 0,
              "im": 0
            },
            {
              "re": 0,
              "im": 0
            },
            {
              "re": 0,
              "im": 0
            }
          ],
          "residualNorm": 0,
          "modulus": 1
        },
        {
          "lambda": {
            "re": -0.5,
            "im": 0.8660254037844386
          },
          "vector": [
            {
              "re": -0.20412414523193143,
              "im": -0.3535533905932737
            },
            {
              "re": -0.40824829046386296,
              "im": 0.7071067811865474
            },
            {
              "re": 0.40824829046386296,
              "im": 0
            }
          ],
          "av": [
            {
              "re": 0.40824829046386296,
              "im": 0
            },
            {
              "re": -0.40824829046386285,
              "im": -0.7071067811865474
            },
            {
              "re": -0.20412414523193148,
              "im": 0.3535533905932737
            }
          ],
          "residual": [
            {
              "re": 5.551115123125783e-17,
              "im": -2.7755575615628914e-17
            },
            {
              "re": 5.551115123125783e-17,
              "im": 0
            },
            {
              "re": 0,
              "im": 0
            }
          ],
          "residualNorm": 8.326672684688674e-17,
          "modulus": 1
        },
        {
          "lambda": {
            "re": -0.5,
            "im": -0.8660254037844386
          },
          "vector": [
            {
              "re": -0.20412414523193143,
              "im": 0.3535533905932737
            },
            {
              "re": -0.40824829046386296,
              "im": -0.7071067811865474
            },
            {
              "re": 0.40824829046386296,
              "im": 0
            }
          ],
          "av": [
            {
              "re": 0.40824829046386296,
              "im": 0
            },
            {
              "re": -0.40824829046386285,
              "im": 0.7071067811865474
            },
            {
              "re": -0.20412414523193148,
              "im": -0.3535533905932737
            }
          ],
          "residual": [
            {
              "re": 5.551115123125783e-17,
              "im": 2.7755575615628914e-17
            },
            {
              "re": 5.551115123125783e-17,
              "im": 0
            },
            {
              "re": 0,
              "im": 0
            }
          ],
          "residualNorm": 8.326672684688674e-17,
          "modulus": 1
        }
      ],
      "right": [
        0.25,
        0.5,
        0.25
      ],
      "left": [
        0.4,
        0.2,
        0.4
      ],
      "rightResidual": [
        0,
        0,
        0
      ],
      "leftResidual": [
        0,
        0,
        0
      ],
      "cube": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "predictedCube": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "cubeGap": [
        [
          0,
          0,
          0
        ],
        [
          0,
          0,
          0
        ],
        [
          0,
          0,
          0
        ]
      ],
      "cubeGapNorm": 0,
      "shiftedMatrix": [
        [
          1,
          0,
          1
        ],
        [
          2,
          1,
          0
        ],
        [
          0,
          0.5,
          1
        ]
      ],
      "power": {
        "rows": [
          {
            "k": 0,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 1,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 2,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 3,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 4,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 5,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 6,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 7,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 8,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 9,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 10,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 11,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 12,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 13,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 14,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 15,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 16,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 17,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 18,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 19,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 20,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 21,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 22,
            "x": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "ax": [
              0.04761904761904762,
              0.380952380952381,
              0.380952380952381
            ],
            "growth": 0.8095238095238095,
            "next": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "delta": 0.8459383753501402,
            "targetError": 0.523809523809524,
            "collatz": {
              "ax": [
                0.04761904761904762,
                0.380952380952381,
                0.380952380952381
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 23,
            "x": [
              0.05882352941176471,
              0.4705882352941177,
              0.4705882352941177
            ],
            "ax": [
              0.4705882352941177,
              0.11764705882352942,
              0.23529411764705885
            ],
            "growth": 0.823529411764706,
            "next": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "delta": 1.0252100840336136,
            "targetError": 0.4411764705882353,
            "collatz": {
              "ax": [
                0.4705882352941177,
                0.11764705882352942,
                0.23529411764705885
              ],
              "ratios": [
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 24,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.2857142857142857,
              1.1428571428571428,
              0.07142857142857142
            ],
            "growth": 1.4999999999999998,
            "next": [
              0.1904761904761905,
              0.761904761904762,
              0.04761904761904762
            ],
            "delta": 1.2380952380952381,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.2857142857142857,
                1.1428571428571428,
                0.07142857142857142
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "2",
                  "value": 0.5
                },
                {
                  "numerator": "8",
                  "denominator": "1",
                  "value": 8
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "8",
                "denominator": "1",
                "value": 8
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          }
        ],
        "stopped": false,
        "initial": [
          1,
          0.25,
          0.5
        ],
        "normalization": "l1",
        "target": [
          0.25,
          0.5,
          0.25
        ]
      },
      "shifted": {
        "rows": [
          {
            "k": 0,
            "x": [
              0.5714285714285714,
              0.14285714285714285,
              0.2857142857142857
            ],
            "ax": [
              0.8571428571428571,
              1.2857142857142856,
              0.3571428571428571
            ],
            "growth": 2.5,
            "next": [
              0.34285714285714286,
              0.5142857142857142,
              0.14285714285714285
            ],
            "delta": 0.7428571428571427,
            "targetError": 0.7142857142857143,
            "collatz": {
              "ax": [
                0.8571428571428571,
                1.2857142857142856,
                0.3571428571428571
              ],
              "ratios": [
                {
                  "numerator": "3",
                  "denominator": "2",
                  "value": 1.5
                },
                {
                  "numerator": "9",
                  "denominator": "1",
                  "value": 9
                },
                {
                  "numerator": "5",
                  "denominator": "4",
                  "value": 1.25
                }
              ],
              "lower": {
                "numerator": "5",
                "denominator": "4",
                "value": 1.25
              },
              "upper": {
                "numerator": "9",
                "denominator": "1",
                "value": 9
              },
              "width": {
                "numerator": "31",
                "denominator": "4",
                "value": 7.75
              }
            }
          },
          {
            "k": 1,
            "x": [
              0.34285714285714286,
              0.5142857142857142,
              0.14285714285714285
            ],
            "ax": [
              0.4857142857142857,
              1.2,
              0.39999999999999997
            ],
            "growth": 2.085714285714286,
            "next": [
              0.2328767123287671,
              0.5753424657534246,
              0.19178082191780818
            ],
            "delta": 0.21996086105675147,
            "targetError": 0.21428571428571425,
            "collatz": {
              "ax": [
                0.4857142857142857,
                1.2,
                0.39999999999999997
              ],
              "ratios": [
                {
                  "numerator": "8749850704605535",
                  "denominator": "6176365203250966",
                  "value": 1.4166666666666667
                },
                {
                  "numerator": "5404319552844595",
                  "denominator": "2316136951219112",
                  "value": 2.3333333333333335
                },
                {
                  "numerator": "7205759403792793",
                  "denominator": "2573485501354569",
                  "value": 2.8
                }
              ],
              "lower": {
                "numerator": "8749850704605535",
                "denominator": "6176365203250966",
                "value": 1.4166666666666667
              },
              "upper": {
                "numerator": "7205759403792793",
                "denominator": "2573485501354569",
                "value": 2.8
              },
              "width": {
                "numerator": "21987787717264829460584926148623",
                "denominator": "15894786301637226698995457763654",
                "value": 1.3833333333333333
              }
            }
          },
          {
            "k": 2,
            "x": [
              0.2328767123287671,
              0.5753424657534246,
              0.19178082191780818
            ],
            "ax": [
              0.42465753424657526,
              1.0410958904109588,
              0.47945205479452047
            ],
            "growth": 1.9452054794520546,
            "next": [
              0.21830985915492956,
              0.5352112676056339,
              0.2464788732394366
            ],
            "delta": 0.10939610264325672,
            "targetError": 0.15068493150684933,
            "collatz": {
              "ax": [
                0.42465753424657526,
                1.0410958904109588,
                0.47945205479452047
              ],
              "ratios": [
                {
                  "numerator": "15299900103943601",
                  "denominator": "8390267798936814",
                  "value": 1.8235294117647056
                },
                {
                  "numerator": "38",
                  "denominator": "21",
                  "value": 1.8095238095238095
                },
                {
                  "numerator": "17274080762516969",
                  "denominator": "6909632305006787",
                  "value": 2.5
                }
              ],
              "lower": {
                "numerator": "38",
                "denominator": "21",
                "value": 1.8095238095238095
              },
              "upper": {
                "numerator": "17274080762516969",
                "denominator": "6909632305006787",
                "value": 2.5
              },
              "width": {
                "numerator": "100189668422598443",
                "denominator": "145102278405142527",
                "value": 0.6904761904761908
              }
            }
          },
          {
            "k": 3,
            "x": [
              0.21830985915492956,
              0.5352112676056339,
              0.2464788732394366
            ],
            "ax": [
              0.46478873239436613,
              0.971830985915493,
              0.5140845070422535
            ],
            "growth": 1.9507042253521125,
            "next": [
              0.23826714801444043,
              0.49819494584837554,
              0.26353790613718414
            ],
            "delta": 0.07403264351451674,
            "targetError": 0.0704225352112677,
            "collatz": {
              "ax": [
                0.46478873239436613,
                0.971830985915493,
                0.5140845070422535
              ],
              "ratios": [
                {
                  "numerator": "5581926298712727",
                  "denominator": "2621813867577190",
                  "value": 2.129032258064516
                },
                {
                  "numerator": "2917825110690744",
                  "denominator": "1606918176902149",
                  "value": 1.8157894736842104
                },
                {
                  "numerator": "6173948784939835",
                  "denominator": "2960112431135537",
                  "value": 2.085714285714286
                }
              ],
              "lower": {
                "numerator": "2917825110690744",
                "denominator": "1606918176902149",
                "value": 1.8157894736842104
              },
              "upper": {
                "numerator": "5581926298712727",
                "denominator": "2621813867577190",
                "value": 2.129032258064516
              },
              "width": {
                "numerator": "1319704493155673603896701420963",
                "denominator": "4213040360263910452826334381310",
                "value": 0.31324278438030567
              }
            }
          },
          {
            "k": 4,
            "x": [
              0.23826714801444043,
              0.49819494584837554,
              0.26353790613718414
            ],
            "ax": [
              0.5018050541516246,
              0.9747292418772564,
              0.5126353790613719
            ],
            "growth": 1.989169675090253,
            "next": [
              0.25226860254083483,
              0.4900181488203266,
              0.2577132486388385
            ],
            "delta": 0.02800290905278896,
            "targetError": 0.02707581227436817,
            "collatz": {
              "ax": [
                0.5018050541516246,
                0.9747292418772564,
                0.5126353790613719
              ],
              "ratios": [
                {
                  "numerator": "9039716219559552",
                  "denominator": "4292239356049859",
                  "value": 2.106060606060606
                },
                {
                  "numerator": "8779580501011076",
                  "denominator": "4487341144961217",
                  "value": 1.9565217391304346
                },
                {
                  "numerator": "9234818008470910",
                  "denominator": "4747476863509693",
                  "value": 1.9452054794520548
                }
              ],
              "lower": {
                "numerator": "9234818008470910",
                "denominator": "4747476863509693",
                "value": 1.9452054794520548
              },
              "upper": {
                "numerator": "9039716219559552",
                "denominator": "4292239356049859",
                "value": 2.106060606060606
              },
              "width": {
                "numerator": "3277794303135461175523031635846",
                "denominator": "20377307035492449031015437783287",
                "value": 0.16085512660855134
              }
            }
          },
          {
            "k": 5,
            "x": [
              0.25226860254083483,
              0.4900181488203266,
              0.2577132486388385
            ],
            "ax": [
              0.5099818511796733,
              0.9945553539019962,
              0.5027223230490018
            ],
            "growth": 2.007259528130671,
            "next": [
              0.2540687160940326,
              0.49547920433996384,
              0.2504520795660036
            ],
            "delta": 0.014522338145669833,
            "targetError": 0.01996370235934669,
            "collatz": {
              "ax": [
                0.5099818511796733,
                0.9945553539019962,
                0.5027223230490018
              ],
              "ratios": [
                {
                  "numerator": "4593508149876985",
                  "denominator": "2272233568800359",
                  "value": 2.02158273381295
                },
                {
                  "numerator": "17916316484929449",
                  "denominator": "8827382209728013",
                  "value": 2.0296296296296297
                },
                {
                  "numerator": "18112480534034517",
                  "denominator": "9285098324306504",
                  "value": 1.9507042253521125
                }
              ],
              "lower": {
                "numerator": "18112480534034517",
                "denominator": "9285098324306504",
                "value": 1.9507042253521125
              },
              "upper": {
                "numerator": "17916316484929449",
                "denominator": "8827382209728013",
                "value": 2.0296296296296297
              },
              "width": {
                "numerator": "6468971731782185187308168011575",
                "denominator": "81963111763558617958960686896552",
                "value": 0.07892540427751715
              }
            }
          },
          {
            "k": 6,
            "x": [
              0.2540687160940326,
              0.49547920433996384,
              0.2504520795660036
            ],
            "ax": [
              0.5045207956600362,
              1.003616636528029,
              0.49819168173598555
            ],
            "growth": 2.0063291139240507,
            "next": [
              0.25146462370437134,
              0.5002253267237494,
              0.24831004957187922
            ],
            "delta": 0.00949224476757124,
            "targetError": 0.009041591320072373,
            "collatz": {
              "ax": [
                0.5045207956600362,
                1.003616636528029,
                0.49819168173598555
              ],
              "ratios": [
                {
                  "numerator": "3029546223113607",
                  "denominator": "1525631700170114",
                  "value": 1.98576512455516
                },
                {
                  "numerator": "4519887510290462",
                  "denominator": "2231439960035291",
                  "value": 2.0255474452554747
                },
                {
                  "numerator": "8974623488901061",
                  "denominator": "4511743568830479",
                  "value": 1.9891696750902528
                }
              ],
              "lower": {
                "numerator": "3029546223113607",
                "denominator": "1525631700170114",
                "value": 1.98576512455516
              },
              "upper": {
                "numerator": "4519887510290462",
                "denominator": "2231439960035291",
                "value": 2.0255474452554747
              },
              "width": {
                "numerator": "135433163872407183475329348031",
                "denominator": "3404355540056172245686143493174",
                "value": 0.03978232070031456
              }
            }
          },
          {
            "k": 7,
            "x": [
              0.25146462370437134,
              0.5002253267237494,
              0.24831004957187922
            ],
            "ax": [
              0.4997746732762506,
              1.003154574132492,
              0.49842271293375395
            ],
            "growth": 2.0013519603424967,
            "next": [
              0.2497185318621932,
              0.5012384598063498,
              0.24904300833145687
            ],
            "delta": 0.0034921836843562204,
            "targetError": 0.003379900856241541,
            "collatz": {
              "ax": [
                0.4997746732762506,
                1.003154574132492,
                0.49842271293375395
              ],
              "ratios": [
                {
                  "numerator": "18006280258689067",
                  "denominator": "9059967884894950",
                  "value": 1.9874551971326164
                },
                {
                  "numerator": "361424525300648",
                  "denominator": "180225167602749",
                  "value": 2.0054054054054054
                },
                {
                  "numerator": "5985856917977189",
                  "denominator": "2982104124598039",
                  "value": 2.0072595281306715
                }
              ],
              "lower": {
                "numerator": "18006280258689067",
                "denominator": "9059967884894950",
                "value": 1.9874551971326164
              },
              "upper": {
                "numerator": "5985856917977189",
                "denominator": "2982104124598039",
                "value": 2.0072595281306715
              },
              "width": {
                "numerator": "535068812344685859303302355937",
                "denominator": "27017767598271001835688491003050",
                "value": 0.019804330998055057
              }
            }
          },
          {
            "k": 8,
            "x": [
              0.2497185318621932,
              0.5012384598063498,
              0.24904300833145687
            ],
            "ax": [
              0.49876154019365004,
              1.0006755235307363,
              0.4996622382346318
            ],
            "growth": 1.9990993019590182,
            "next": [
              0.24949312908312682,
              0.5005631899076368,
              0.2499436810092363
            ],
            "delta": 0.0018013453555588421,
            "targetError": 0.002476919612699774,
            "collatz": {
              "ax": [
                0.49876154019365004,
                1.0006755235307363,
                0.4996622382346318
              ],
              "ratios": [
                {
                  "numerator": "17969778292502857",
                  "denominator": "8997058296336645",
                  "value": 1.9972948602344454
                },
                {
                  "numerator": "18026567659567199",
                  "denominator": "9029509363230554",
                  "value": 1.9964061096136565
                },
                {
                  "numerator": "818283152699853",
                  "denominator": "407850908916646",
                  "value": 2.0063291139240507
                }
              ],
              "lower": {
                "numerator": "18026567659567199",
                "denominator": "9029509363230554",
                "value": 1.9964061096136565
              },
              "upper": {
                "numerator": "818283152699853",
                "denominator": "407850908916646",
                "value": 2.0063291139240507
              },
              "width": {
                "numerator": "9135846118810427043218553502",
                "denominator": "920673400216236725502716600471",
                "value": 0.009923004310393576
              }
            }
          },
          {
            "k": 9,
            "x": [
              0.24949312908312682,
              0.5005631899076368,
              0.2499436810092363
            ],
            "ax": [
              0.4994368100923631,
              0.9995494480738905,
              0.5002252759630548
            ],
            "growth": 1.9992115341293084,
            "next": [
              0.2498168910924559,
              0.49997182939883933,
              0.25021127950870475
            ],
            "delta": 0.0011827210175950065,
            "targetError": 0.0011263798152736926,
            "collatz": {
              "ax": [
                0.4994368100923631,
                0.9995494480738905,
                0.5002252759630548
              ],
              "ratios": [
                {
                  "numerator": "8997053727308303",
                  "denominator": "4494468652681076",
                  "value": 2.001805869074492
                },
                {
                  "numerator": "2250785260941979",
                  "denominator": "1127168097771710",
                  "value": 1.996849684968497
                },
                {
                  "numerator": "9011257465714067",
                  "denominator": "4502585074627227",
                  "value": 2.0013519603424963
                }
              ],
              "lower": {
                "numerator": "2250785260941979",
                "denominator": "1127168097771710",
                "value": 1.996849684968497
              },
              "upper": {
                "numerator": "8997053727308303",
                "denominator": "4494468652681076",
                "value": 2.001805869074492
              },
              "width": {
                "numerator": "12554068069826363993427109363",
                "denominator": "2533010840868554393396442579980",
                "value": 0.004956184105995238
              }
            }
          },
          {
            "k": 10,
            "x": [
              0.2498168910924559,
              0.49997182939883933,
              0.25021127950870475
            ],
            "ax": [
              0.5000281706011607,
              0.999605611583751,
              0.5001971942081245
            ],
            "growth": 1.9998309763930362,
            "next": [
              0.25003521622763775,
              0.49984504859839407,
              0.2501197351739682
            ],
            "delta": 0.00043665027036368653,
            "targetError": 0.00042255901740953505,
            "collatz": {
              "ax": [
                0.5000281706011607,
                0.999605611583751,
                0.5001971942081245
              ],
              "ratios": [
                {
                  "numerator": "18015413462353103",
                  "denominator": "9000602061078721",
                  "value": 2.0015787099684257
                },
                {
                  "numerator": "18007293839384153",
                  "denominator": "9006691778305432",
                  "value": 1.9993238674780256
                },
                {
                  "numerator": "9010751589789907",
                  "denominator": "4507405700637191",
                  "value": 1.9990993019590177
                }
              ],
              "lower": {
                "numerator": "9010751589789907",
                "denominator": "4507405700637191",
                "value": 1.9990993019590177
              },
              "upper": {
                "numerator": "18015413462353103",
                "denominator": "9000602061078721",
                "value": 2.0015787099684257
              },
              "width": {
                "numerator": "100588008614972317279157784726",
                "denominator": "40569365039273077812010511312711",
                "value": 0.0024794080094080436
              }
            }
          },
          {
            "k": 11,
            "x": [
              0.25003521622763775,
              0.49984504859839407,
              0.2501197351739682
            ],
            "ax": [
              0.5001549514016059,
              0.9999154810536696,
              0.5000422594731653
            ],
            "growth": 2.000112691928441,
            "next": [
              0.25006338563822295,
              0.4999295715130856,
              0.2500070428486914
            ],
            "delta": 0.0002253846505534951,
            "targetError": 0.0003099028032118589,
            "collatz": {
              "ax": [
                0.5001549514016059,
                0.9999154810536696,
                0.5000422594731653
              ],
              "ratios": [
                {
                  "numerator": "9009990611039124",
                  "denominator": "4504234026529163",
                  "value": 2.000338028169014
                },
                {
                  "numerator": "9006437975750593",
                  "denominator": "4502203949221430",
                  "value": 2.000450907451246
                },
                {
                  "numerator": "9007960533731391",
                  "denominator": "4505756584509961",
                  "value": 1.999211534129308
                }
              ],
              "lower": {
                "numerator": "9007960533731391",
                "denominator": "4505756584509961",
                "value": 1.999211534129308
              },
              "upper": {
                "numerator": "9006437975750593",
                "denominator": "4502203949221430",
                "value": 2.000450907451246
              },
              "width": {
                "numerator": "25141722822549901758859247743",
                "denominator": "20285835089011208324544029664230",
                "value": 0.0012393733219377848
              }
            }
          },
          {
            "k": 12,
            "x": [
              0.25006338563822295,
              0.4999295715130856,
              0.2500070428486914
            ],
            "ax": [
              0.5000704284869144,
              1.0000563427895315,
              0.4999718286052342
            ],
            "growth": 2.0000985998816803,
            "next": [
              0.25002288812986373,
              0.5000035212507482,
              0.24997359061938798
            ],
            "delta": 0.00014789947532525827,
            "targetError": 0.0001408569738287624,
            "collatz": {
              "ax": [
                0.5000704284869144,
                1.0000563427895315,
                0.4999718286052342
              ],
              "ratios": [
                {
                  "numerator": "9008467981570687",
                  "denominator": "4504741481517222",
                  "value": 1.9997746859685683
                },
                {
                  "numerator": "4503853372736435",
                  "denominator": "2251482631977824",
                  "value": 2.0003944550884705
                },
                {
                  "numerator": "9006691764009113",
                  "denominator": "4503726500053465",
                  "value": 1.9998309763930364
                }
              ],
              "lower": {
                "numerator": "9008467981570687",
                "denominator": "4504741481517222",
                "value": 1.9997746859685683
              },
              "upper": {
                "numerator": "4503853372736435",
                "denominator": "2251482631977824",
                "value": 2.0003944550884705
              },
              "width": {
                "numerator": "3142956801169599432423469241",
                "denominator": "5071173603593038597397089042464",
                "value": 0.0006197691199020962
              }
            }
          },
          {
            "k": 13,
            "x": [
              0.25002288812986373,
              0.5000035212507482,
              0.24997359061938798
            ],
            "ax": [
              0.4999964787492517,
              1.0000492975104756,
              0.4999753512447621
            ],
            "growth": 2.0000211275044895,
            "next": [
              0.2499955984830612,
              0.5000193666745306,
              0.24998503484240808
            ],
            "delta": 0.00005457929360505598,
            "targetError": 0.00005281876122395501,
            "collatz": {
              "ax": [
                0.4999964787492517,
                1.0000492975104756,
                0.4999753512447621
              ],
              "ratios": [
                {
                  "numerator": "18014271643053521",
                  "denominator": "9008023886525996",
                  "value": 1.9998028280096893
                },
                {
                  "numerator": "9007643287240609",
                  "denominator": "4503631343977611",
                  "value": 2.0000845094228006
                },
                {
                  "numerator": "2001501160498083",
                  "denominator": "1000694195169725",
                  "value": 2.0001126919284404
                }
              ],
              "lower": {
                "numerator": "18014271643053521",
                "denominator": "9008023886525996",
                "value": 1.9998028280096893
              },
              "upper": {
                "numerator": "2001501160498083",
                "denominator": "1000694195169725",
                "value": 2.0001126919284404
              },
              "width": {
                "numerator": "2793199261990132000033813943",
                "denominator": "9014277213196789767933844671100",
                "value": 0.0003098639187511255
              }
            }
          },
          {
            "k": 14,
            "x": [
              0.2499955984830612,
              0.5000193666745306,
              0.24998503484240808
            ],
            "ax": [
              0.49998063332546927,
              1.0000105636406529,
              0.4999947181796734
            ],
            "growth": 1.9999859151457955,
            "next": [
              0.24999207721371455,
              0.5000088030958727,
              0.24999911969041275
            ],
            "delta": 0.000028169696009217038,
            "targetError": 0.0000387333490613484,
            "collatz": {
              "ax": [
                0.49998063332546927,
                1.0000105636406529,
                0.4999947181796734
              ],
              "ratios": [
                {
                  "numerator": "4503425187874096",
                  "denominator": "2251760168345157",
                  "value": 1.9999577446934378
                },
                {
                  "numerator": "3002431467852403",
                  "denominator": "1501258022288965",
                  "value": 1.9999436627653133
                },
                {
                  "numerator": "9007104105924773",
                  "denominator": "4503330039057878",
                  "value": 2.00009859988168
                }
              ],
              "lower": {
                "numerator": "3002431467852403",
                "denominator": "1501258022288965",
                "value": 1.9999436627653133
              },
              "upper": {
                "numerator": "9007104105924773",
                "denominator": "4503330039057878",
                "value": 2.00009859988168
              },
              "width": {
                "numerator": "1047477219077056017479649111",
                "denominator": "6760660348150517434533675716270",
                "value": 0.00015493711636668887
              }
            }
          },
          {
            "k": 15,
            "x": [
              0.24999207721371455,
              0.5000088030958727,
              0.24999911969041275
            ],
            "ax": [
              0.4999911969041273,
              0.9999929575233018,
              0.5000035212383491
            ],
            "growth": 1.9999876756657782,
            "next": [
              0.24999713897621126,
              0.499999559842494,
              0.2500033011812947
            ],
            "delta": 0.00001848650675737029,
            "targetError": 0.00001760619174540068,
            "collatz": {
              "ax": [
                0.4999911969041273,
                0.9999929575233018,
                0.5000035212383491
              ],
              "ratios": [
                {
                  "numerator": "18014081344527648",
                  "denominator": "9006913806282089",
                  "value": 2.0000281707995575
                },
                {
                  "numerator": "18014271643500249",
                  "denominator": "9007357837218160",
                  "value": 1.9999507035310358
                },
                {
                  "numerator": "18014525375463719",
                  "denominator": "9007167538245559",
                  "value": 2.000021127504489
                }
              ],
              "lower": {
                "numerator": "18014271643500249",
                "denominator": "9007357837218160",
                "value": 1.9999507035310358
              },
              "upper": {
                "numerator": "18014081344527648",
                "denominator": "9006913806282089",
                "value": 2.0000281707995575
              },
              "width": {
                "numerator": "6284802958228505918491947519",
                "denominator": "81128495662163422502859993536240",
                "value": 0.00007746726852177542
              }
            }
          },
          {
            "k": 16,
            "x": [
              0.24999713897621126,
              0.499999559842494,
              0.2500033011812947
            ],
            "ax": [
              0.500000440157506,
              0.9999938377949165,
              0.5000030811025418
            ],
            "growth": 1.9999973590549642,
            "next": [
              0.250000550197609,
              0.4999975791305205,
              0.2500018706718705
            ],
            "delta": 0.000006822442795401118,
            "targetError": 0.000006602362589452904,
            "collatz": {
              "ax": [
                0.500000440157506,
                0.9999938377949165,
                0.5000030811025418
              ],
              "ratios": [
                {
                  "numerator": "948127071990917",
                  "denominator": "474057693447139",
                  "value": 2.0000246491024205
                },
                {
                  "numerator": "18014287501063913",
                  "denominator": "9007191325568272",
                  "value": 1.9999894362105575
                },
                {
                  "numerator": "9007254758950027",
                  "denominator": "4503659096165891",
                  "value": 1.9999859151457955
                }
              ],
              "lower": {
                "numerator": "9007254758950027",
                "denominator": "4503659096165891",
                "value": 1.9999859151457955
              },
              "upper": {
                "numerator": "948127071990917",
                "denominator": "474057693447139",
                "value": 2.0000246491024205
              },
              "width": {
                "numerator": "82696774410136960810089294",
                "denominator": "2134994243200629057349983335849",
                "value": 0.00003873395662470917
              }
            }
          },
          {
            "k": 17,
            "x": [
              0.250000550197609,
              0.4999975791305205,
              0.2500018706718705
            ],
            "ax": [
              0.5000024208694795,
              0.9999986795257385,
              0.5000006602371307
            ],
            "growth": 2.000001760632349,
            "next": [
              0.25000099035482437,
              0.4999988996057507,
              0.2500001100394249
            ],
            "delta": 0.0000035212648912263944,
            "targetError": 0.000004841738958982766,
            "collatz": {
              "ax": [
                0.5000024208694795,
                0.9999986795257385,
                0.5000006602371307
              ],
              "ratios": [
                {
                  "numerator": "147659719102435",
                  "denominator": "73829664571303",
                  "value": 2.000005281885422
                },
                {
                  "numerator": "18014374721932415",
                  "denominator": "9007155644233449",
                  "value": 2.000007042563493
                },
                {
                  "numerator": "6004807432343851",
                  "denominator": "3002422217599368",
                  "value": 1.9999876756657782
                }
              ],
              "lower": {
                "numerator": "6004807432343851",
                "denominator": "3002422217599368",
                "value": 1.9999876756657782
              },
              "upper": {
                "numerator": "18014374721932415",
                "denominator": "9007155644233449",
                "value": 2.000007042563493
              },
              "width": {
                "numerator": "174581506479247726986347207",
                "denominator": "9014428074540685358769782286744",
                "value": 0.000019366897715043694
              }
            }
          },
          {
            "k": 18,
            "x": [
              0.25000099035482437,
              0.4999988996057507,
              0.2500001100394249
            ],
            "ax": [
              0.5000011003942493,
              1.0000008803153995,
              0.49999955984230027
            ],
            "growth": 2.000001540551949,
            "next": [
              0.25000035762785555,
              0.50000005501967,
              0.24999958735247435
            ],
            "delta": 0.0000023108278386918535,
            "targetError": 0.0000022007884985519865,
            "collatz": {
              "ax": [
                0.5000011003942493,
                1.0000008803153995,
                0.49999955984230027
              ],
              "ratios": [
                {
                  "numerator": "2251804769420379",
                  "denominator": "1125904367004242",
                  "value": 1.9999964787523512
                },
                {
                  "numerator": "4503603591958601",
                  "denominator": "2251794857950117",
                  "value": 2.0000061622213576
                },
                {
                  "numerator": "4503595662782391",
                  "denominator": "2251800804832274",
                  "value": 1.9999973590549642
                }
              ],
              "lower": {
                "numerator": "2251804769420379",
                "denominator": "1125904367004242",
                "value": 1.9999964787523512
              },
              "upper": {
                "numerator": "4503603591958601",
                "denominator": "2251794857950117",
                "value": 2.0000061622213576
              },
              "width": {
                "numerator": "24550553820940249470151099",
                "denominator": "2535305664163733512248363396314",
                "value": 0.000009683469006502697
              }
            }
          },
          {
            "k": 19,
            "x": [
              0.25000035762785555,
              0.50000005501967,
              0.24999958735247435
            ],
            "ax": [
              0.4999999449803299,
              1.0000007702753813,
              0.49999961486230937
            ],
            "growth": 2.0000003301180205,
            "next": [
              0.24999993122542374,
              0.5000003026081355,
              0.24999976616644073
            ],
            "delta": 8.52804863699097e-7,
            "targetError": 8.252950512432911e-7,
            "collatz": {
              "ax": [
                0.4999999449803299,
                1.0000007702753813,
                0.49999961486230937
              ],
              "ratios": [
                {
                  "numerator": "9007198263594729",
                  "denominator": "4503606069821204",
                  "value": 1.9999969189028828
                },
                {
                  "numerator": "9007206192764831",
                  "denominator": "4503600122943627",
                  "value": 2.0000013204719367
                },
                {
                  "numerator": "9007192316717152",
                  "denominator": "4503592193773525",
                  "value": 2.000001760632349
                }
              ],
              "lower": {
                "numerator": "9007198263594729",
                "denominator": "4503606069821204",
                "value": 1.9999969189028828
              },
              "upper": {
                "numerator": "9007192316717152",
                "denominator": "4503592193773525",
                "value": 2.000001760632349
              },
              "width": {
                "numerator": "98201918607585655070341283",
                "denominator": "20282405139877839125418818824100",
                "value": 0.000004841729466024123
              }
            }
          },
          {
            "k": 20,
            "x": [
              0.24999993122542374,
              0.5000003026081355,
              0.24999976616644073
            ],
            "ax": [
              0.49999969739186445,
              1.000000165058983,
              0.49999991747050854
            ],
            "growth": 1.999999779921356,
            "next": [
              0.2499998762057491,
              0.5000001375491676,
              0.24999998624508324
            ],
            "delta": 4.4015728509205765e-7,
            "targetError": 6.052162710712405e-7,
            "collatz": {
              "ax": [
                0.49999969739186445,
                1.000000165058983,
                0.49999991747050854
              ],
              "ratios": [
                {
                  "numerator": "18014387606874893",
                  "denominator": "9007196776875744",
                  "value": 1.9999993397638862
                },
                {
                  "numerator": "9007200741460141",
                  "denominator": "4503602353022269",
                  "value": 1.9999991196859563
                },
                {
                  "numerator": "18014395536043687",
                  "denominator": "9007190829999149",
                  "value": 2.000001540551949
                }
              ],
              "lower": {
                "numerator": "9007200741460141",
                "denominator": "4503602353022269",
                "value": 1.9999991196859563
              },
              "upper": {
                "numerator": "18014395536043687",
                "denominator": "9007190829999149",
                "value": 2.000001540551949
              },
              "width": {
                "numerator": "98201958889960311620445794",
                "denominator": "40564805816104771556990848049081",
                "value": 0.0000024208659924355616
              }
            }
          },
          {
            "k": 21,
            "x": [
              0.2499998762057491,
              0.5000001375491676,
              0.24999998624508324
            ],
            "ax": [
              0.49999986245083233,
              0.9999998899606658,
              0.500000055019667
            ],
            "growth": 1.9999998074311651,
            "next": [
              0.24999995529651622,
              0.49999999312254095,
              0.25000005158094285
            ],
            "delta": 2.888532533995569e-7,
            "targetError": 2.750983352783898e-7,
            "collatz": {
              "ax": [
                0.49999986245083233,
                0.9999998899606658,
                0.500000055019667
              ],
              "ratios": [
                {
                  "numerator": "3002398925625157",
                  "denominator": "1501199132430509",
                  "value": 2.0000004401575544
                },
                {
                  "numerator": "3002399421198261",
                  "denominator": "1501200288767752",
                  "value": 1.999999229724873
                },
                {
                  "numerator": "375300010245300",
                  "denominator": "187649974149331",
                  "value": 2.0000003301180205
                }
              ],
              "lower": {
                "numerator": "3002399421198261",
                "denominator": "1501200288767752",
                "value": 1.999999229724873
              },
              "upper": {
                "numerator": "3002398925625157",
                "denominator": "1501199132430509",
                "value": 2.0000004401575544
              },
              "width": {
                "numerator": "2727831782262861687392215",
                "denominator": "2253600571102578887108380145768",
                "value": 0.000001210432681479249
              }
            }
          },
          {
            "k": 22,
            "x": [
              0.24999995529651622,
              0.49999999312254095,
              0.25000005158094285
            ],
            "ax": [
              0.500000006877459,
              0.9999999037155733,
              0.5000000481422133
            ],
            "growth": 1.9999999587352457,
            "next": [
              0.250000008596824,
              0.49999996217397447,
              0.25000002922920156
            ],
            "delta": 1.0660061552925093e-7,
            "targetError": 1.0316188567283113e-7,
            "collatz": {
              "ax": [
                0.500000006877459,
                0.9999999037155733,
                0.5000000481422133
              ],
              "ratios": [
                {
                  "numerator": "18014398757268561",
                  "denominator": "9007197644128249",
                  "value": 2.0000003851377754
                },
                {
                  "numerator": "18014396774975953",
                  "denominator": "9007199130847704",
                  "value": 1.9999998349409807
                },
                {
                  "numerator": "2251800030498502",
                  "denominator": "1125900139142539",
                  "value": 1.9999997799213558
                }
              ],
              "lower": {
                "numerator": "2251800030498502",
                "denominator": "1125900139142539",
                "value": 1.9999997799213558
              },
              "upper": {
                "numerator": "18014398757268561",
                "denominator": "9007197644128249",
                "value": 2.0000003851377754
              },
              "width": {
                "numerator": "6137623828012651592033381",
                "denominator": "10141205080808345027923007484211",
                "value": 6.052164194596317e-7
              }
            }
          },
          {
            "k": 23,
            "x": [
              0.250000008596824,
              0.49999996217397447,
              0.25000002922920156
            ],
            "ax": [
              0.5000000378260255,
              0.9999999793676224,
              0.5000000103161888
            ],
            "growth": 2.0000000275098366,
            "next": [
              0.25000001547428297,
              0.49999998280635227,
              0.2500000017193648
            ],
            "delta": 5.501967353938042e-8,
            "targetError": 7.565205106807582e-8,
            "collatz": {
              "ax": [
                0.5000000378260255,
                0.9999999793676224,
                0.5000000103161888
              ],
              "ratios": [
                {
                  "numerator": "9007199936154090",
                  "denominator": "4503599782237109",
                  "value": 2.0000000825295077
                },
                {
                  "numerator": "9007199068901056",
                  "denominator": "4503599286663947",
                  "value": 2.0000001100393554
                },
                {
                  "numerator": "9007199440580928",
                  "denominator": "4503600153916981",
                  "value": 1.9999998074311651
                }
              ],
              "lower": {
                "numerator": "9007199440580928",
                "denominator": "4503600153916981",
                "value": 1.9999998074311651
              },
              "upper": {
                "numerator": "9007199068901056",
                "denominator": "4503599286663947",
                "value": 2.0000001100393554
              },
              "width": {
                "numerator": "6137623513939868733829120",
                "denominator": "20282410440600157546268283784007",
                "value": 3.0260819008247304e-7
              }
            }
          },
          {
            "k": 24,
            "x": [
              0.25000001547428297,
              0.49999998280635227,
              0.2500000017193648
            ],
            "ax": [
              0.5000000171936478,
              1.000000013754918,
              0.49999999312254095
            ],
            "growth": 2.000000024071107,
            "next": [
              0.2500000055879355,
              0.5000000008596823,
              0.2499999935523822
            ],
            "delta": 3.6106660133983226e-8,
            "targetError": 3.438729551108466e-8,
            "collatz": {
              "ax": [
                0.5000000171936478,
                1.000000013754918,
                0.49999999312254095
              ],
              "ratios": [
                {
                  "numerator": "9007199564474215",
                  "denominator": "4503599906130396",
                  "value": 1.9999999449803305
                },
                {
                  "numerator": "9007199378634281",
                  "denominator": "4503599472503885",
                  "value": 2.00000009628443
                },
                {
                  "numerator": "9007199130847704",
                  "denominator": "4503599658343819",
                  "value": 1.9999999587352455
                }
              ],
              "lower": {
                "numerator": "9007199564474215",
                "denominator": "4503599906130396",
                "value": 1.9999999449803305
              },
              "upper": {
                "numerator": "9007199378634281",
                "denominator": "4503599472503885",
                "value": 2.00000009628443
              },
              "width": {
                "numerator": "3068811811705994411880001",
                "denominator": "20282410161617397427451426588460",
                "value": 1.5130409982110705e-7
              }
            }
          }
        ],
        "stopped": false,
        "initial": [
          1,
          0.25,
          0.5
        ],
        "normalization": "l1",
        "target": [
          0.25,
          0.5,
          0.25
        ]
      },
      "subdominantRatio": 1
    }
  },
  "periodic": {
    "parameters": {
      "mode": "two",
      "a": 0,
      "b": 1,
      "c": 1,
      "d": 0,
      "scaleExponent": 0,
      "x1": 1,
      "x2": 0.25,
      "x3": 0.5,
      "steps": 24,
      "w1": 1,
      "w2": 1,
      "w3": 1,
      "shift": 0,
      "network": "cycle",
      "alpha": 0.875,
      "lazy": 0,
      "teleport1": 0.5,
      "teleport2": 0.25,
      "mass1": 1,
      "mass2": 0
    },
    "result": {
      "mode": "two",
      "scale": 1,
      "A": [
        [
          0,
          1
        ],
        [
          1,
          0
        ]
      ],
      "graph": {
        "edges": [
          {
            "from": 0,
            "to": 1,
            "weight": 1
          },
          {
            "from": 1,
            "to": 0,
            "weight": 1
          }
        ],
        "reach": [
          [
            true,
            true
          ],
          [
            true,
            true
          ]
        ],
        "classes": [
          {
            "vertices": [
              0,
              1
            ],
            "distances": [
              0,
              1
            ],
            "periodEdges": [
              {
                "from": 0,
                "to": 1,
                "weight": 1,
                "difference": 0
              },
              {
                "from": 1,
                "to": 0,
                "weight": 1,
                "difference": 2
              }
            ],
            "period": 2,
            "closed": true,
            "matrix": [
              [
                0,
                1
              ],
              [
                1,
                0
              ]
            ]
          }
        ],
        "irreducible": true,
        "period": 2,
        "primitive": false,
        "positive": false
      },
      "determinant": {
        "numerator": "-1",
        "denominator": "1",
        "value": -1
      },
      "discriminant": 2,
      "rho": 1,
      "other": -1,
      "spectrum": [
        {
          "re": 1,
          "im": 0,
          "modulus": 1
        },
        {
          "re": -1,
          "im": 0,
          "modulus": 1
        }
      ],
      "right": [
        [
          0.5,
          0.5
        ]
      ],
      "left": [
        [
          0.5,
          0.5
        ]
      ],
      "rightResiduals": [
        [
          0,
          0
        ]
      ],
      "leftResiduals": [
        [
          0,
          0
        ]
      ],
      "dimension": 1,
      "algebraicMultiplicity": 1,
      "caseName": "irreducible",
      "simple": true,
      "rightSupport": [
        [
          0,
          1
        ]
      ],
      "criticalClasses": [
        0
      ],
      "projection": {
        "numerator": "5",
        "denominator": "4",
        "value": 1.25
      },
      "projectionReason": "对称等对角模型：精确左方向(1,1)",
      "approximateProjection": 0.625,
      "theoremNonnegative": false,
      "subdominantRatio": 1,
      "power": {
        "rows": [
          {
            "k": 0,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 1,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 2,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 3,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 4,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 5,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 6,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 7,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 8,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 9,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 10,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 11,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 12,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 13,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 14,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 15,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 16,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 17,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 18,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 19,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 20,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 21,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 22,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 23,
            "x": [
              0.2,
              0.8
            ],
            "ax": [
              0.8,
              0.2
            ],
            "growth": 1,
            "next": [
              0.8,
              0.2
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.8,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 24,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              0.2,
              0.8
            ],
            "growth": 1,
            "next": [
              0.2,
              0.8
            ],
            "delta": 1.2000000000000002,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                0.2,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                },
                {
                  "numerator": "4",
                  "denominator": "1",
                  "value": 4
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              },
              "upper": {
                "numerator": "4",
                "denominator": "1",
                "value": 4
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          }
        ],
        "stopped": false,
        "initial": [
          1,
          0.25
        ],
        "normalization": "l1",
        "target": [
          0.5,
          0.5
        ]
      },
      "shiftedMatrix": [
        [
          1,
          1
        ],
        [
          1,
          1
        ]
      ],
      "shifted": {
        "rows": [
          {
            "k": 0,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0.6000000000000001,
            "targetError": 0.6000000000000001,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "5",
                  "denominator": "4",
                  "value": 1.25
                },
                {
                  "numerator": "5",
                  "denominator": "1",
                  "value": 5
                }
              ],
              "lower": {
                "numerator": "5",
                "denominator": "4",
                "value": 1.25
              },
              "upper": {
                "numerator": "5",
                "denominator": "1",
                "value": 5
              },
              "width": {
                "numerator": "15",
                "denominator": "4",
                "value": 3.75
              }
            }
          },
          {
            "k": 1,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 2,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 3,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 4,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 5,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 6,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 7,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 8,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 9,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 10,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 11,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 12,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 13,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 14,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 15,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 16,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 17,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 18,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 19,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 20,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 21,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 22,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 23,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          },
          {
            "k": 24,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              1
            ],
            "growth": 2,
            "next": [
              0.5,
              0.5
            ],
            "delta": 0,
            "targetError": 0,
            "collatz": {
              "ax": [
                1,
                1
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "0",
                "denominator": "1",
                "value": 0
              }
            }
          }
        ],
        "stopped": false,
        "initial": [
          1,
          0.25
        ],
        "normalization": "l1",
        "target": [
          0.5,
          0.5
        ]
      }
    }
  },
  "jordan": {
    "parameters": {
      "mode": "two",
      "a": 1,
      "b": 1,
      "c": 0,
      "d": 1,
      "scaleExponent": 0,
      "x1": 1,
      "x2": 1,
      "x3": 0.5,
      "steps": 24,
      "w1": 1,
      "w2": 1,
      "w3": 1,
      "shift": 0,
      "network": "cycle",
      "alpha": 0.875,
      "lazy": 0,
      "teleport1": 0.5,
      "teleport2": 0.25,
      "mass1": 1,
      "mass2": 0
    },
    "result": {
      "mode": "two",
      "scale": 1,
      "A": [
        [
          1,
          1
        ],
        [
          0,
          1
        ]
      ],
      "graph": {
        "edges": [
          {
            "from": 0,
            "to": 0,
            "weight": 1
          },
          {
            "from": 1,
            "to": 0,
            "weight": 1
          },
          {
            "from": 1,
            "to": 1,
            "weight": 1
          }
        ],
        "reach": [
          [
            true,
            false
          ],
          [
            true,
            true
          ]
        ],
        "classes": [
          {
            "vertices": [
              0
            ],
            "distances": [
              0,
              null
            ],
            "periodEdges": [
              {
                "from": 0,
                "to": 0,
                "weight": 1,
                "difference": 1
              }
            ],
            "period": 1,
            "closed": true,
            "matrix": [
              [
                1
              ]
            ]
          },
          {
            "vertices": [
              1
            ],
            "distances": [
              null,
              0
            ],
            "periodEdges": [
              {
                "from": 1,
                "to": 1,
                "weight": 1,
                "difference": 1
              }
            ],
            "period": 1,
            "closed": false,
            "matrix": [
              [
                1
              ]
            ]
          }
        ],
        "irreducible": false,
        "period": null,
        "primitive": false,
        "positive": false
      },
      "determinant": {
        "numerator": "1",
        "denominator": "1",
        "value": 1
      },
      "discriminant": 0,
      "rho": 1,
      "other": 1,
      "spectrum": [
        {
          "re": 1,
          "im": 0,
          "modulus": 1
        },
        {
          "re": 1,
          "im": 0,
          "modulus": 1
        }
      ],
      "right": [
        [
          1,
          0
        ]
      ],
      "left": [
        [
          0,
          1
        ]
      ],
      "rightResiduals": [
        [
          0,
          0
        ]
      ],
      "leftResiduals": [
        [
          0,
          0
        ]
      ],
      "dimension": 1,
      "algebraicMultiplicity": 2,
      "caseName": "jordan-upper",
      "simple": false,
      "rightSupport": [
        [
          0
        ]
      ],
      "criticalClasses": [
        0,
        1
      ],
      "projection": null,
      "projectionReason": "非简单主根不使用单一左右向量投影公式",
      "approximateProjection": null,
      "theoremNonnegative": false,
      "subdominantRatio": 1,
      "power": {
        "rows": [
          {
            "k": 0,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1,
              0.5
            ],
            "growth": 1.5,
            "next": [
              0.6666666666666666,
              0.3333333333333333
            ],
            "delta": 0.3333333333333333,
            "targetError": 1,
            "collatz": {
              "ax": [
                1,
                0.5
              ],
              "ratios": [
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "width": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              }
            }
          },
          {
            "k": 1,
            "x": [
              0.6666666666666666,
              0.3333333333333333
            ],
            "ax": [
              1,
              0.3333333333333333
            ],
            "growth": 1.3333333333333333,
            "next": [
              0.75,
              0.25
            ],
            "delta": 0.16666666666666669,
            "targetError": 0.6666666666666667,
            "collatz": {
              "ax": [
                1,
                0.3333333333333333
              ],
              "ratios": [
                {
                  "numerator": "3",
                  "denominator": "2",
                  "value": 1.5
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "3",
                "denominator": "2",
                "value": 1.5
              },
              "width": {
                "numerator": "1",
                "denominator": "2",
                "value": 0.5
              }
            }
          },
          {
            "k": 2,
            "x": [
              0.75,
              0.25
            ],
            "ax": [
              1,
              0.25
            ],
            "growth": 1.25,
            "next": [
              0.8,
              0.2
            ],
            "delta": 0.10000000000000003,
            "targetError": 0.5,
            "collatz": {
              "ax": [
                1,
                0.25
              ],
              "ratios": [
                {
                  "numerator": "4",
                  "denominator": "3",
                  "value": 1.3333333333333333
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "4",
                "denominator": "3",
                "value": 1.3333333333333333
              },
              "width": {
                "numerator": "1",
                "denominator": "3",
                "value": 0.3333333333333333
              }
            }
          },
          {
            "k": 3,
            "x": [
              0.8,
              0.2
            ],
            "ax": [
              1,
              0.2
            ],
            "growth": 1.2,
            "next": [
              0.8333333333333334,
              0.16666666666666669
            ],
            "delta": 0.06666666666666665,
            "targetError": 0.39999999999999997,
            "collatz": {
              "ax": [
                1,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "5",
                  "denominator": "4",
                  "value": 1.25
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "5",
                "denominator": "4",
                "value": 1.25
              },
              "width": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              }
            }
          },
          {
            "k": 4,
            "x": [
              0.8333333333333334,
              0.16666666666666669
            ],
            "ax": [
              1,
              0.16666666666666669
            ],
            "growth": 1.1666666666666667,
            "next": [
              0.8571428571428571,
              0.14285714285714288
            ],
            "delta": 0.04761904761904753,
            "targetError": 0.3333333333333333,
            "collatz": {
              "ax": [
                1,
                0.16666666666666669
              ],
              "ratios": [
                {
                  "numerator": "18014398509481985",
                  "denominator": "15011998757901654",
                  "value": 1.2
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "18014398509481985",
                "denominator": "15011998757901654",
                "value": 1.2
              },
              "width": {
                "numerator": "3002399751580331",
                "denominator": "15011998757901654",
                "value": 0.2
              }
            }
          },
          {
            "k": 5,
            "x": [
              0.8571428571428571,
              0.14285714285714288
            ],
            "ax": [
              1,
              0.14285714285714288
            ],
            "growth": 1.1428571428571428,
            "next": [
              0.875,
              0.12500000000000003
            ],
            "delta": 0.035714285714285754,
            "targetError": 0.2857142857142858,
            "collatz": {
              "ax": [
                1,
                0.14285714285714288
              ],
              "ratios": [
                {
                  "numerator": "36028797018963967",
                  "denominator": "30881826016254828",
                  "value": 1.1666666666666665
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "36028797018963967",
                "denominator": "30881826016254828",
                "value": 1.1666666666666665
              },
              "width": {
                "numerator": "5146971002709139",
                "denominator": "30881826016254828",
                "value": 0.1666666666666667
              }
            }
          },
          {
            "k": 6,
            "x": [
              0.875,
              0.12500000000000003
            ],
            "ax": [
              1,
              0.12500000000000003
            ],
            "growth": 1.125,
            "next": [
              0.8888888888888888,
              0.11111111111111113
            ],
            "delta": 0.027777777777777735,
            "targetError": 0.25,
            "collatz": {
              "ax": [
                1,
                0.12500000000000003
              ],
              "ratios": [
                {
                  "numerator": "36028797018963969",
                  "denominator": "31525197391593472",
                  "value": 1.1428571428571428
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "36028797018963969",
                "denominator": "31525197391593472",
                "value": 1.1428571428571428
              },
              "width": {
                "numerator": "4503599627370497",
                "denominator": "31525197391593472",
                "value": 0.14285714285714288
              }
            }
          },
          {
            "k": 7,
            "x": [
              0.8888888888888888,
              0.11111111111111113
            ],
            "ax": [
              1,
              0.11111111111111113
            ],
            "growth": 1.1111111111111112,
            "next": [
              0.8999999999999999,
              0.10000000000000002
            ],
            "delta": 0.022222222222222185,
            "targetError": 0.2222222222222223,
            "collatz": {
              "ax": [
                1,
                0.11111111111111113
              ],
              "ratios": [
                {
                  "numerator": "36028797018963967",
                  "denominator": "32025597350190192",
                  "value": 1.125
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "36028797018963967",
                "denominator": "32025597350190192",
                "value": 1.125
              },
              "width": {
                "numerator": "4003199668773775",
                "denominator": "32025597350190192",
                "value": 0.12500000000000003
              }
            }
          },
          {
            "k": 8,
            "x": [
              0.8999999999999999,
              0.10000000000000002
            ],
            "ax": [
              0.9999999999999999,
              0.10000000000000002
            ],
            "growth": 1.0999999999999999,
            "next": [
              0.9090909090909091,
              0.09090909090909094
            ],
            "delta": 0.01818181818181823,
            "targetError": 0.20000000000000012,
            "collatz": {
              "ax": [
                0.9999999999999999,
                0.10000000000000002
              ],
              "ratios": [
                {
                  "numerator": "72057594037927931",
                  "denominator": "64851834634135136",
                  "value": 1.1111111111111112
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "72057594037927931",
                "denominator": "64851834634135136",
                "value": 1.1111111111111112
              },
              "width": {
                "numerator": "7205759403792795",
                "denominator": "64851834634135136",
                "value": 0.11111111111111115
              }
            }
          },
          {
            "k": 9,
            "x": [
              0.9090909090909091,
              0.09090909090909094
            ],
            "ax": [
              1,
              0.09090909090909094
            ],
            "growth": 1.0909090909090908,
            "next": [
              0.9166666666666667,
              0.08333333333333337
            ],
            "delta": 0.015151515151515249,
            "targetError": 0.18181818181818188,
            "collatz": {
              "ax": [
                1,
                0.09090909090909094
              ],
              "ratios": [
                {
                  "numerator": "9007199254740992",
                  "denominator": "8188362958855447",
                  "value": 1.1
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "9007199254740992",
                "denominator": "8188362958855447",
                "value": 1.1
              },
              "width": {
                "numerator": "818836295885545",
                "denominator": "8188362958855447",
                "value": 0.10000000000000003
              }
            }
          },
          {
            "k": 10,
            "x": [
              0.9166666666666667,
              0.08333333333333337
            ],
            "ax": [
              1,
              0.08333333333333337
            ],
            "growth": 1.0833333333333335,
            "next": [
              0.9230769230769229,
              0.07692307692307694
            ],
            "delta": 0.012820512820512595,
            "targetError": 0.16666666666666663,
            "collatz": {
              "ax": [
                1,
                0.08333333333333337
              ],
              "ratios": [
                {
                  "numerator": "3002399751580331",
                  "denominator": "2752199772281970",
                  "value": 1.090909090909091
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "3002399751580331",
                "denominator": "2752199772281970",
                "value": 1.090909090909091
              },
              "width": {
                "numerator": "250199979298361",
                "denominator": "2752199772281970",
                "value": 0.09090909090909094
              }
            }
          },
          {
            "k": 11,
            "x": [
              0.9230769230769229,
              0.07692307692307694
            ],
            "ax": [
              0.9999999999999999,
              0.07692307692307694
            ],
            "growth": 1.0769230769230769,
            "next": [
              0.9285714285714285,
              0.07142857142857145
            ],
            "delta": 0.010989010989011075,
            "targetError": 0.15384615384615402,
            "collatz": {
              "ax": [
                0.9999999999999999,
                0.07692307692307694
              ],
              "ratios": [
                {
                  "numerator": "10293942005418275",
                  "denominator": "9502100312693792",
                  "value": 1.0833333333333333
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "10293942005418275",
                "denominator": "9502100312693792",
                "value": 1.0833333333333333
              },
              "width": {
                "numerator": "791841692724483",
                "denominator": "9502100312693792",
                "value": 0.08333333333333337
              }
            }
          },
          {
            "k": 12,
            "x": [
              0.9285714285714285,
              0.07142857142857145
            ],
            "ax": [
              1,
              0.07142857142857145
            ],
            "growth": 1.0714285714285714,
            "next": [
              0.9333333333333333,
              0.0666666666666667
            ],
            "delta": 0.009523809523809615,
            "targetError": 0.14285714285714296,
            "collatz": {
              "ax": [
                1,
                0.07142857142857145
              ],
              "ratios": [
                {
                  "numerator": "18014398509481983",
                  "denominator": "16727655758804698",
                  "value": 1.0769230769230769
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "18014398509481983",
                "denominator": "16727655758804698",
                "value": 1.0769230769230769
              },
              "width": {
                "numerator": "1286742750677285",
                "denominator": "16727655758804698",
                "value": 0.07692307692307696
              }
            }
          },
          {
            "k": 13,
            "x": [
              0.9333333333333333,
              0.0666666666666667
            ],
            "ax": [
              1,
              0.0666666666666667
            ],
            "growth": 1.0666666666666667,
            "next": [
              0.9375,
              0.06250000000000003
            ],
            "delta": 0.008333333333333318,
            "targetError": 0.13333333333333336,
            "collatz": {
              "ax": [
                1,
                0.0666666666666667
              ],
              "ratios": [
                {
                  "numerator": "72057594037927939",
                  "denominator": "67253754435399408",
                  "value": 1.0714285714285714
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "72057594037927939",
                "denominator": "67253754435399408",
                "value": 1.0714285714285714
              },
              "width": {
                "numerator": "4803839602528531",
                "denominator": "67253754435399408",
                "value": 0.07142857142857145
              }
            }
          },
          {
            "k": 14,
            "x": [
              0.9375,
              0.06250000000000003
            ],
            "ax": [
              1,
              0.06250000000000003
            ],
            "growth": 1.0625,
            "next": [
              0.9411764705882353,
              0.05882352941176473
            ],
            "delta": 0.007352941176470576,
            "targetError": 0.12500000000000003,
            "collatz": {
              "ax": [
                1,
                0.06250000000000003
              ],
              "ratios": [
                {
                  "numerator": "12009599006321323",
                  "denominator": "11258999068426240",
                  "value": 1.0666666666666667
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "12009599006321323",
                "denominator": "11258999068426240",
                "value": 1.0666666666666667
              },
              "width": {
                "numerator": "750599937895083",
                "denominator": "11258999068426240",
                "value": 0.0666666666666667
              }
            }
          },
          {
            "k": 15,
            "x": [
              0.9411764705882353,
              0.05882352941176473
            ],
            "ax": [
              1,
              0.05882352941176473
            ],
            "growth": 1.0588235294117647,
            "next": [
              0.9444444444444444,
              0.05555555555555558
            ],
            "delta": 0.006535947712418291,
            "targetError": 0.11764705882352945,
            "collatz": {
              "ax": [
                1,
                0.05882352941176473
              ],
              "ratios": [
                {
                  "numerator": "72057594037927937",
                  "denominator": "67818912035696880",
                  "value": 1.0625
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "72057594037927937",
                "denominator": "67818912035696880",
                "value": 1.0625
              },
              "width": {
                "numerator": "4238682002231057",
                "denominator": "67818912035696880",
                "value": 0.06250000000000003
              }
            }
          },
          {
            "k": 16,
            "x": [
              0.9444444444444444,
              0.05555555555555558
            ],
            "ax": [
              1,
              0.05555555555555558
            ],
            "growth": 1.0555555555555556,
            "next": [
              0.9473684210526315,
              0.052631578947368446
            ],
            "delta": 0.005847953216374241,
            "targetError": 0.11111111111111116,
            "collatz": {
              "ax": [
                1,
                0.05555555555555558
              ],
              "ratios": [
                {
                  "numerator": "4503599627370496",
                  "denominator": "4253399648072135",
                  "value": 1.0588235294117647
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "4503599627370496",
                "denominator": "4253399648072135",
                "value": 1.0588235294117647
              },
              "width": {
                "numerator": "250199979298361",
                "denominator": "4253399648072135",
                "value": 0.05882352941176473
              }
            }
          },
          {
            "k": 17,
            "x": [
              0.9473684210526315,
              0.052631578947368446
            ],
            "ax": [
              1,
              0.052631578947368446
            ],
            "growth": 1.0526315789473684,
            "next": [
              0.9500000000000001,
              0.050000000000000024
            ],
            "delta": 0.0052631578947369625,
            "targetError": 0.10526315789473692,
            "collatz": {
              "ax": [
                1,
                0.052631578947368446
              ],
              "ratios": [
                {
                  "numerator": "36028797018963967",
                  "denominator": "34132544544281652",
                  "value": 1.0555555555555556
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "36028797018963967",
                "denominator": "34132544544281652",
                "value": 1.0555555555555556
              },
              "width": {
                "numerator": "1896252474682315",
                "denominator": "34132544544281652",
                "value": 0.05555555555555559
              }
            }
          },
          {
            "k": 18,
            "x": [
              0.9500000000000001,
              0.050000000000000024
            ],
            "ax": [
              1,
              0.050000000000000024
            ],
            "growth": 1.05,
            "next": [
              0.9523809523809523,
              0.04761904761904764
            ],
            "delta": 0.004761904761904648,
            "targetError": 0.09999999999999995,
            "collatz": {
              "ax": [
                1,
                0.050000000000000024
              ],
              "ratios": [
                {
                  "numerator": "144115188075855885",
                  "denominator": "136909428672063088",
                  "value": 1.0526315789473684
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "144115188075855885",
                "denominator": "136909428672063088",
                "value": 1.0526315789473684
              },
              "width": {
                "numerator": "7205759403792797",
                "denominator": "136909428672063088",
                "value": 0.05263157894736844
              }
            }
          },
          {
            "k": 19,
            "x": [
              0.9523809523809523,
              0.04761904761904764
            ],
            "ax": [
              1,
              0.04761904761904764
            ],
            "growth": 1.0476190476190477,
            "next": [
              0.9545454545454545,
              0.04545454545454547
            ],
            "delta": 0.004329004329004314,
            "targetError": 0.09523809523809532,
            "collatz": {
              "ax": [
                1,
                0.04761904761904764
              ],
              "ratios": [
                {
                  "numerator": "48038396025285289",
                  "denominator": "45750853357414560",
                  "value": 1.05
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "48038396025285289",
                "denominator": "45750853357414560",
                "value": 1.05
              },
              "width": {
                "numerator": "2287542667870729",
                "denominator": "45750853357414560",
                "value": 0.050000000000000024
              }
            }
          },
          {
            "k": 20,
            "x": [
              0.9545454545454545,
              0.04545454545454547
            ],
            "ax": [
              1,
              0.04545454545454547
            ],
            "growth": 1.0454545454545454,
            "next": [
              0.9565217391304348,
              0.04347826086956524
            ],
            "delta": 0.0039525691699605695,
            "targetError": 0.090909090909091,
            "collatz": {
              "ax": [
                1,
                0.04545454545454547
              ],
              "ratios": [
                {
                  "numerator": "2573485501354569",
                  "denominator": "2456508887656634",
                  "value": 1.0476190476190477
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "2573485501354569",
                "denominator": "2456508887656634",
                "value": 1.0476190476190477
              },
              "width": {
                "numerator": "116976613697935",
                "denominator": "2456508887656634",
                "value": 0.04761904761904764
              }
            }
          },
          {
            "k": 21,
            "x": [
              0.9565217391304348,
              0.04347826086956524
            ],
            "ax": [
              1,
              0.04347826086956524
            ],
            "growth": 1.0434782608695652,
            "next": [
              0.9583333333333334,
              0.041666666666666685
            ],
            "delta": 0.0036231884057971106,
            "targetError": 0.08695652173913043,
            "collatz": {
              "ax": [
                1,
                0.04347826086956524
              ],
              "ratios": [
                {
                  "numerator": "144115188075855879",
                  "denominator": "137849310333427360",
                  "value": 1.0454545454545454
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "144115188075855879",
                "denominator": "137849310333427360",
                "value": 1.0454545454545454
              },
              "width": {
                "numerator": "6265877742428519",
                "denominator": "137849310333427360",
                "value": 0.04545454545454548
              }
            }
          },
          {
            "k": 22,
            "x": [
              0.9583333333333334,
              0.041666666666666685
            ],
            "ax": [
              1,
              0.041666666666666685
            ],
            "growth": 1.0416666666666667,
            "next": [
              0.96,
              0.040000000000000015
            ],
            "delta": 0.0033333333333332646,
            "targetError": 0.08333333333333331,
            "collatz": {
              "ax": [
                1,
                0.041666666666666685
              ],
              "ratios": [
                {
                  "numerator": "18014398509481985",
                  "denominator": "17263798571586902",
                  "value": 1.0434782608695652
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "18014398509481985",
                "denominator": "17263798571586902",
                "value": 1.0434782608695652
              },
              "width": {
                "numerator": "750599937895083",
                "denominator": "17263798571586902",
                "value": 0.04347826086956524
              }
            }
          },
          {
            "k": 23,
            "x": [
              0.96,
              0.040000000000000015
            ],
            "ax": [
              1,
              0.040000000000000015
            ],
            "growth": 1.04,
            "next": [
              0.9615384615384615,
              0.03846153846153848
            ],
            "delta": 0.0030769230769230257,
            "targetError": 0.08000000000000004,
            "collatz": {
              "ax": [
                1,
                0.040000000000000015
              ],
              "ratios": [
                {
                  "numerator": "144115188075855869",
                  "denominator": "138350580552821632",
                  "value": 1.0416666666666665
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "144115188075855869",
                "denominator": "138350580552821632",
                "value": 1.0416666666666665
              },
              "width": {
                "numerator": "5764607523034237",
                "denominator": "138350580552821632",
                "value": 0.041666666666666685
              }
            }
          },
          {
            "k": 24,
            "x": [
              0.9615384615384615,
              0.03846153846153848
            ],
            "ax": [
              0.9999999999999999,
              0.03846153846153848
            ],
            "growth": 1.0384615384615383,
            "next": [
              0.962962962962963,
              0.037037037037037056
            ],
            "delta": 0.0028490028490029892,
            "targetError": 0.07692307692307702,
            "collatz": {
              "ax": [
                0.9999999999999999,
                0.03846153846153848
              ],
              "ratios": [
                {
                  "numerator": "72057594037927931",
                  "denominator": "69286148113392240",
                  "value": 1.04
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                }
              ],
              "lower": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              },
              "upper": {
                "numerator": "72057594037927931",
                "denominator": "69286148113392240",
                "value": 1.04
              },
              "width": {
                "numerator": "2771445924535691",
                "denominator": "69286148113392240",
                "value": 0.04000000000000002
              }
            }
          }
        ],
        "stopped": false,
        "initial": [
          1,
          1
        ],
        "normalization": "l1",
        "target": [
          1,
          0
        ]
      },
      "shiftedMatrix": [
        [
          2,
          1
        ],
        [
          0,
          2
        ]
      ],
      "shifted": {
        "rows": [
          {
            "k": 0,
            "x": [
              0.5,
              0.5
            ],
            "ax": [
              1.5,
              1
            ],
            "growth": 2.5,
            "next": [
              0.6,
              0.4
            ],
            "delta": 0.19999999999999996,
            "targetError": 1,
            "collatz": {
              "ax": [
                1.5,
                1
              ],
              "ratios": [
                {
                  "numerator": "3",
                  "denominator": "1",
                  "value": 3
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "3",
                "denominator": "1",
                "value": 3
              },
              "width": {
                "numerator": "1",
                "denominator": "1",
                "value": 1
              }
            }
          },
          {
            "k": 1,
            "x": [
              0.6,
              0.4
            ],
            "ax": [
              1.6,
              0.8
            ],
            "growth": 2.4000000000000004,
            "next": [
              0.6666666666666666,
              0.3333333333333333
            ],
            "delta": 0.13333333333333336,
            "targetError": 0.8,
            "collatz": {
              "ax": [
                1.6,
                0.8
              ],
              "ratios": [
                {
                  "numerator": "14411518807585587",
                  "denominator": "5404319552844595",
                  "value": 2.6666666666666665
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "14411518807585587",
                "denominator": "5404319552844595",
                "value": 2.6666666666666665
              },
              "width": {
                "numerator": "3602879701896397",
                "denominator": "5404319552844595",
                "value": 0.6666666666666667
              }
            }
          },
          {
            "k": 2,
            "x": [
              0.6666666666666666,
              0.3333333333333333
            ],
            "ax": [
              1.6666666666666665,
              0.6666666666666666
            ],
            "growth": 2.333333333333333,
            "next": [
              0.7142857142857143,
              0.28571428571428575
            ],
            "delta": 0.09523809523809523,
            "targetError": 0.6666666666666667,
            "collatz": {
              "ax": [
                1.6666666666666665,
                0.6666666666666666
              ],
              "ratios": [
                {
                  "numerator": "5",
                  "denominator": "2",
                  "value": 2.5
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "5",
                "denominator": "2",
                "value": 2.5
              },
              "width": {
                "numerator": "1",
                "denominator": "2",
                "value": 0.5
              }
            }
          },
          {
            "k": 3,
            "x": [
              0.7142857142857143,
              0.28571428571428575
            ],
            "ax": [
              1.7142857142857144,
              0.5714285714285715
            ],
            "growth": 2.285714285714286,
            "next": [
              0.75,
              0.25
            ],
            "delta": 0.07142857142857145,
            "targetError": 0.5714285714285714,
            "collatz": {
              "ax": [
                1.7142857142857144,
                0.5714285714285715
              ],
              "ratios": [
                {
                  "numerator": "30881826016254831",
                  "denominator": "12867427506772846",
                  "value": 2.4
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "30881826016254831",
                "denominator": "12867427506772846",
                "value": 2.4
              },
              "width": {
                "numerator": "5146971002709139",
                "denominator": "12867427506772846",
                "value": 0.4
              }
            }
          },
          {
            "k": 4,
            "x": [
              0.75,
              0.25
            ],
            "ax": [
              1.75,
              0.5
            ],
            "growth": 2.25,
            "next": [
              0.7777777777777778,
              0.2222222222222222
            ],
            "delta": 0.05555555555555558,
            "targetError": 0.5,
            "collatz": {
              "ax": [
                1.75,
                0.5
              ],
              "ratios": [
                {
                  "numerator": "7",
                  "denominator": "3",
                  "value": 2.3333333333333335
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "7",
                "denominator": "3",
                "value": 2.3333333333333335
              },
              "width": {
                "numerator": "1",
                "denominator": "3",
                "value": 0.3333333333333333
              }
            }
          },
          {
            "k": 5,
            "x": [
              0.7777777777777778,
              0.2222222222222222
            ],
            "ax": [
              1.7777777777777777,
              0.4444444444444444
            ],
            "growth": 2.2222222222222223,
            "next": [
              0.7999999999999999,
              0.19999999999999998
            ],
            "delta": 0.04444444444444437,
            "targetError": 0.4444444444444444,
            "collatz": {
              "ax": [
                1.7777777777777777,
                0.4444444444444444
              ],
              "ratios": [
                {
                  "numerator": "16012798675095097",
                  "denominator": "7005599420354105",
                  "value": 2.2857142857142856
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "16012798675095097",
                "denominator": "7005599420354105",
                "value": 2.2857142857142856
              },
              "width": {
                "numerator": "2001599834386887",
                "denominator": "7005599420354105",
                "value": 0.2857142857142857
              }
            }
          },
          {
            "k": 6,
            "x": [
              0.7999999999999999,
              0.19999999999999998
            ],
            "ax": [
              1.7999999999999998,
              0.39999999999999997
            ],
            "growth": 2.1999999999999997,
            "next": [
              0.8181818181818182,
              0.18181818181818182
            ],
            "delta": 0.03636363636363646,
            "targetError": 0.4,
            "collatz": {
              "ax": [
                1.7999999999999998,
                0.39999999999999997
              ],
              "ratios": [
                {
                  "numerator": "9",
                  "denominator": "4",
                  "value": 2.25
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "9",
                "denominator": "4",
                "value": 2.25
              },
              "width": {
                "numerator": "1",
                "denominator": "4",
                "value": 0.25
              }
            }
          },
          {
            "k": 7,
            "x": [
              0.8181818181818182,
              0.18181818181818182
            ],
            "ax": [
              1.8181818181818183,
              0.36363636363636365
            ],
            "growth": 2.181818181818182,
            "next": [
              0.8333333333333333,
              0.16666666666666666
            ],
            "delta": 0.030303030303030193,
            "targetError": 0.3636363636363636,
            "collatz": {
              "ax": [
                1.8181818181818183,
                0.36363636363636365
              ],
              "ratios": [
                {
                  "numerator": "32753451835421791",
                  "denominator": "14739053325939806",
                  "value": 2.222222222222222
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "32753451835421791",
                "denominator": "14739053325939806",
                "value": 2.222222222222222
              },
              "width": {
                "numerator": "3275345183542179",
                "denominator": "14739053325939806",
                "value": 0.2222222222222222
              }
            }
          },
          {
            "k": 8,
            "x": [
              0.8333333333333333,
              0.16666666666666666
            ],
            "ax": [
              1.8333333333333333,
              0.3333333333333333
            ],
            "growth": 2.1666666666666665,
            "next": [
              0.8461538461538461,
              0.15384615384615385
            ],
            "delta": 0.02564102564102569,
            "targetError": 0.33333333333333337,
            "collatz": {
              "ax": [
                1.8333333333333333,
                0.3333333333333333
              ],
              "ratios": [
                {
                  "numerator": "66052794534767269",
                  "denominator": "30023997515803304",
                  "value": 2.1999999999999997
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "66052794534767269",
                "denominator": "30023997515803304",
                "value": 2.1999999999999997
              },
              "width": {
                "numerator": "6004799503160661",
                "denominator": "30023997515803304",
                "value": 0.2
              }
            }
          },
          {
            "k": 9,
            "x": [
              0.8461538461538461,
              0.15384615384615385
            ],
            "ax": [
              1.8461538461538463,
              0.3076923076923077
            ],
            "growth": 2.153846153846154,
            "next": [
              0.8571428571428571,
              0.14285714285714285
            ],
            "delta": 0.021978021978021955,
            "targetError": 0.3076923076923077,
            "collatz": {
              "ax": [
                1.8461538461538463,
                0.3076923076923077
              ],
              "ratios": [
                {
                  "numerator": "16628675547214139",
                  "denominator": "7621476292473147",
                  "value": 2.1818181818181817
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "16628675547214139",
                "denominator": "7621476292473147",
                "value": 2.1818181818181817
              },
              "width": {
                "numerator": "1385722962267845",
                "denominator": "7621476292473147",
                "value": 0.18181818181818182
              }
            }
          },
          {
            "k": 10,
            "x": [
              0.8571428571428571,
              0.14285714285714285
            ],
            "ax": [
              1.857142857142857,
              0.2857142857142857
            ],
            "growth": 2.142857142857143,
            "next": [
              0.8666666666666666,
              0.13333333333333333
            ],
            "delta": 0.019047619047619008,
            "targetError": 0.28571428571428575,
            "collatz": {
              "ax": [
                1.857142857142857,
                0.2857142857142857
              ],
              "ratios": [
                {
                  "numerator": "13",
                  "denominator": "6",
                  "value": 2.1666666666666665
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "13",
                "denominator": "6",
                "value": 2.1666666666666665
              },
              "width": {
                "numerator": "1",
                "denominator": "6",
                "value": 0.16666666666666666
              }
            }
          },
          {
            "k": 11,
            "x": [
              0.8666666666666666,
              0.13333333333333333
            ],
            "ax": [
              1.8666666666666665,
              0.26666666666666666
            ],
            "growth": 2.1333333333333333,
            "next": [
              0.8749999999999999,
              0.125
            ],
            "delta": 0.016666666666666635,
            "targetError": 0.2666666666666667,
            "collatz": {
              "ax": [
                1.8666666666666665,
                0.26666666666666666
              ],
              "ratios": [
                {
                  "numerator": "67253754435399401",
                  "denominator": "31224957416435436",
                  "value": 2.1538461538461537
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "67253754435399401",
                "denominator": "31224957416435436",
                "value": 2.1538461538461537
              },
              "width": {
                "numerator": "4803839602528529",
                "denominator": "31224957416435436",
                "value": 0.15384615384615385
              }
            }
          },
          {
            "k": 12,
            "x": [
              0.8749999999999999,
              0.125
            ],
            "ax": [
              1.8749999999999998,
              0.25
            ],
            "growth": 2.125,
            "next": [
              0.8823529411764705,
              0.11764705882352941
            ],
            "delta": 0.014705882352941152,
            "targetError": 0.2500000000000001,
            "collatz": {
              "ax": [
                1.8749999999999998,
                0.25
              ],
              "ratios": [
                {
                  "numerator": "16888498602639358",
                  "denominator": "7881299347898367",
                  "value": 2.142857142857143
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "16888498602639358",
                "denominator": "7881299347898367",
                "value": 2.142857142857143
              },
              "width": {
                "numerator": "1125899906842624",
                "denominator": "7881299347898367",
                "value": 0.14285714285714288
              }
            }
          },
          {
            "k": 13,
            "x": [
              0.8823529411764705,
              0.11764705882352941
            ],
            "ax": [
              1.8823529411764703,
              0.23529411764705882
            ],
            "growth": 2.117647058823529,
            "next": [
              0.888888888888889,
              0.11111111111111113
            ],
            "delta": 0.013071895424836777,
            "targetError": 0.23529411764705896,
            "collatz": {
              "ax": [
                1.8823529411764703,
                0.23529411764705882
              ],
              "ratios": [
                {
                  "numerator": "22606304011898957",
                  "denominator": "10596705005577636",
                  "value": 2.1333333333333333
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "22606304011898957",
                "denominator": "10596705005577636",
                "value": 2.1333333333333333
              },
              "width": {
                "numerator": "1412894000743685",
                "denominator": "10596705005577636",
                "value": 0.13333333333333336
              }
            }
          },
          {
            "k": 14,
            "x": [
              0.888888888888889,
              0.11111111111111113
            ],
            "ax": [
              1.888888888888889,
              0.22222222222222227
            ],
            "growth": 2.111111111111111,
            "next": [
              0.8947368421052632,
              0.10526315789473686
            ],
            "delta": 0.011695906432748482,
            "targetError": 0.22222222222222218,
            "collatz": {
              "ax": [
                1.888888888888889,
                0.22222222222222227
              ],
              "ratios": [
                {
                  "numerator": "68054394369154167",
                  "denominator": "32025597350190196",
                  "value": 2.125
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "68054394369154167",
                "denominator": "32025597350190196",
                "value": 2.125
              },
              "width": {
                "numerator": "4003199668773775",
                "denominator": "32025597350190196",
                "value": 0.12500000000000003
              }
            }
          },
          {
            "k": 15,
            "x": [
              0.8947368421052632,
              0.10526315789473686
            ],
            "ax": [
              1.8947368421052633,
              0.21052631578947373
            ],
            "growth": 2.105263157894737,
            "next": [
              0.8999999999999999,
              0.1
            ],
            "delta": 0.010526315789473606,
            "targetError": 0.2105263157894737,
            "collatz": {
              "ax": [
                1.8947368421052633,
                0.21052631578947373
              ],
              "ratios": [
                {
                  "numerator": "68265089088563309",
                  "denominator": "32236292069599340",
                  "value": 2.1176470588235294
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "68265089088563309",
                "denominator": "32236292069599340",
                "value": 2.1176470588235294
              },
              "width": {
                "numerator": "3792504949364629",
                "denominator": "32236292069599340",
                "value": 0.11764705882352944
              }
            }
          },
          {
            "k": 16,
            "x": [
              0.8999999999999999,
              0.1
            ],
            "ax": [
              1.9,
              0.2
            ],
            "growth": 2.1,
            "next": [
              0.9047619047619047,
              0.09523809523809523
            ],
            "delta": 0.009523809523809518,
            "targetError": 0.2000000000000001,
            "collatz": {
              "ax": [
                1.9,
                0.2
              ],
              "ratios": [
                {
                  "numerator": "68454714336031533",
                  "denominator": "32425917317067568",
                  "value": 2.111111111111111
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "68454714336031533",
                "denominator": "32425917317067568",
                "value": 2.111111111111111
              },
              "width": {
                "numerator": "3602879701896397",
                "denominator": "32425917317067568",
                "value": 0.11111111111111113
              }
            }
          },
          {
            "k": 17,
            "x": [
              0.9047619047619047,
              0.09523809523809523
            ],
            "ax": [
              1.9047619047619047,
              0.19047619047619047
            ],
            "growth": 2.095238095238095,
            "next": [
              0.9090909090909092,
              0.09090909090909093
            ],
            "delta": 0.008658008658008823,
            "targetError": 0.19047619047619058,
            "collatz": {
              "ax": [
                1.9047619047619047,
                0.19047619047619047
              ],
              "ratios": [
                {
                  "numerator": "17156570009030459",
                  "denominator": "8149370754289468",
                  "value": 2.1052631578947367
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "17156570009030459",
                "denominator": "8149370754289468",
                "value": 2.1052631578947367
              },
              "width": {
                "numerator": "857828500451523",
                "denominator": "8149370754289468",
                "value": 0.10526315789473685
              }
            }
          },
          {
            "k": 18,
            "x": [
              0.9090909090909092,
              0.09090909090909093
            ],
            "ax": [
              1.9090909090909092,
              0.18181818181818185
            ],
            "growth": 2.090909090909091,
            "next": [
              0.9130434782608696,
              0.08695652173913046
            ],
            "delta": 0.007905138339920917,
            "targetError": 0.18181818181818177,
            "collatz": {
              "ax": [
                1.9090909090909092,
                0.18181818181818185
              ],
              "ratios": [
                {
                  "numerator": "137564497708771527",
                  "denominator": "65506903670843584",
                  "value": 2.1
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "137564497708771527",
                "denominator": "65506903670843584",
                "value": 2.1
              },
              "width": {
                "numerator": "6550690367084359",
                "denominator": "65506903670843584",
                "value": 0.1
              }
            }
          },
          {
            "k": 19,
            "x": [
              0.9130434782608696,
              0.08695652173913046
            ],
            "ax": [
              1.9130434782608696,
              0.17391304347826092
            ],
            "growth": 2.0869565217391304,
            "next": [
              0.9166666666666667,
              0.08333333333333336
            ],
            "delta": 0.007246376811594221,
            "targetError": 0.17391304347826084,
            "collatz": {
              "ax": [
                1.9130434782608696,
                0.17391304347826092
              ],
              "ratios": [
                {
                  "numerator": "68924655166713683",
                  "denominator": "32895858147749712",
                  "value": 2.0952380952380953
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "68924655166713683",
                "denominator": "32895858147749712",
                "value": 2.0952380952380953
              },
              "width": {
                "numerator": "3132938871214259",
                "denominator": "32895858147749712",
                "value": 0.09523809523809526
              }
            }
          },
          {
            "k": 20,
            "x": [
              0.9166666666666667,
              0.08333333333333336
            ],
            "ax": [
              1.9166666666666667,
              0.1666666666666667
            ],
            "growth": 2.0833333333333335,
            "next": [
              0.9199999999999999,
              0.08000000000000002
            ],
            "delta": 0.006666666666666529,
            "targetError": 0.16666666666666663,
            "collatz": {
              "ax": [
                1.9166666666666667,
                0.1666666666666667
              ],
              "ratios": [
                {
                  "numerator": "138110388572695223",
                  "denominator": "66052794534767280",
                  "value": 2.090909090909091
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "138110388572695223",
                "denominator": "66052794534767280",
                "value": 2.090909090909091
              },
              "width": {
                "numerator": "6004799503160663",
                "denominator": "66052794534767280",
                "value": 0.09090909090909093
              }
            }
          },
          {
            "k": 21,
            "x": [
              0.9199999999999999,
              0.08000000000000002
            ],
            "ax": [
              1.92,
              0.16000000000000003
            ],
            "growth": 2.08,
            "next": [
              0.923076923076923,
              0.07692307692307694
            ],
            "delta": 0.0061538461538461625,
            "targetError": 0.1600000000000001,
            "collatz": {
              "ax": [
                1.92,
                0.16000000000000003
              ],
              "ratios": [
                {
                  "numerator": "3843071682022823",
                  "denominator": "1841471847635936",
                  "value": 2.0869565217391304
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "3843071682022823",
                "denominator": "1841471847635936",
                "value": 2.0869565217391304
              },
              "width": {
                "numerator": "160127986750951",
                "denominator": "1841471847635936",
                "value": 0.08695652173913046
              }
            }
          },
          {
            "k": 22,
            "x": [
              0.923076923076923,
              0.07692307692307694
            ],
            "ax": [
              1.923076923076923,
              0.15384615384615388
            ],
            "growth": 2.0769230769230766,
            "next": [
              0.9259259259259259,
              0.0740740740740741
            ],
            "delta": 0.005698005698005756,
            "targetError": 0.1538461538461539,
            "collatz": {
              "ax": [
                1.923076923076923,
                0.15384615384615388
              ],
              "ratios": [
                {
                  "numerator": "138572296226784485",
                  "denominator": "66514702188856552",
                  "value": 2.0833333333333335
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "138572296226784485",
                "denominator": "66514702188856552",
                "value": 2.0833333333333335
              },
              "width": {
                "numerator": "5542891849071381",
                "denominator": "66514702188856552",
                "value": 0.08333333333333336
              }
            }
          },
          {
            "k": 23,
            "x": [
              0.9259259259259259,
              0.0740740740740741
            ],
            "ax": [
              1.925925925925926,
              0.1481481481481482
            ],
            "growth": 2.0740740740740744,
            "next": [
              0.9285714285714285,
              0.07142857142857144
            ],
            "delta": 0.005291005291005221,
            "targetError": 0.14814814814814817,
            "collatz": {
              "ax": [
                1.925925925925926,
                0.1481481481481482
              ],
              "ratios": [
                {
                  "numerator": "69388794258745421",
                  "denominator": "33359997239781452",
                  "value": 2.08
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "69388794258745421",
                "denominator": "33359997239781452",
                "value": 2.08
              },
              "width": {
                "numerator": "2668799779182517",
                "denominator": "33359997239781452",
                "value": 0.08000000000000003
              }
            }
          },
          {
            "k": 24,
            "x": [
              0.9285714285714285,
              0.07142857142857144
            ],
            "ax": [
              1.9285714285714284,
              0.14285714285714288
            ],
            "growth": 2.071428571428571,
            "next": [
              0.9310344827586207,
              0.06896551724137932
            ],
            "delta": 0.004926108374384286,
            "targetError": 0.14285714285714296,
            "collatz": {
              "ax": [
                1.9285714285714284,
                0.14285714285714288
              ],
              "ratios": [
                {
                  "numerator": "138968217073146723",
                  "denominator": "66910623035218792",
                  "value": 2.076923076923077
                },
                {
                  "numerator": "2",
                  "denominator": "1",
                  "value": 2
                }
              ],
              "lower": {
                "numerator": "2",
                "denominator": "1",
                "value": 2
              },
              "upper": {
                "numerator": "138968217073146723",
                "denominator": "66910623035218792",
                "value": 2.076923076923077
              },
              "width": {
                "numerator": "5146971002709139",
                "denominator": "66910623035218792",
                "value": 0.07692307692307694
              }
            }
          }
        ],
        "stopped": false,
        "initial": [
          1,
          1
        ],
        "normalization": "l1",
        "target": [
          1,
          0
        ]
      }
    }
  },
  "pagerank": {
    "parameters": {
      "mode": "markov",
      "a": 2,
      "b": 1,
      "c": 1,
      "d": 2,
      "scaleExponent": 0,
      "x1": 1,
      "x2": 0.25,
      "x3": 0.5,
      "steps": 24,
      "w1": 1,
      "w2": 1,
      "w3": 1,
      "shift": 0,
      "network": "cycle",
      "alpha": 0.5,
      "lazy": 0,
      "teleport1": 0.5,
      "teleport2": 0.25,
      "mass1": 1,
      "mass2": 0
    },
    "result": {
      "mode": "markov",
      "network": "cycle",
      "raw": [
        [
          0,
          0,
          1
        ],
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ]
      ],
      "dangling": [
        false,
        false,
        false
      ],
      "completed": [
        [
          0,
          0,
          1
        ],
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ]
      ],
      "P": [
        [
          0,
          0,
          1
        ],
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ]
      ],
      "G": [
        [
          0.25,
          0.25,
          0.75
        ],
        [
          0.625,
          0.125,
          0.125
        ],
        [
          0.125,
          0.625,
          0.125
        ]
      ],
      "B": [
        [
          1,
          0,
          -0.5
        ],
        [
          -0.5,
          1,
          0
        ],
        [
          0,
          -0.5,
          1
        ]
      ],
      "b": [
        0.25,
        0.125,
        0.125
      ],
      "v": [
        0.5,
        0.25,
        0.25
      ],
      "initial": [
        1,
        0,
        0
      ],
      "alpha": 0.5,
      "lazy": 0,
      "colSums": [
        {
          "numerator": "1",
          "denominator": "1",
          "value": 1
        },
        {
          "numerator": "1",
          "denominator": "1",
          "value": 1
        },
        {
          "numerator": "1",
          "denominator": "1",
          "value": 1
        }
      ],
      "stochasticExact": true,
      "graph": {
        "edges": [
          {
            "from": 0,
            "to": 1,
            "weight": 1
          },
          {
            "from": 1,
            "to": 2,
            "weight": 1
          },
          {
            "from": 2,
            "to": 0,
            "weight": 1
          }
        ],
        "reach": [
          [
            true,
            true,
            true
          ],
          [
            true,
            true,
            true
          ],
          [
            true,
            true,
            true
          ]
        ],
        "classes": [
          {
            "vertices": [
              0,
              1,
              2
            ],
            "distances": [
              0,
              1,
              2
            ],
            "periodEdges": [
              {
                "from": 0,
                "to": 1,
                "weight": 1,
                "difference": 0
              },
              {
                "from": 1,
                "to": 2,
                "weight": 1,
                "difference": 0
              },
              {
                "from": 2,
                "to": 0,
                "weight": 1,
                "difference": 3
              }
            ],
            "period": 3,
            "closed": true,
            "matrix": [
              [
                0,
                0,
                1
              ],
              [
                1,
                0,
                0
              ],
              [
                0,
                1,
                0
              ]
            ]
          }
        ],
        "irreducible": true,
        "period": 3,
        "primitive": false,
        "positive": false
      },
      "googleGraph": {
        "edges": [
          {
            "from": 0,
            "to": 0,
            "weight": 0.25
          },
          {
            "from": 0,
            "to": 1,
            "weight": 0.625
          },
          {
            "from": 0,
            "to": 2,
            "weight": 0.125
          },
          {
            "from": 1,
            "to": 0,
            "weight": 0.25
          },
          {
            "from": 1,
            "to": 1,
            "weight": 0.125
          },
          {
            "from": 1,
            "to": 2,
            "weight": 0.625
          },
          {
            "from": 2,
            "to": 0,
            "weight": 0.75
          },
          {
            "from": 2,
            "to": 1,
            "weight": 0.125
          },
          {
            "from": 2,
            "to": 2,
            "weight": 0.125
          }
        ],
        "reach": [
          [
            true,
            true,
            true
          ],
          [
            true,
            true,
            true
          ],
          [
            true,
            true,
            true
          ]
        ],
        "classes": [
          {
            "vertices": [
              0,
              1,
              2
            ],
            "distances": [
              0,
              1,
              1
            ],
            "periodEdges": [
              {
                "from": 0,
                "to": 0,
                "weight": 0.25,
                "difference": 1
              },
              {
                "from": 0,
                "to": 1,
                "weight": 0.625,
                "difference": 0
              },
              {
                "from": 0,
                "to": 2,
                "weight": 0.125,
                "difference": 0
              },
              {
                "from": 1,
                "to": 0,
                "weight": 0.25,
                "difference": 2
              },
              {
                "from": 1,
                "to": 1,
                "weight": 0.125,
                "difference": 1
              },
              {
                "from": 1,
                "to": 2,
                "weight": 0.625,
                "difference": 1
              },
              {
                "from": 2,
                "to": 0,
                "weight": 0.75,
                "difference": 2
              },
              {
                "from": 2,
                "to": 1,
                "weight": 0.125,
                "difference": 1
              },
              {
                "from": 2,
                "to": 2,
                "weight": 0.125,
                "difference": 1
              }
            ],
            "period": 1,
            "closed": true,
            "matrix": [
              [
                0.25,
                0.25,
                0.75
              ],
              [
                0.625,
                0.125,
                0.125
              ],
              [
                0.125,
                0.625,
                0.125
              ]
            ]
          }
        ],
        "irreducible": true,
        "period": 1,
        "primitive": true,
        "positive": true
      },
      "solve": {
        "rank": 3,
        "consistent": true,
        "unique": true,
        "pivots": [
          0,
          1,
          2
        ],
        "trace": [
          {
            "stage": "input",
            "matrix": [
              [
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "-1",
                  "denominator": "2",
                  "value": -0.5
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              [
                {
                  "numerator": "-1",
                  "denominator": "2",
                  "value": -0.5
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "1",
                  "denominator": "8",
                  "value": 0.125
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "-1",
                  "denominator": "2",
                  "value": -0.5
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "1",
                  "denominator": "8",
                  "value": 0.125
                }
              ]
            ]
          },
          {
            "stage": "pivot",
            "row": 0,
            "col": 0,
            "swapped": 0,
            "pivot": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "matrix": [
              [
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "-1",
                  "denominator": "2",
                  "value": -0.5
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "-1",
                  "denominator": "4",
                  "value": -0.25
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "-1",
                  "denominator": "2",
                  "value": -0.5
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "1",
                  "denominator": "8",
                  "value": 0.125
                }
              ]
            ]
          },
          {
            "stage": "pivot",
            "row": 1,
            "col": 1,
            "swapped": 1,
            "pivot": {
              "numerator": "1",
              "denominator": "1",
              "value": 1
            },
            "matrix": [
              [
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "-1",
                  "denominator": "2",
                  "value": -0.5
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "-1",
                  "denominator": "4",
                  "value": -0.25
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "7",
                  "denominator": "8",
                  "value": 0.875
                },
                {
                  "numerator": "1",
                  "denominator": "4",
                  "value": 0.25
                }
              ]
            ]
          },
          {
            "stage": "pivot",
            "row": 2,
            "col": 2,
            "swapped": 2,
            "pivot": {
              "numerator": "7",
              "denominator": "8",
              "value": 0.875
            },
            "matrix": [
              [
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "11",
                  "denominator": "28",
                  "value": 0.39285714285714285
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "9",
                  "denominator": "28",
                  "value": 0.32142857142857145
                }
              ],
              [
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "0",
                  "denominator": "1",
                  "value": 0
                },
                {
                  "numerator": "1",
                  "denominator": "1",
                  "value": 1
                },
                {
                  "numerator": "2",
                  "denominator": "7",
                  "value": 0.2857142857142857
                }
              ]
            ]
          }
        ],
        "solution": [
          {
            "numerator": "11",
            "denominator": "28",
            "value": 0.39285714285714285
          },
          {
            "numerator": "9",
            "denominator": "28",
            "value": 0.32142857142857145
          },
          {
            "numerator": "2",
            "denominator": "7",
            "value": 0.2857142857142857
          }
        ]
      },
      "rows": [
        {
          "k": 0,
          "x": [
            1,
            0,
            0
          ],
          "px": [
            0,
            1,
            0
          ],
          "linearNext": [
            0.25,
            0.625,
            0.125
          ],
          "matrixNext": [
            0.25,
            0.625,
            0.125
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.75,
            0.625,
            0.125
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "4",
              "value": -0.75
            },
            {
              "numerator": "5",
              "denominator": "8",
              "value": 0.625
            },
            {
              "numerator": "1",
              "denominator": "8",
              "value": 0.125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "2",
            "value": 1.5
          },
          "bound": {
            "numerator": "3",
            "denominator": "1",
            "value": 3
          },
          "error": {
            "numerator": "17",
            "denominator": "14",
            "value": 1.2142857142857142
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 1,
          "x": [
            0.25,
            0.625,
            0.125
          ],
          "px": [
            0.125,
            0.25,
            0.625
          ],
          "linearNext": [
            0.3125,
            0.25,
            0.4375
          ],
          "matrixNext": [
            0.3125,
            0.25,
            0.4375
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.0625,
            -0.375,
            0.3125
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "16",
              "value": 0.0625
            },
            {
              "numerator": "-3",
              "denominator": "8",
              "value": -0.375
            },
            {
              "numerator": "5",
              "denominator": "16",
              "value": 0.3125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "4",
            "value": 0.75
          },
          "bound": {
            "numerator": "3",
            "denominator": "2",
            "value": 1.5
          },
          "error": {
            "numerator": "17",
            "denominator": "28",
            "value": 0.6071428571428571
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 2,
          "x": [
            0.3125,
            0.25,
            0.4375
          ],
          "px": [
            0.4375,
            0.3125,
            0.25
          ],
          "linearNext": [
            0.46875,
            0.28125,
            0.25
          ],
          "matrixNext": [
            0.46875,
            0.28125,
            0.25
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.15625,
            0.03125,
            -0.1875
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "32",
              "value": 0.15625
            },
            {
              "numerator": "1",
              "denominator": "32",
              "value": 0.03125
            },
            {
              "numerator": "-3",
              "denominator": "16",
              "value": -0.1875
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "8",
            "value": 0.375
          },
          "bound": {
            "numerator": "3",
            "denominator": "4",
            "value": 0.75
          },
          "error": {
            "numerator": "17",
            "denominator": "56",
            "value": 0.30357142857142855
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 3,
          "x": [
            0.46875,
            0.28125,
            0.25
          ],
          "px": [
            0.25,
            0.46875,
            0.28125
          ],
          "linearNext": [
            0.375,
            0.359375,
            0.265625
          ],
          "matrixNext": [
            0.375,
            0.359375,
            0.265625
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.09375,
            0.078125,
            0.015625
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "32",
              "value": -0.09375
            },
            {
              "numerator": "5",
              "denominator": "64",
              "value": 0.078125
            },
            {
              "numerator": "1",
              "denominator": "64",
              "value": 0.015625
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "16",
            "value": 0.1875
          },
          "bound": {
            "numerator": "3",
            "denominator": "8",
            "value": 0.375
          },
          "error": {
            "numerator": "17",
            "denominator": "112",
            "value": 0.15178571428571427
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 4,
          "x": [
            0.375,
            0.359375,
            0.265625
          ],
          "px": [
            0.265625,
            0.375,
            0.359375
          ],
          "linearNext": [
            0.3828125,
            0.3125,
            0.3046875
          ],
          "matrixNext": [
            0.3828125,
            0.3125,
            0.3046875
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.0078125,
            -0.046875,
            0.0390625
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "128",
              "value": 0.0078125
            },
            {
              "numerator": "-3",
              "denominator": "64",
              "value": -0.046875
            },
            {
              "numerator": "5",
              "denominator": "128",
              "value": 0.0390625
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "32",
            "value": 0.09375
          },
          "bound": {
            "numerator": "3",
            "denominator": "16",
            "value": 0.1875
          },
          "error": {
            "numerator": "17",
            "denominator": "224",
            "value": 0.07589285714285714
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 5,
          "x": [
            0.3828125,
            0.3125,
            0.3046875
          ],
          "px": [
            0.3046875,
            0.3828125,
            0.3125
          ],
          "linearNext": [
            0.40234375,
            0.31640625,
            0.28125
          ],
          "matrixNext": [
            0.40234375,
            0.31640625,
            0.28125
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.01953125,
            0.00390625,
            -0.0234375
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "256",
              "value": 0.01953125
            },
            {
              "numerator": "1",
              "denominator": "256",
              "value": 0.00390625
            },
            {
              "numerator": "-3",
              "denominator": "128",
              "value": -0.0234375
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "64",
            "value": 0.046875
          },
          "bound": {
            "numerator": "3",
            "denominator": "32",
            "value": 0.09375
          },
          "error": {
            "numerator": "17",
            "denominator": "448",
            "value": 0.03794642857142857
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 6,
          "x": [
            0.40234375,
            0.31640625,
            0.28125
          ],
          "px": [
            0.28125,
            0.40234375,
            0.31640625
          ],
          "linearNext": [
            0.390625,
            0.326171875,
            0.283203125
          ],
          "matrixNext": [
            0.390625,
            0.326171875,
            0.283203125
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.01171875,
            0.009765625,
            0.001953125
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "256",
              "value": -0.01171875
            },
            {
              "numerator": "5",
              "denominator": "512",
              "value": 0.009765625
            },
            {
              "numerator": "1",
              "denominator": "512",
              "value": 0.001953125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "128",
            "value": 0.0234375
          },
          "bound": {
            "numerator": "3",
            "denominator": "64",
            "value": 0.046875
          },
          "error": {
            "numerator": "17",
            "denominator": "896",
            "value": 0.018973214285714284
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 7,
          "x": [
            0.390625,
            0.326171875,
            0.283203125
          ],
          "px": [
            0.283203125,
            0.390625,
            0.326171875
          ],
          "linearNext": [
            0.3916015625,
            0.3203125,
            0.2880859375
          ],
          "matrixNext": [
            0.3916015625,
            0.3203125,
            0.2880859375
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.0009765625,
            -0.005859375,
            0.0048828125
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "1024",
              "value": 0.0009765625
            },
            {
              "numerator": "-3",
              "denominator": "512",
              "value": -0.005859375
            },
            {
              "numerator": "5",
              "denominator": "1024",
              "value": 0.0048828125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "256",
            "value": 0.01171875
          },
          "bound": {
            "numerator": "3",
            "denominator": "128",
            "value": 0.0234375
          },
          "error": {
            "numerator": "17",
            "denominator": "1792",
            "value": 0.009486607142857142
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 8,
          "x": [
            0.3916015625,
            0.3203125,
            0.2880859375
          ],
          "px": [
            0.2880859375,
            0.3916015625,
            0.3203125
          ],
          "linearNext": [
            0.39404296875,
            0.32080078125,
            0.28515625
          ],
          "matrixNext": [
            0.39404296875,
            0.32080078125,
            0.28515625
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.00244140625,
            0.00048828125,
            -0.0029296875
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "2048",
              "value": 0.00244140625
            },
            {
              "numerator": "1",
              "denominator": "2048",
              "value": 0.00048828125
            },
            {
              "numerator": "-3",
              "denominator": "1024",
              "value": -0.0029296875
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "512",
            "value": 0.005859375
          },
          "bound": {
            "numerator": "3",
            "denominator": "256",
            "value": 0.01171875
          },
          "error": {
            "numerator": "17",
            "denominator": "3584",
            "value": 0.004743303571428571
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 9,
          "x": [
            0.39404296875,
            0.32080078125,
            0.28515625
          ],
          "px": [
            0.28515625,
            0.39404296875,
            0.32080078125
          ],
          "linearNext": [
            0.392578125,
            0.322021484375,
            0.285400390625
          ],
          "matrixNext": [
            0.392578125,
            0.322021484375,
            0.285400390625
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.00146484375,
            0.001220703125,
            0.000244140625
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "2048",
              "value": -0.00146484375
            },
            {
              "numerator": "5",
              "denominator": "4096",
              "value": 0.001220703125
            },
            {
              "numerator": "1",
              "denominator": "4096",
              "value": 0.000244140625
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "1024",
            "value": 0.0029296875
          },
          "bound": {
            "numerator": "3",
            "denominator": "512",
            "value": 0.005859375
          },
          "error": {
            "numerator": "17",
            "denominator": "7168",
            "value": 0.0023716517857142855
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 10,
          "x": [
            0.392578125,
            0.322021484375,
            0.285400390625
          ],
          "px": [
            0.285400390625,
            0.392578125,
            0.322021484375
          ],
          "linearNext": [
            0.3927001953125,
            0.3212890625,
            0.2860107421875
          ],
          "matrixNext": [
            0.3927001953125,
            0.3212890625,
            0.2860107421875
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.0001220703125,
            -0.000732421875,
            0.0006103515625
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "8192",
              "value": 0.0001220703125
            },
            {
              "numerator": "-3",
              "denominator": "4096",
              "value": -0.000732421875
            },
            {
              "numerator": "5",
              "denominator": "8192",
              "value": 0.0006103515625
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "2048",
            "value": 0.00146484375
          },
          "bound": {
            "numerator": "3",
            "denominator": "1024",
            "value": 0.0029296875
          },
          "error": {
            "numerator": "17",
            "denominator": "14336",
            "value": 0.0011858258928571428
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 11,
          "x": [
            0.3927001953125,
            0.3212890625,
            0.2860107421875
          ],
          "px": [
            0.2860107421875,
            0.3927001953125,
            0.3212890625
          ],
          "linearNext": [
            0.39300537109375,
            0.32135009765625,
            0.28564453125
          ],
          "matrixNext": [
            0.39300537109375,
            0.32135009765625,
            0.28564453125
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.00030517578125,
            0.00006103515625,
            -0.0003662109375
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "16384",
              "value": 0.00030517578125
            },
            {
              "numerator": "1",
              "denominator": "16384",
              "value": 0.00006103515625
            },
            {
              "numerator": "-3",
              "denominator": "8192",
              "value": -0.0003662109375
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "4096",
            "value": 0.000732421875
          },
          "bound": {
            "numerator": "3",
            "denominator": "2048",
            "value": 0.00146484375
          },
          "error": {
            "numerator": "17",
            "denominator": "28672",
            "value": 0.0005929129464285714
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 12,
          "x": [
            0.39300537109375,
            0.32135009765625,
            0.28564453125
          ],
          "px": [
            0.28564453125,
            0.39300537109375,
            0.32135009765625
          ],
          "linearNext": [
            0.392822265625,
            0.321502685546875,
            0.285675048828125
          ],
          "matrixNext": [
            0.392822265625,
            0.321502685546875,
            0.285675048828125
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.00018310546875,
            0.000152587890625,
            0.000030517578125
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "16384",
              "value": -0.00018310546875
            },
            {
              "numerator": "5",
              "denominator": "32768",
              "value": 0.000152587890625
            },
            {
              "numerator": "1",
              "denominator": "32768",
              "value": 0.000030517578125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "8192",
            "value": 0.0003662109375
          },
          "bound": {
            "numerator": "3",
            "denominator": "4096",
            "value": 0.000732421875
          },
          "error": {
            "numerator": "17",
            "denominator": "57344",
            "value": 0.0002964564732142857
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 13,
          "x": [
            0.392822265625,
            0.321502685546875,
            0.285675048828125
          ],
          "px": [
            0.285675048828125,
            0.392822265625,
            0.321502685546875
          ],
          "linearNext": [
            0.3928375244140625,
            0.3214111328125,
            0.2857513427734375
          ],
          "matrixNext": [
            0.3928375244140625,
            0.3214111328125,
            0.2857513427734375
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.0000152587890625,
            -0.000091552734375,
            0.0000762939453125
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "65536",
              "value": 0.0000152587890625
            },
            {
              "numerator": "-3",
              "denominator": "32768",
              "value": -0.000091552734375
            },
            {
              "numerator": "5",
              "denominator": "65536",
              "value": 0.0000762939453125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "16384",
            "value": 0.00018310546875
          },
          "bound": {
            "numerator": "3",
            "denominator": "8192",
            "value": 0.0003662109375
          },
          "error": {
            "numerator": "17",
            "denominator": "114688",
            "value": 0.00014822823660714285
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 14,
          "x": [
            0.3928375244140625,
            0.3214111328125,
            0.2857513427734375
          ],
          "px": [
            0.2857513427734375,
            0.3928375244140625,
            0.3214111328125
          ],
          "linearNext": [
            0.39287567138671875,
            0.32141876220703125,
            0.28570556640625
          ],
          "matrixNext": [
            0.39287567138671875,
            0.32141876220703125,
            0.28570556640625
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.00003814697265625,
            0.00000762939453125,
            -0.0000457763671875
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "131072",
              "value": 0.00003814697265625
            },
            {
              "numerator": "1",
              "denominator": "131072",
              "value": 0.00000762939453125
            },
            {
              "numerator": "-3",
              "denominator": "65536",
              "value": -0.0000457763671875
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "32768",
            "value": 0.000091552734375
          },
          "bound": {
            "numerator": "3",
            "denominator": "16384",
            "value": 0.00018310546875
          },
          "error": {
            "numerator": "17",
            "denominator": "229376",
            "value": 0.00007411411830357142
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 15,
          "x": [
            0.39287567138671875,
            0.32141876220703125,
            0.28570556640625
          ],
          "px": [
            0.28570556640625,
            0.39287567138671875,
            0.32141876220703125
          ],
          "linearNext": [
            0.392852783203125,
            0.3214378356933594,
            0.2857093811035156
          ],
          "matrixNext": [
            0.392852783203125,
            0.3214378356933594,
            0.2857093811035156
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.00002288818359375,
            0.000019073486328125,
            0.000003814697265625
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "131072",
              "value": -0.00002288818359375
            },
            {
              "numerator": "5",
              "denominator": "262144",
              "value": 0.000019073486328125
            },
            {
              "numerator": "1",
              "denominator": "262144",
              "value": 0.000003814697265625
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "65536",
            "value": 0.0000457763671875
          },
          "bound": {
            "numerator": "3",
            "denominator": "32768",
            "value": 0.000091552734375
          },
          "error": {
            "numerator": "17",
            "denominator": "458752",
            "value": 0.00003705705915178571
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 16,
          "x": [
            0.392852783203125,
            0.3214378356933594,
            0.2857093811035156
          ],
          "px": [
            0.2857093811035156,
            0.392852783203125,
            0.3214378356933594
          ],
          "linearNext": [
            0.3928546905517578,
            0.3214263916015625,
            0.2857189178466797
          ],
          "matrixNext": [
            0.3928546905517578,
            0.3214263916015625,
            0.2857189178466797
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.0000019073486328125,
            -0.000011444091796875,
            0.0000095367431640625
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "524288",
              "value": 0.0000019073486328125
            },
            {
              "numerator": "-3",
              "denominator": "262144",
              "value": -0.000011444091796875
            },
            {
              "numerator": "5",
              "denominator": "524288",
              "value": 0.0000095367431640625
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "131072",
            "value": 0.00002288818359375
          },
          "bound": {
            "numerator": "3",
            "denominator": "65536",
            "value": 0.0000457763671875
          },
          "error": {
            "numerator": "17",
            "denominator": "917504",
            "value": 0.000018528529575892856
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 17,
          "x": [
            0.3928546905517578,
            0.3214263916015625,
            0.2857189178466797
          ],
          "px": [
            0.2857189178466797,
            0.3928546905517578,
            0.3214263916015625
          ],
          "linearNext": [
            0.39285945892333984,
            0.3214273452758789,
            0.28571319580078125
          ],
          "matrixNext": [
            0.39285945892333984,
            0.3214273452758789,
            0.28571319580078125
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            0.00000476837158203125,
            9.5367431640625e-7,
            -0.0000057220458984375
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "1048576",
              "value": 0.00000476837158203125
            },
            {
              "numerator": "1",
              "denominator": "1048576",
              "value": 9.5367431640625e-7
            },
            {
              "numerator": "-3",
              "denominator": "524288",
              "value": -0.0000057220458984375
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "262144",
            "value": 0.000011444091796875
          },
          "bound": {
            "numerator": "3",
            "denominator": "131072",
            "value": 0.00002288818359375
          },
          "error": {
            "numerator": "17",
            "denominator": "1835008",
            "value": 0.000009264264787946428
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 18,
          "x": [
            0.39285945892333984,
            0.3214273452758789,
            0.28571319580078125
          ],
          "px": [
            0.28571319580078125,
            0.39285945892333984,
            0.3214273452758789
          ],
          "linearNext": [
            0.3928565979003906,
            0.3214297294616699,
            0.28571367263793945
          ],
          "matrixNext": [
            0.3928565979003906,
            0.3214297294616699,
            0.28571367263793945
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -0.00000286102294921875,
            0.000002384185791015625,
            4.76837158203125e-7
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "1048576",
              "value": -0.00000286102294921875
            },
            {
              "numerator": "5",
              "denominator": "2097152",
              "value": 0.000002384185791015625
            },
            {
              "numerator": "1",
              "denominator": "2097152",
              "value": 4.76837158203125e-7
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "524288",
            "value": 0.0000057220458984375
          },
          "bound": {
            "numerator": "3",
            "denominator": "262144",
            "value": 0.000011444091796875
          },
          "error": {
            "numerator": "17",
            "denominator": "3670016",
            "value": 0.000004632132393973214
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 19,
          "x": [
            0.3928565979003906,
            0.3214297294616699,
            0.28571367263793945
          ],
          "px": [
            0.28571367263793945,
            0.3928565979003906,
            0.3214297294616699
          ],
          "linearNext": [
            0.3928568363189697,
            0.3214282989501953,
            0.28571486473083496
          ],
          "matrixNext": [
            0.3928568363189697,
            0.3214282989501953,
            0.28571486473083496
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            2.384185791015625e-7,
            -0.000001430511474609375,
            0.0000011920928955078125
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "4194304",
              "value": 2.384185791015625e-7
            },
            {
              "numerator": "-3",
              "denominator": "2097152",
              "value": -0.000001430511474609375
            },
            {
              "numerator": "5",
              "denominator": "4194304",
              "value": 0.0000011920928955078125
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "1048576",
            "value": 0.00000286102294921875
          },
          "bound": {
            "numerator": "3",
            "denominator": "524288",
            "value": 0.0000057220458984375
          },
          "error": {
            "numerator": "17",
            "denominator": "7340032",
            "value": 0.000002316066196986607
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 20,
          "x": [
            0.3928568363189697,
            0.3214282989501953,
            0.28571486473083496
          ],
          "px": [
            0.28571486473083496,
            0.3928568363189697,
            0.3214282989501953
          ],
          "linearNext": [
            0.3928574323654175,
            0.32142841815948486,
            0.28571414947509766
          ],
          "matrixNext": [
            0.3928574323654175,
            0.32142841815948486,
            0.28571414947509766
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            5.960464477539062e-7,
            1.1920928955078125e-7,
            -7.152557373046875e-7
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "8388608",
              "value": 5.960464477539062e-7
            },
            {
              "numerator": "1",
              "denominator": "8388608",
              "value": 1.1920928955078125e-7
            },
            {
              "numerator": "-3",
              "denominator": "4194304",
              "value": -7.152557373046875e-7
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "2097152",
            "value": 0.000001430511474609375
          },
          "bound": {
            "numerator": "3",
            "denominator": "1048576",
            "value": 0.00000286102294921875
          },
          "error": {
            "numerator": "17",
            "denominator": "14680064",
            "value": 0.0000011580330984933035
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 21,
          "x": [
            0.3928574323654175,
            0.32142841815948486,
            0.28571414947509766
          ],
          "px": [
            0.28571414947509766,
            0.3928574323654175,
            0.32142841815948486
          ],
          "linearNext": [
            0.39285707473754883,
            0.32142871618270874,
            0.28571420907974243
          ],
          "matrixNext": [
            0.39285707473754883,
            0.32142871618270874,
            0.28571420907974243
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -3.5762786865234375e-7,
            2.980232238769531e-7,
            5.960464477539063e-8
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "8388608",
              "value": -3.5762786865234375e-7
            },
            {
              "numerator": "5",
              "denominator": "16777216",
              "value": 2.980232238769531e-7
            },
            {
              "numerator": "1",
              "denominator": "16777216",
              "value": 5.960464477539063e-8
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "4194304",
            "value": 7.152557373046875e-7
          },
          "bound": {
            "numerator": "3",
            "denominator": "2097152",
            "value": 0.000001430511474609375
          },
          "error": {
            "numerator": "17",
            "denominator": "29360128",
            "value": 5.790165492466517e-7
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 22,
          "x": [
            0.39285707473754883,
            0.32142871618270874,
            0.28571420907974243
          ],
          "px": [
            0.28571420907974243,
            0.39285707473754883,
            0.32142871618270874
          ],
          "linearNext": [
            0.3928571045398712,
            0.3214285373687744,
            0.28571435809135437
          ],
          "matrixNext": [
            0.3928571045398712,
            0.3214285373687744,
            0.28571435809135437
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            2.9802322387695312e-8,
            -1.7881393432617188e-7,
            1.4901161193847656e-7
          ],
          "exactResidual": [
            {
              "numerator": "1",
              "denominator": "33554432",
              "value": 2.9802322387695312e-8
            },
            {
              "numerator": "-3",
              "denominator": "16777216",
              "value": -1.7881393432617188e-7
            },
            {
              "numerator": "5",
              "denominator": "33554432",
              "value": 1.4901161193847656e-7
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "8388608",
            "value": 3.5762786865234375e-7
          },
          "bound": {
            "numerator": "3",
            "denominator": "4194304",
            "value": 7.152557373046875e-7
          },
          "error": {
            "numerator": "17",
            "denominator": "58720256",
            "value": 2.8950827462332587e-7
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 23,
          "x": [
            0.3928571045398712,
            0.3214285373687744,
            0.28571435809135437
          ],
          "px": [
            0.28571435809135437,
            0.3928571045398712,
            0.3214285373687744
          ],
          "linearNext": [
            0.3928571790456772,
            0.3214285522699356,
            0.2857142686843872
          ],
          "matrixNext": [
            0.3928571790456772,
            0.3214285522699356,
            0.2857142686843872
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            7.450580596923828e-8,
            1.4901161193847656e-8,
            -8.940696716308594e-8
          ],
          "exactResidual": [
            {
              "numerator": "5",
              "denominator": "67108864",
              "value": 7.450580596923828e-8
            },
            {
              "numerator": "1",
              "denominator": "67108864",
              "value": 1.4901161193847656e-8
            },
            {
              "numerator": "-3",
              "denominator": "33554432",
              "value": -8.940696716308594e-8
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "16777216",
            "value": 1.7881393432617188e-7
          },
          "bound": {
            "numerator": "3",
            "denominator": "8388608",
            "value": 3.5762786865234375e-7
          },
          "error": {
            "numerator": "17",
            "denominator": "117440512",
            "value": 1.4475413731166294e-7
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        },
        {
          "k": 24,
          "x": [
            0.3928571790456772,
            0.3214285522699356,
            0.2857142686843872
          ],
          "px": [
            0.2857142686843872,
            0.3928571790456772,
            0.3214285522699356
          ],
          "linearNext": [
            0.3928571343421936,
            0.3214285895228386,
            0.2857142761349678
          ],
          "matrixNext": [
            0.3928571343421936,
            0.3214285895228386,
            0.2857142761349678
          ],
          "matrixGap": [
            0,
            0,
            0
          ],
          "fixedResidual": [
            -4.470348358154297e-8,
            3.725290298461914e-8,
            7.450580596923828e-9
          ],
          "exactResidual": [
            {
              "numerator": "-3",
              "denominator": "67108864",
              "value": -4.470348358154297e-8
            },
            {
              "numerator": "5",
              "denominator": "134217728",
              "value": 3.725290298461914e-8
            },
            {
              "numerator": "1",
              "denominator": "134217728",
              "value": 7.450580596923828e-9
            }
          ],
          "residualNorm": {
            "numerator": "3",
            "denominator": "33554432",
            "value": 8.940696716308594e-8
          },
          "bound": {
            "numerator": "3",
            "denominator": "16777216",
            "value": 1.7881393432617188e-7
          },
          "error": {
            "numerator": "17",
            "denominator": "234881024",
            "value": 7.237706865583147e-8
          },
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          },
          "massDefect": {
            "numerator": "0",
            "denominator": "1",
            "value": 0
          },
          "arithmeticDefect": [
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            },
            {
              "numerator": "0",
              "denominator": "1",
              "value": 0
            }
          ]
        }
      ],
      "rawRows": [
        {
          "k": 0,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            1,
            0,
            0
          ],
          "delta": 2,
          "averageResidual": [
            -1,
            1,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 1,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.5,
            0.5,
            0
          ],
          "delta": 2,
          "averageResidual": [
            -0.5,
            0,
            0.5
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 2,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 3,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.5,
            0.25,
            0.25
          ],
          "delta": 2,
          "averageResidual": [
            -0.25,
            0.25,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 4,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.4,
            0.4,
            0.2
          ],
          "delta": 2,
          "averageResidual": [
            -0.2,
            0,
            0.2
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 5,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 6,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.42857142857142855,
            0.2857142857142857,
            0.2857142857142857
          ],
          "delta": 2,
          "averageResidual": [
            -0.14285714285714285,
            0.14285714285714285,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 7,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.375,
            0.375,
            0.25
          ],
          "delta": 2,
          "averageResidual": [
            -0.125,
            0,
            0.125
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 8,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 9,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.4,
            0.3,
            0.3
          ],
          "delta": 2,
          "averageResidual": [
            -0.10000000000000003,
            0.10000000000000003,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 10,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.36363636363636365,
            0.36363636363636365,
            0.2727272727272727
          ],
          "delta": 2,
          "averageResidual": [
            -0.09090909090909094,
            0,
            0.09090909090909094
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 11,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 12,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.38461538461538464,
            0.3076923076923077,
            0.3076923076923077
          ],
          "delta": 2,
          "averageResidual": [
            -0.07692307692307693,
            0.07692307692307693,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 13,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.35714285714285715,
            0.35714285714285715,
            0.2857142857142857
          ],
          "delta": 2,
          "averageResidual": [
            -0.07142857142857145,
            0,
            0.07142857142857145
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 14,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 15,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.375,
            0.3125,
            0.3125
          ],
          "delta": 2,
          "averageResidual": [
            -0.0625,
            0.0625,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 16,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.35294117647058826,
            0.35294117647058826,
            0.29411764705882354
          ],
          "delta": 2,
          "averageResidual": [
            -0.05882352941176472,
            0,
            0.05882352941176472
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 17,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 18,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.3684210526315789,
            0.3157894736842105,
            0.3157894736842105
          ],
          "delta": 2,
          "averageResidual": [
            -0.05263157894736842,
            0.05263157894736842,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 19,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.35,
            0.35,
            0.3
          ],
          "delta": 2,
          "averageResidual": [
            -0.04999999999999999,
            0,
            0.04999999999999999
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 20,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 21,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.36363636363636365,
            0.3181818181818182,
            0.3181818181818182
          ],
          "delta": 2,
          "averageResidual": [
            -0.04545454545454547,
            0.04545454545454547,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 22,
          "x": [
            0,
            1,
            0
          ],
          "next": [
            0,
            0,
            1
          ],
          "average": [
            0.34782608695652173,
            0.34782608695652173,
            0.30434782608695654
          ],
          "delta": 2,
          "averageResidual": [
            -0.04347826086956519,
            0,
            0.04347826086956519
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 23,
          "x": [
            0,
            0,
            1
          ],
          "next": [
            1,
            0,
            0
          ],
          "average": [
            0.3333333333333333,
            0.3333333333333333,
            0.3333333333333333
          ],
          "delta": 2,
          "averageResidual": [
            0,
            0,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        },
        {
          "k": 24,
          "x": [
            1,
            0,
            0
          ],
          "next": [
            0,
            1,
            0
          ],
          "average": [
            0.36,
            0.32,
            0.32
          ],
          "delta": 2,
          "averageResidual": [
            -0.03999999999999998,
            0.03999999999999998,
            0
          ],
          "mass": {
            "numerator": "1",
            "denominator": "1",
            "value": 1
          }
        }
      ],
      "contraction": 0.5
    }
  }
}