{
  "matrices": [
    [
      [
        1.18,
        0.22
      ],
      [
        0.04,
        0.82
      ]
    ],
    [
      [
        0.86,
        0.16
      ],
      [
        -0.1,
        1.26
      ]
    ]
  ],
  "stationary_check_p05": {
    "empirical_pi": [
      0.493125,
      0.506875
    ],
    "theoretical_pi": [
      0.5,
      0.5
    ],
    "mass_equation_max_residual": 0.00687500000000002
  },
  "stationary_check_p095": {
    "empirical_pi": [
      0.5105,
      0.4895
    ],
    "theoretical_pi": [
      0.5,
      0.5
    ],
    "mass_equation_max_residual": 0.01050000000000001
  },
  "smoothness_fd": {
    "symmetry_point": {
      "p": 0.5,
      "predicted_derivative": 0.0,
      "rows": [
        {
          "h": 0.08,
          "derivative": 0.08604483944413381,
          "abs_error_vs_predicted_zero": 0.08604483944413381
        },
        {
          "h": 0.04,
          "derivative": 0.06598617028438936,
          "abs_error_vs_predicted_zero": 0.06598617028438936
        },
        {
          "h": 0.02,
          "derivative": -0.0035553233883770657,
          "abs_error_vs_predicted_zero": 0.0035553233883770657
        },
        {
          "h": 0.01,
          "derivative": -0.028830274117891755,
          "abs_error_vs_predicted_zero": 0.028830274117891755
        },
        {
          "h": 0.005,
          "derivative": 0.016807390162384278,
          "abs_error_vs_predicted_zero": 0.016807390162384278
        }
      ]
    },
    "interior_point": {
      "p": 0.35,
      "rows": [
        {
          "h": 0.04,
          "derivative": 0.057535700217820104
        },
        {
          "h": 0.02,
          "derivative": 0.024060335784685007
        },
        {
          "h": 0.01,
          "derivative": 0.014878132091934206
        },
        {
          "h": 0.005,
          "derivative": -0.04080460977431456
        }
      ]
    }
  },
  "boundary_sweep": [
    {
      "p": 0.05,
      "mean_lambda": 0.014440067036664131,
      "std_over_seeds": 0.000229287803093258
    },
    {
      "p": 0.1,
      "mean_lambda": 0.01603810748597485,
      "std_over_seeds": 0.0004167124270967387
    },
    {
      "p": 0.25,
      "mean_lambda": 0.021485863538148547,
      "std_over_seeds": 0.0008744452911053991
    },
    {
      "p": 0.5,
      "mean_lambda": 0.032439754459780486,
      "std_over_seeds": 0.0011245488617561102
    },
    {
      "p": 0.75,
      "mean_lambda": 0.06176584551297099,
      "std_over_seeds": 0.0021265752746986027
    },
    {
      "p": 0.9,
      "mean_lambda": 0.1117609970916824,
      "std_over_seeds": 0.0012845996163561514
    },
    {
      "p": 0.95,
      "mean_lambda": 0.14526129666461574,
      "std_over_seeds": 0.000600277379423307
    }
  ],
  "controller": {
    "target_lambda": 0.03407972489448906,
    "initial_p": 0.2,
    "final_p": 0.20040328581658762,
    "trace": [
      0.017883118489610605,
      0.017850025521083477,
      0.018602873777378147,
      0.01893958123637008,
      0.0175831409546936,
      0.020314420683836643,
      0.019373077954501692,
      0.017538683541248885,
      0.017749856631798597,
      0.01796167244382069,
      0.01926271808275504,
      0.017999524357872304
    ]
  },
  "predictions": [
    "For primitive p in (0,1), empirical stationary masses should approach pi=(.5,.5).",
    "In the smooth interior, central finite-difference derivative error should decrease approximately quadratically with h after accounting for Monte Carlo noise.",
    "Near p=0 or p=1, mixing slows and finite-time Lyapunov estimates should have larger seed variance than at p=.5."
  ]
}