1{
  2  "matrices": [
  3    [
  4      [
  5        1.18,
  6        0.22
  7      ],
  8      [
  9        0.04,
 10        0.82
 11      ]
 12    ],
 13    [
 14      [
 15        0.86,
 16        0.16
 17      ],
 18      [
 19        -0.1,
 20        1.26
 21      ]
 22    ]
 23  ],
 24  "stationary_check_p05": {
 25    "empirical_pi": [
 26      0.493125,
 27      0.506875
 28    ],
 29    "theoretical_pi": [
 30      0.5,
 31      0.5
 32    ],
 33    "mass_equation_max_residual": 0.00687500000000002
 34  },
 35  "stationary_check_p095": {
 36    "empirical_pi": [
 37      0.5105,
 38      0.4895
 39    ],
 40    "theoretical_pi": [
 41      0.5,
 42      0.5
 43    ],
 44    "mass_equation_max_residual": 0.01050000000000001
 45  },
 46  "smoothness_fd": {
 47    "symmetry_point": {
 48      "p": 0.5,
 49      "predicted_derivative": 0.0,
 50      "rows": [
 51        {
 52          "h": 0.08,
 53          "derivative": 0.08604483944413381,
 54          "abs_error_vs_predicted_zero": 0.08604483944413381
 55        },
 56        {
 57          "h": 0.04,
 58          "derivative": 0.06598617028438936,
 59          "abs_error_vs_predicted_zero": 0.06598617028438936
 60        },
 61        {
 62          "h": 0.02,
 63          "derivative": -0.0035553233883770657,
 64          "abs_error_vs_predicted_zero": 0.0035553233883770657
 65        },
 66        {
 67          "h": 0.01,
 68          "derivative": -0.028830274117891755,
 69          "abs_error_vs_predicted_zero": 0.028830274117891755
 70        },
 71        {
 72          "h": 0.005,
 73          "derivative": 0.016807390162384278,
 74          "abs_error_vs_predicted_zero": 0.016807390162384278
 75        }
 76      ]
 77    },
 78    "interior_point": {
 79      "p": 0.35,
 80      "rows": [
 81        {
 82          "h": 0.04,
 83          "derivative": 0.057535700217820104
 84        },
 85        {
 86          "h": 0.02,
 87          "derivative": 0.024060335784685007
 88        },
 89        {
 90          "h": 0.01,
 91          "derivative": 0.014878132091934206
 92        },
 93        {
 94          "h": 0.005,
 95          "derivative": -0.04080460977431456
 96        }
 97      ]
 98    }
 99  },
100  "boundary_sweep": [
101    {
102      "p": 0.05,
103      "mean_lambda": 0.014440067036664131,
104      "std_over_seeds": 0.000229287803093258
105    },
106    {
107      "p": 0.1,
108      "mean_lambda": 0.01603810748597485,
109      "std_over_seeds": 0.0004167124270967387
110    },
111    {
112      "p": 0.25,
113      "mean_lambda": 0.021485863538148547,
114      "std_over_seeds": 0.0008744452911053991
115    },
116    {
117      "p": 0.5,
118      "mean_lambda": 0.032439754459780486,
119      "std_over_seeds": 0.0011245488617561102
120    },
121    {
122      "p": 0.75,
123      "mean_lambda": 0.06176584551297099,
124      "std_over_seeds": 0.0021265752746986027
125    },
126    {
127      "p": 0.9,
128      "mean_lambda": 0.1117609970916824,
129      "std_over_seeds": 0.0012845996163561514
130    },
131    {
132      "p": 0.95,
133      "mean_lambda": 0.14526129666461574,
134      "std_over_seeds": 0.000600277379423307
135    }
136  ],
137  "controller": {
138    "target_lambda": 0.03407972489448906,
139    "initial_p": 0.2,
140    "final_p": 0.20040328581658762,
141    "trace": [
142      0.017883118489610605,
143      0.017850025521083477,
144      0.018602873777378147,
145      0.01893958123637008,
146      0.0175831409546936,
147      0.020314420683836643,
148      0.019373077954501692,
149      0.017538683541248885,
150      0.017749856631798597,
151      0.01796167244382069,
152      0.01926271808275504,
153      0.017999524357872304
154    ]
155  },
156  "predictions": [
157    "For primitive p in (0,1), empirical stationary masses should approach pi=(.5,.5).",
158    "In the smooth interior, central finite-difference derivative error should decrease approximately quadratically with h after accounting for Monte Carlo noise.",
159    "Near p=0 or p=1, mixing slows and finite-time Lyapunov estimates should have larger seed variance than at p=.5."
160  ]
161}