1{
  2  "seed": 2040,
  3  "system": {
  4    "alpha": 1.2,
  5    "q": 0.8,
  6    "K": [
  7      [
  8        1.0,
  9        0.0
 10      ],
 11      [
 12        0.0,
 13        -1.0
 14      ]
 15    ],
 16    "B": [
 17      0.7,
 18      -0.35
 19    ]
 20  },
 21  "predictions": {
 22    "averaging_error_power": "O(eps), predicted log-log slope 1",
 23    "contraction_certificate": "max_s mu_2(A(s)) = -alpha+q; boundary q=alpha",
 24    "perturbation_decay": "late log-distance slope equals -alpha, and is bounded by -(alpha-q)"
 25  },
 26  "averaging_sweep": {
 27    "rows": [
 28      {
 29        "eps": 0.5,
 30        "max_error": 0.09088685716871418,
 31        "rms_error": 0.0353748782470963
 32      },
 33      {
 34        "eps": 0.25,
 35        "max_error": 0.05054718387201525,
 36        "rms_error": 0.017862900268138422
 37      },
 38      {
 39        "eps": 0.125,
 40        "max_error": 0.026779873868539184,
 41        "rms_error": 0.008967909220573956
 42      },
 43      {
 44        "eps": 0.0625,
 45        "max_error": 0.013767425349338452,
 46        "rms_error": 0.004492041843398243
 47      },
 48      {
 49        "eps": 0.03125,
 50        "max_error": 0.006994276731176045,
 51        "rms_error": 0.002247908668634097
 52      }
 53    ],
 54    "observed_loglog_slope": 0.9276021738593212
 55  },
 56  "contraction_boundary_sweep": [
 57    {
 58      "q": 0.0,
 59      "predicted_max_mu": -1.2,
 60      "observed_max_mu": -1.2,
 61      "certificate_holds": true
 62    },
 63    {
 64      "q": 0.6,
 65      "predicted_max_mu": -0.6,
 66      "observed_max_mu": -0.6,
 67      "certificate_holds": true
 68    },
 69    {
 70      "q": 1.19,
 71      "predicted_max_mu": -0.010000000000000009,
 72      "observed_max_mu": -0.010000000000000009,
 73      "certificate_holds": true
 74    },
 75    {
 76      "q": 1.2,
 77      "predicted_max_mu": 0.0,
 78      "observed_max_mu": 0.0,
 79      "certificate_holds": false
 80    },
 81    {
 82      "q": 1.4,
 83      "predicted_max_mu": 0.19999999999999996,
 84      "observed_max_mu": 0.19999999999999996,
 85      "certificate_holds": false
 86    }
 87  ],
 88  "perturbation_decay": [
 89    {
 90      "q": 0.0,
 91      "predicted_long_run_slope": -1.2,
 92      "observed_late_log_slope": -1.2000000000495423,
 93      "predicted_certificate_rate": 1.2,
 94      "max_log_envelope_margin": 7.479350472294755e-11
 95    },
 96    {
 97      "q": 0.4,
 98      "predicted_long_run_slope": -1.2,
 99      "observed_late_log_slope": -1.2000000558102943,
100      "predicted_certificate_rate": 0.7999999999999999,
101      "max_log_envelope_margin": 0.0
102    },
103    {
104      "q": 0.8,
105      "predicted_long_run_slope": -1.2,
106      "observed_late_log_slope": -1.200000185887473,
107      "predicted_certificate_rate": 0.3999999999999999,
108      "max_log_envelope_margin": 0.0
109    },
110    {
111      "q": 1.1,
112      "predicted_long_run_slope": -1.2,
113      "observed_late_log_slope": -1.2000000001627347,
114      "predicted_certificate_rate": 0.09999999999999987,
115      "max_log_envelope_margin": 0.0
116    }
117  ],
118  "rollout_speed": {
119    "eps": 0.0625,
120    "fast_seconds_median": 0.7832107629947131,
121    "averaged_seconds_median": 0.05431261299236212,
122    "speedup": 14.420421332055128
123  }
124}