{
  "seed": 2040,
  "system": {
    "alpha": 1.2,
    "q": 0.8,
    "K": [
      [
        1.0,
        0.0
      ],
      [
        0.0,
        -1.0
      ]
    ],
    "B": [
      0.7,
      -0.35
    ]
  },
  "predictions": {
    "averaging_error_power": "O(eps), predicted log-log slope 1",
    "contraction_certificate": "max_s mu_2(A(s)) = -alpha+q; boundary q=alpha",
    "perturbation_decay": "late log-distance slope equals -alpha, and is bounded by -(alpha-q)"
  },
  "averaging_sweep": {
    "rows": [
      {
        "eps": 0.5,
        "max_error": 0.09088685716871418,
        "rms_error": 0.0353748782470963
      },
      {
        "eps": 0.25,
        "max_error": 0.05054718387201525,
        "rms_error": 0.017862900268138422
      },
      {
        "eps": 0.125,
        "max_error": 0.026779873868539184,
        "rms_error": 0.008967909220573956
      },
      {
        "eps": 0.0625,
        "max_error": 0.013767425349338452,
        "rms_error": 0.004492041843398243
      },
      {
        "eps": 0.03125,
        "max_error": 0.006994276731176045,
        "rms_error": 0.002247908668634097
      }
    ],
    "observed_loglog_slope": 0.9276021738593212
  },
  "contraction_boundary_sweep": [
    {
      "q": 0.0,
      "predicted_max_mu": -1.2,
      "observed_max_mu": -1.2,
      "certificate_holds": true
    },
    {
      "q": 0.6,
      "predicted_max_mu": -0.6,
      "observed_max_mu": -0.6,
      "certificate_holds": true
    },
    {
      "q": 1.19,
      "predicted_max_mu": -0.010000000000000009,
      "observed_max_mu": -0.010000000000000009,
      "certificate_holds": true
    },
    {
      "q": 1.2,
      "predicted_max_mu": 0.0,
      "observed_max_mu": 0.0,
      "certificate_holds": false
    },
    {
      "q": 1.4,
      "predicted_max_mu": 0.19999999999999996,
      "observed_max_mu": 0.19999999999999996,
      "certificate_holds": false
    }
  ],
  "perturbation_decay": [
    {
      "q": 0.0,
      "predicted_long_run_slope": -1.2,
      "observed_late_log_slope": -1.2000000000495423,
      "predicted_certificate_rate": 1.2,
      "max_log_envelope_margin": 7.479350472294755e-11
    },
    {
      "q": 0.4,
      "predicted_long_run_slope": -1.2,
      "observed_late_log_slope": -1.2000000558102943,
      "predicted_certificate_rate": 0.7999999999999999,
      "max_log_envelope_margin": 0.0
    },
    {
      "q": 0.8,
      "predicted_long_run_slope": -1.2,
      "observed_late_log_slope": -1.200000185887473,
      "predicted_certificate_rate": 0.3999999999999999,
      "max_log_envelope_margin": 0.0
    },
    {
      "q": 1.1,
      "predicted_long_run_slope": -1.2,
      "observed_late_log_slope": -1.2000000001627347,
      "predicted_certificate_rate": 0.09999999999999987,
      "max_log_envelope_margin": 0.0
    }
  ],
  "rollout_speed": {
    "eps": 0.0625,
    "fast_seconds_median": 0.7832107629947131,
    "averaged_seconds_median": 0.05431261299236212,
    "speedup": 14.420421332055128
  }
}