{
  "system": {
    "A": [
      [
        0.0,
        1.0
      ],
      [
        -1.0,
        -0.35
      ]
    ],
    "B": [
      [
        0.0
      ],
      [
        1.0
      ]
    ],
    "P": [
      [
        1.0893608743737986,
        0.33496360441970086
      ],
      [
        0.33496360441970086,
        0.6780191526917446
      ]
    ],
    "rho": 0.2
  },
  "predictions": {
    "generator": {
      "claim": "finite-difference generator error is O(dt)",
      "parameter": [
        0.2,
        0.1,
        0.05,
        0.025,
        0.0125
      ],
      "observed_error": [
        0.11854838586322324,
        0.0597972616384505,
        0.030012323197751888,
        0.015032504837023727,
        0.007522581499392927
      ],
      "observed_loglog_slope": 0.9948202751188921,
      "predicted_slope": 1.0
    },
    "identification": {
      "claim": "fixed-noise regression error is approximately O(N^-1/2)",
      "parameter": [
        32,
        64,
        128,
        256,
        512,
        1024
      ],
      "observed_error": [
        0.007069385942795279,
        0.004098720988256112,
        0.0031383961531861702,
        0.0023080018336099186,
        0.0016216067170625487,
        0.0009790730912664096
      ],
      "observed_loglog_slope": -0.5347747062917038,
      "predicted_slope": -0.5
    },
    "lifted_generator": {
      "claim": "EDMD lifted generator predicts observable derivatives",
      "dictionary_dim": 6,
      "holdout_rms_derivative_error": 0.5133639534165326
    },
    "hjb_sensitivity": {
      "claim": "zero at exact dynamics and first-order in multiplicative G error",
      "parameter": [
        0.0,
        0.01,
        0.02,
        0.05,
        0.1,
        0.2
      ],
      "observed_rms_residual": [
        9.096312563282697e-16,
        0.01132200581171509,
        0.022756668397676868,
        0.05773659680103777,
        0.11828961295822452,
        0.24784490334104237
      ],
      "zero_error_residual": 9.096312563282697e-16,
      "observed_loglog_slope": 1.0285208392996161,
      "predicted_slope": 1.0
    }
  },
  "comparison": {
    "metric": "RMS value error against discounted CARE solution after 220 updates",
    "hjb": 0.20341287553310394,
    "td_baseline": 3.0930304527282715,
    "device": "cuda"
  }
}