{
  "seed": 5,
  "replicas": 256,
  "tau_mix": 1.0,
  "input_sd": 0.05,
  "dt": 0.05,
  "observed_time_per_replica": 1500.0,
  "lags": [
    5.0,
    15.0
  ],
  "scalar_gauge": {
    "0.02": {
      "rate_scale": 0.02,
      "epsilon": 0.033870573230894874,
      "true_rates": [
        0.006390013832782487,
        0.033870573230894874
      ],
      "fluctuation_rates": [
        0.006733628965463172,
        0.03294006744671255
      ],
      "fluctuation_rates_se": [
        0.000428020875010798,
        0.0009726694802056711
      ],
      "fluctuation_rates_with_observation_noise": [
        0.007464862267171136,
        0.03301052852615403
      ],
      "fluctuation_rates_with_observation_noise_se": [
        0.0016165303022867435,
        0.0016682672664118307
      ],
      "recovery_rates": [
        0.006288655167558858,
        0.03358974282563946
      ],
      "mean_offset_from_averaged_equilibrium": 0.0005693457482220943,
      "stationary_mean": [
        -1.2039728354340682,
        -1.6093370690277153,
        -0.9162907609156156
      ],
      "cov_trace": 0.00037587617588499887,
      "cov_trace_se": 2.9985108230650095e-06,
      "predicted_cov_trace": 0.0003790816724872826,
      "relative_cov_error": 0.008431572707285841,
      "conserved_spread": 8.542814097648173e-15
    },
    "0.04": {
      "rate_scale": 0.04,
      "epsilon": 0.06774114645436974,
      "true_rates": [
        0.012780027667156859,
        0.06774114645436974
      ],
      "fluctuation_rates": [
        0.01248132349434662,
        0.06739329521815023
      ],
      "fluctuation_rates_se": [
        0.0006729655133359665,
        0.0024466009046473025
      ],
      "fluctuation_rates_with_observation_noise": [
        0.012147276689117548,
        0.06843478826836293
      ],
      "fluctuation_rates_with_observation_noise_se": [
        0.001108186746579271,
        0.0030873251838190066
      ],
      "recovery_rates": [
        0.012569913435458442,
        0.0672246561408945
      ],
      "mean_offset_from_averaged_equilibrium": 0.000350224307405389,
      "stationary_mean": [
        -1.2039728354058128,
        -1.6093370690710938,
        -0.9162907609458203
      ],
      "cov_trace": 0.0007417230004421213,
      "cov_trace_se": 6.999290140570901e-06,
      "predicted_cov_trace": 0.0007374786977074239,
      "relative_cov_error": 0.009354507367189171,
      "conserved_spread": 7.4039079035572e-15
    },
    "0.08": {
      "rate_scale": 0.08,
      "epsilon": 0.1354822929205515,
      "true_rates": [
        0.025560055337517564,
        0.1354822929205515
      ],
      "fluctuation_rates": [
        0.026142710619858334,
        0.13120441377169775
      ],
      "fluctuation_rates_se": [
        0.0009401724830131528,
        0.005522040457762956
      ],
      "fluctuation_rates_with_observation_noise": [
        0.026538066441775955,
        0.1270264466659522
      ],
      "fluctuation_rates_with_observation_noise_se": [
        0.0017462176713264835,
        0.008678885809183171
      ],
      "recovery_rates": [
        0.025144954306612535,
        0.1346727070136496
      ],
      "mean_offset_from_averaged_equilibrium": 0.00010667408022635438,
      "stationary_mean": [
        -1.2039728354042498,
        -1.6093370690734932,
        -0.9162907609474911
      ],
      "cov_trace": 0.001389808918828427,
      "cov_trace_se": 1.0437670603274375e-05,
      "predicted_cov_trace": 0.0013992691505811553,
      "relative_cov_error": 0.0072300127836848705,
      "conserved_spread": 7.202374166773245e-15
    }
  },
  "general_gauge": {
    "C": [
      [
        1.0,
        0.8
      ],
      [
        -0.3,
        0.6
      ]
    ],
    "mean_difference": 1.7169154986618196e-11,
    "cov_G": [
      [
        0.0005273842491799112,
        -0.0002799592077642153
      ],
      [
        -0.0002799592077642153,
        0.0002096086015717605
      ]
    ],
    "cov_GC": [
      [
        0.0002995038918652379,
        -0.00032189547749859773
      ],
      [
        -0.00032189547749859773,
        0.0003591743289211725
      ]
    ],
    "max_cov_difference_in_se": 54.90190075830718,
    "predicted_cov_G": [
      [
        0.0005245411534421688,
        -0.00028093427033888576
      ],
      [
        -0.0002809342703388857,
        0.0002129375442652551
      ]
    ],
    "predicted_cov_GC": [
      [
        0.0002981561170359362,
        -0.00031915169857221775
      ],
      [
        -0.00031915169857221775,
        0.0003544296253518796
      ]
    ]
  },
  "hidden_state_control": {
    "cascade_time": 78.24709195034688,
    "lag_pairs": [
      [
        2.0,
        6.0
      ],
      [
        5.0,
        15.0
      ],
      [
        10.0,
        30.0
      ]
    ],
    "true_rates": [
      0.012780027667156859,
      0.06774114645436974
    ],
    "direct_estimates": [
      [
        0.013991944258928229,
        0.0635869978307591
      ],
      [
        0.013174714736772388,
        0.0688862900684555
      ],
      [
        0.013018869685285104,
        0.0702698068497268
      ]
    ],
    "direct_lag_dependence": 0.059099922843249636,
    "cascade_estimates": [
      [
        0.001721348496870586,
        0.001721348496870586
      ],
      [
        0.004246501845788229,
        0.004246501845788229
      ],
      [
        0.008562494050163518,
        0.008562494050163518
      ]
    ],
    "cascade_lag_dependence": 0.767850881991455
  },
  "gates": {
    "regulation slow relative to activity (epsilon < 0.15 at every rate)": true,
    "stationary mean independent of rate (< 0.1 of spread)": true,
    "spread grows with rate: 4x rate gives > 3x variance": true,
    "variance ratio matches linear theory (within 4 SE)": true,
    "stationary covariance matches Lyapunov prediction (< 10%)": true,
    "conserved quantities do not fluctuate": true,
    "fluctuation rates match true rates (< 10%)": true,
    "fluctuation rates within 3 SE of true rates": true,
    "recovery rates match true rates (< 3%)": true,
    "Onsager: fluctuation and recovery rates agree (< 10%)": true,
    "observation noise as large as the fluctuations: rates within 3 SE of true": true,
    "non-scalar C: equal means": true,
    "non-scalar C: covariances differ (> 5 SE)": true,
    "direct observation: estimate independent of lag (< 10%)": true,
    "hidden cascade: estimate depends on lag (> 2x the direct dependence)": true
  }
}