1{
  2  "seed": 1120,
  3  "model": "h[t+1]=r R(omega) h[t]+sigma Normal(0,I), y=h[0]",
  4  "predictions": {
  5    "decay_time": "tau=-1/log(r); fitted resonance radius predicts correlation decay",
  6    "frequency": "PSD peak and fitted omega equal injected omega",
  7    "independence": "additive noise changes variance, not J-based Lambda or resonance"
  8  },
  9  "radius_sweep": [
 10    {
 11      "r": 0.7,
 12      "fitted_r": 0.7034267653385271,
 13      "tau_pred": 2.8036732520571284,
 14      "tau_fit": 2.842592775655428,
 15      "lyapunov": -0.35667494393873245,
 16      "rel_tau_error": 0.013881618897545741
 17    },
 18    {
 19      "r": 0.8,
 20      "fitted_r": 0.8000406392805042,
 21      "tau_pred": 4.481420117724551,
 22      "tau_fit": 4.482440528857972,
 23      "lyapunov": -0.22314355131420976,
 24      "rel_tau_error": 0.00022769816411214353
 25    },
 26    {
 27      "r": 0.9,
 28      "fitted_r": 0.8999502249921175,
 29      "tau_pred": 9.491221581029905,
 30      "tau_fit": 9.486241950194362,
 31      "lyapunov": -0.10536051565782632,
 32      "rel_tau_error": 0.000524656472618374
 33    },
 34    {
 35      "r": 0.95,
 36      "fitted_r": 0.9513785486439428,
 37      "tau_pred": 19.495725746223673,
 38      "tau_fit": 20.06290024762786,
 39      "lyapunov": -0.05129329438755065,
 40      "rel_tau_error": 0.029092248669637097
 41    },
 42    {
 43      "r": 0.98,
 44      "fitted_r": 0.9797565041189408,
 45      "tau_pred": 49.49831645250911,
 46      "tau_fit": 48.89687817730976,
 47      "lyapunov": -0.020202707317519462,
 48      "rel_tau_error": 0.012150681443406185
 49    }
 50  ],
 51  "frequency_sweep": [
 52    {
 53      "omega": 0.25,
 54      "fitted_omega": 0.24863147848964415,
 55      "psd_peak": 0.26030339129744,
 56      "predicted": 0.25,
 57      "peak_abs_error": 0.010303391297440012,
 58      "relative_error": 0.04121356518976005
 59    },
 60    {
 61      "omega": 0.42,
 62      "fitted_omega": 0.4185664231447004,
 63      "psd_peak": 0.4146902302738527,
 64      "predicted": 0.42,
 65      "peak_abs_error": 0.005309769726147273,
 66      "relative_error": 0.012642308871779223
 67    },
 68    {
 69      "omega": 0.7,
 70      "fitted_omega": 0.6997844235370086,
 71      "psd_peak": 0.7126927334143702,
 72      "predicted": 0.7,
 73      "peak_abs_error": 0.012692733414370272,
 74      "relative_error": 0.018132476306243248
 75    },
 76    {
 77      "omega": 1.0,
 78      "fitted_omega": 0.999159863137488,
 79      "psd_peak": 1.0035144533466827,
 80      "predicted": 1.0,
 81      "peak_abs_error": 0.0035144533466826555,
 82      "relative_error": 0.0035144533466826555
 83    }
 84  ],
 85  "noise_sweep": [
 86    {
 87      "sigma": 0.03,
 88      "fitted_r": 0.9314177422652783,
 89      "fitted_omega": 0.4193830018943419,
 90      "lyapunov": -0.07257069283483542,
 91      "variance": 0.006688245206206876
 92    },
 93    {
 94      "sigma": 0.12,
 95      "fitted_r": 0.9299692025798508,
 96      "fitted_omega": 0.4193736326910304,
 97      "lyapunov": -0.07257069283483542,
 98      "variance": 0.10755494007243742
 99    },
100    {
101      "sigma": 0.4,
102      "fitted_r": 0.9303895923523557,
103      "fitted_omega": 0.4222108423811429,
104      "lyapunov": -0.07257069283483542,
105      "variance": 1.1937186348619224
106    },
107    {
108      "sigma": 0.8,
109      "fitted_r": 0.9298517654805027,
110      "fitted_omega": 0.4196132638016788,
111      "lyapunov": -0.07257069283483542,
112      "variance": 4.7345430222524385
113    }
114  ],
115  "control": {
116    "uncontrolled": {
117      "fitted_r": 0.9752652124757705,
118      "fitted_omega": 0.4188032303923567,
119      "decay_time": 39.926802707809806,
120      "peak_frequency": 0.4194026192542374,
121      "peak_power": 25.511866235218225,
122      "long_lag_corr": 0.06225150327776391,
123      "lyapunov": -0.02531780798428996
124    },
125    "resonance_control": {
126      "fitted_r": 0.8996346421972676,
127      "fitted_omega": 0.4183753804168158,
128      "decay_time": 9.454784983703435,
129      "peak_frequency": 0.4194026192542374,
130      "peak_power": 1.7077026060796374,
131      "long_lag_corr": 0.004897474469038448,
132      "lyapunov": -0.10536051565782632
133    },
134    "target_radius": 0.9
135  },
136  "quantitative_checks": {
137    "decay_time_max_relative_error": 0.029092248669637097,
138    "decay_time_pass_under_5pct": true,
139    "frequency_max_relative_error": 0.04121356518976005,
140    "frequency_pass_under_10pct": true,
141    "noise_fitted_radius_span": 0.0015659767847755468,
142    "noise_fitted_frequency_span": 0.00283720969011253,
143    "noise_invariance_pass_under_0.01": true,
144    "baseline_peak_power": 25.511866235218225,
145    "idea_peak_power": 1.7077026060796374,
146    "peak_power_reduction_factor": 14.939291036034467,
147    "baseline_long_lag_abs_corr": 0.06225150327776391,
148    "idea_long_lag_abs_corr": 0.004897474469038448
149  }
150}