1{
  2  "seed": 2340,
  3  "predictions": {
  4    "P1_exact_decorrelation": "max |T^T R T-I| should remain at floating point precision for all c and Q=I",
  5    "P2_identity_fidelity": "min fidelity should equal [sqrt(1+(p-1)c)+(p-1)sqrt(1-c)]/p",
  6    "P3_threshold_transition": "identity anchor is feasible iff rho <= rho0(c), where rho0 is the P2 curve"
  7  },
  8  "decorrelation_sweep": [
  9    {
 10      "c": 0.0,
 11      "max_cov_error": 0.0,
 12      "fidelity_min": 1.0
 13    },
 14    {
 15      "c": 0.1,
 16      "max_cov_error": 6.661338147750939e-16,
 17      "fidelity_min": 0.994693560274026
 18    },
 19    {
 20      "c": 0.3,
 21      "max_cov_error": 1.2212453270876722e-15,
 22      "fidelity_min": 0.9607398271257608
 23    },
 24    {
 25      "c": 0.6,
 26      "max_cov_error": 7.771561172376096e-16,
 27      "fidelity_min": 0.8603796100280627
 28    },
 29    {
 30      "c": 0.9,
 31      "max_cov_error": 1.176836406102666e-14,
 32      "fidelity_min": 0.6543911183326493
 33    }
 34  ],
 35  "fidelity_sweep": [
 36    {
 37      "c": 0.0,
 38      "predicted": 1.0,
 39      "observed": 1.0,
 40      "abs_error": 0.0
 41    },
 42    {
 43      "c": 0.1,
 44      "predicted": 0.9946935602740264,
 45      "observed": 0.994693560274026,
 46      "abs_error": 4.440892098500626e-16
 47    },
 48    {
 49      "c": 0.3,
 50      "predicted": 0.9607398271257613,
 51      "observed": 0.9607398271257608,
 52      "abs_error": 5.551115123125783e-16
 53    },
 54    {
 55      "c": 0.6,
 56      "predicted": 0.8603796100280633,
 57      "observed": 0.8603796100280627,
 58      "abs_error": 5.551115123125783e-16
 59    },
 60    {
 61      "c": 0.9,
 62      "predicted": 0.6543911183326507,
 63      "observed": 0.6543911183326493,
 64      "abs_error": 1.4432899320127035e-15
 65    }
 66  ],
 67  "threshold_sweep": [
 68    {
 69      "c": 0.0,
 70      "rho": 0.98,
 71      "predicted_feasible": true,
 72      "observed_feasible": true,
 73      "rho0_predicted": 1.0,
 74      "min_fidelity": 1.0
 75    },
 76    {
 77      "c": 0.0,
 78      "rho": 1.02,
 79      "predicted_feasible": false,
 80      "observed_feasible": false,
 81      "rho0_predicted": 1.0,
 82      "min_fidelity": 1.0
 83    },
 84    {
 85      "c": 0.1,
 86      "rho": 0.9746935602740264,
 87      "predicted_feasible": true,
 88      "observed_feasible": true,
 89      "rho0_predicted": 0.9946935602740264,
 90      "min_fidelity": 0.994693560274026
 91    },
 92    {
 93      "c": 0.1,
 94      "rho": 1.0146935602740264,
 95      "predicted_feasible": false,
 96      "observed_feasible": false,
 97      "rho0_predicted": 0.9946935602740264,
 98      "min_fidelity": 0.994693560274026
 99    },
100    {
101      "c": 0.3,
102      "rho": 0.9407398271257613,
103      "predicted_feasible": true,
104      "observed_feasible": true,
105      "rho0_predicted": 0.9607398271257613,
106      "min_fidelity": 0.9607398271257608
107    },
108    {
109      "c": 0.3,
110      "rho": 0.9807398271257614,
111      "predicted_feasible": false,
112      "observed_feasible": false,
113      "rho0_predicted": 0.9607398271257613,
114      "min_fidelity": 0.9607398271257608
115    },
116    {
117      "c": 0.6,
118      "rho": 0.8403796100280633,
119      "predicted_feasible": true,
120      "observed_feasible": true,
121      "rho0_predicted": 0.8603796100280633,
122      "min_fidelity": 0.8603796100280627
123    },
124    {
125      "c": 0.6,
126      "rho": 0.8803796100280633,
127      "predicted_feasible": false,
128      "observed_feasible": false,
129      "rho0_predicted": 0.8603796100280633,
130      "min_fidelity": 0.8603796100280627
131    },
132    {
133      "c": 0.9,
134      "rho": 0.6343911183326507,
135      "predicted_feasible": true,
136      "observed_feasible": true,
137      "rho0_predicted": 0.6543911183326507,
138      "min_fidelity": 0.6543911183326493
139    },
140    {
141      "c": 0.9,
142      "rho": 0.6743911183326508,
143      "predicted_feasible": false,
144      "observed_feasible": false,
145      "rho0_predicted": 0.6543911183326507,
146      "min_fidelity": 0.6543911183326493
147    }
148  ],
149  "toy": {
150    "accuracy_bn_like": 0.8897142857142857,
151    "accuracy_zca_q_identity": 0.8897142857142857,
152    "bn_like_offdiag_fro": 3.314475478163808,
153    "zca_offdiag_fro": 1.89921721890737e-15,
154    "zca_max_cov_error": 1.0547118733938987e-15,
155    "zca_min_input_fidelity": 0.8523132299144632,
156    "rho_identity_prediction": 0.8603796100280633,
157    "n_train": 3250
158  }
159}