1{
  2  "seed": 2716,
  3  "depths": [
  4    32,
  5    64,
  6    128,
  7    256,
  8    512,
  9    1024,
 10    2048,
 11    4096,
 12    8192,
 13    16384,
 14    32768
 15  ],
 16  "formula_sweeps": [
 17    {
 18      "gamma": 0.3,
 19      "s1_slope_observed": 0.7055120547793522,
 20      "s1_slope_predicted": 0.7,
 21      "s2_slope_observed": 0.4259993229498566,
 22      "s2_slope_predicted": 0.4,
 23      "s1_at_final": 2067.9099490388685,
 24      "s2_at_final": 158.0483151112958,
 25      "s1_tail_slope_observed": 0.7008663230515949,
 26      "s2_tail_slope_observed": 0.40906193432470234,
 27      "s2_normalized_final": 2.4695049236139965,
 28      "gaussian_q2_empirical_L128": 21493.061717758712,
 29      "gaussian_q2_exact_L128": 21558.605545692786,
 30      "gaussian_excess_per_2L": 19.213302912862446
 31    },
 32    {
 33      "gamma": 0.5,
 34      "s1_slope_observed": 0.5160477810910512,
 35      "s1_slope_predicted": 0.5,
 36      "s2_slope_observed": 0.14037684743002116,
 37      "s2_slope_predicted": 0.0,
 38      "s1_at_final": 360.58107958754226,
 39      "s2_at_final": 10.974438632012166,
 40      "s1_tail_slope_observed": 0.504317063981964,
 41      "s2_tail_slope_observed": 0.10491115550690087,
 42      "s2_normalized_final": null,
 43      "gaussian_q2_empirical_L128": 18297.134124307093,
 44      "gaussian_q2_exact_L128": 18419.503899776013,
 45      "gaussian_excess_per_2L": 6.951187108500051
 46    },
 47    {
 48      "gamma": 0.75,
 49      "s1_slope_observed": 0.30145542420151533,
 50      "s1_slope_predicted": 0.25,
 51      "s2_slope_observed": 0.017733224648378922,
 52      "s2_slope_predicted": 0.0,
 53      "s1_at_final": 50.37629048548575,
 54      "s2_at_final": 2.6013268895225026,
 55      "s1_tail_slope_observed": 0.27539738774215705,
 56      "s2_tail_slope_observed": 0.004570156281511213,
 57      "s2_normalized_final": null,
 58      "gaussian_q2_empirical_L128": 17273.024169617125,
 59      "gaussian_q2_exact_L128": 17300.10180338721,
 60      "gaussian_excess_per_2L": 2.5785226694812877
 61    },
 62    {
 63      "gamma": 1.0,
 64      "s1_slope_observed": 0.1403768474300212,
 65      "s1_slope_predicted": 0.0,
 66      "s2_slope_observed": 0.001985491711703831,
 67      "s2_slope_predicted": 0.0,
 68      "s1_at_final": 10.974438632012166,
 69      "s2_at_final": 1.6449035497357587,
 70      "s1_tail_slope_observed": 0.10491115550690087,
 71      "s2_tail_slope_observed": 9.634683849950251e-05,
 72      "s2_normalized_final": null,
 73      "gaussian_q2_empirical_L128": 16891.13941232137,
 74      "gaussian_q2_exact_L128": 16951.037846186147,
 75      "gaussian_excess_per_2L": 1.2149915866646381
 76    },
 77    {
 78      "gamma": 1.25,
 79      "s1_slope_observed": 0.052641441487315116,
 80      "s1_slope_predicted": 0.0,
 81      "s2_slope_observed": 0.00024345211321796616,
 82      "s2_slope_predicted": 0.0,
 83      "s1_at_final": 4.297811181201336,
 84      "s2_at_final": 1.341487144861894,
 85      "s1_tail_slope_observed": 0.02574985464263504,
 86      "s2_tail_slope_observed": 1.761675772098138e-06,
 87      "s2_normalized_final": null,
 88      "gaussian_q2_empirical_L128": 16934.23825275766,
 89      "gaussian_q2_exact_L128": 16810.227495399868,
 90      "gaussian_excess_per_2L": 0.6649511539057329
 91    }
 92  ],
 93  "critical_log_checks": [
 94    {
 95      "gamma": 0.5,
 96      "quantity": "S2",
 97      "log_fit_slope": 0.14037684743002116,
 98      "endpoints": [
 99        4.05849519543652,
100        10.974438632012166
101      ],
102      "log_ratio_start": 1.1710341783855904,
103      "log_ratio_end": 1.055517879396281
104    },
105    {
106      "gamma": 1.0,
107      "quantity": "S1",
108      "log_fit_slope": 0.1403768474300212,
109      "endpoints": [
110        4.05849519543652,
111        10.974438632012166
112      ],
113      "log_ratio_start": 1.1710341783855904,
114      "log_ratio_end": 1.055517879396281
115    }
116  ],
117  "network_jacobian_sanity": [
118    {
119      "depth": 16,
120      "iid": {
121        "median_sv": 0.9992318380178953,
122        "max_sv": 1.3548490695423971,
123        "normalized_gradient_fourth": 1.0062354085612784
124      },
125      "powerlaw_gamma_0.3": {
126        "median_sv": 1.0124693364158148,
127        "max_sv": 2.5138964582934546,
128        "normalized_gradient_fourth": 1.0827352203586673
129      }
130    },
131    {
132      "depth": 32,
133      "iid": {
134        "median_sv": 0.9982063276567298,
135        "max_sv": 1.3644839170724725,
136        "normalized_gradient_fourth": 1.0070338422749523
137      },
138      "powerlaw_gamma_0.3": {
139        "median_sv": 0.9877556861745743,
140        "max_sv": 2.888992305970983,
141        "normalized_gradient_fourth": 1.1146772071572455
142      }
143    },
144    {
145      "depth": 64,
146      "iid": {
147        "median_sv": 0.9949002849902472,
148        "max_sv": 1.3586440681930814,
149        "normalized_gradient_fourth": 1.007257281950197
150      },
151      "powerlaw_gamma_0.3": {
152        "median_sv": 0.9839729015509657,
153        "max_sv": 3.967246737588677,
154        "normalized_gradient_fourth": 1.1691086453482293
155      }
156    },
157    {
158      "depth": 128,
159      "iid": {
160        "median_sv": 0.9938653952485531,
161        "max_sv": 1.3566726344044833,
162        "normalized_gradient_fourth": 1.007058792334494
163      },
164      "powerlaw_gamma_0.3": {
165        "median_sv": 1.0114593042006408,
166        "max_sv": 5.327694756783201,
167        "normalized_gradient_fourth": 1.2286738627508607
168      }
169    }
170  ],
171  "notes": "S1=sum_{t=1}^L t^(-gamma), S2=sum c_t^2. Slopes use finite-depth log-log regression. Gaussian check uses exact Wick formula."
172}