1{
 2  "seed": 7,
 3  "math_checks": {
 4    "regular_direction_loglog_slope": 1.0398056110840164,
 5    "predicted_regular_slope": 1.0,
 6    "gate_noise_levels": [
 7      0.01,
 8      0.05,
 9      0.15,
10      0.4
11    ],
12    "gate_regular_fraction": [
13      0.99,
14      0.99,
15      0.83,
16      0.33
17    ],
18    "predicted_gate_trend": "decreases as noise increases",
19    "degenerate_direction_loglog_slope": 1.0250923357969701,
20    "predicted_worst_case_exponent": 0.5,
21    "regular_reduced_eigenvalue": 0.7668787351931636,
22    "degenerate_reduced_eigenvalue": 4.76140256803781e-17,
23    "degenerate_curvature_prediction": "near-zero curvature => fallback",
24    "degenerate_curvature_observed": "near-zero curvature; sensitivity exponent was not sublinear"
25  },
26  "benchmark": {
27    "uniform": {
28      "mean_final": 1.7779841292916871,
29      "worst_final": 2.2408481851173567,
30      "mean_best": 1.7777783663810858,
31      "worst_best": 2.1768515944260045,
32      "direction_change": 0.18334240479769104,
33      "regular_fraction": 0.0
34    },
35    "uniform_std": {
36      "mean_final": 0.00018887023577259483,
37      "worst_final": 0.012357649210901631,
38      "mean_best": 3.7315061445819435e-07,
39      "worst_best": 0.009978898098043478,
40      "direction_change": 0.002611286469693151,
41      "regular_fraction": 0.0
42    },
43    "mgda": {
44      "mean_final": 1.976632096531923,
45      "worst_final": 2.8746929694462926,
46      "mean_best": 1.976632096531923,
47      "worst_best": 2.8667433880631337,
48      "direction_change": 0.05377375622257376,
49      "regular_fraction": 0.0
50    },
51    "mgda_std": {
52      "mean_final": 0.005361086825994062,
53      "worst_final": 0.01141293331311631,
54      "mean_best": 0.005361086825994062,
55      "worst_best": 0.01222652270339705,
56      "direction_change": 0.0027866200628133657,
57      "regular_fraction": 0.0
58    },
59    "gated": {
60      "mean_final": 1.7779841491037414,
61      "worst_final": 2.24084841716066,
62      "mean_best": 1.7777781630278373,
63      "worst_best": 2.199101719607222,
64      "direction_change": 0.1872844354629059,
65      "regular_fraction": 0.11933333333333333
66    },
67    "gated_std": {
68      "mean_final": 0.00018892297863517453,
69      "worst_final": 0.012356767325243824,
70      "mean_best": 2.3382598744402486e-07,
71      "worst_best": 0.0042639550623940715,
72      "direction_change": 0.0009570646841997197,
73      "regular_fraction": 0.011813363431112897
74    }
75  }
76}