1{
 2  "seed": 3140,
 3  "alpha_exact_threshold": 0.73,
 4  "representation_checks": {
 5    "h": {
 6      "D_at_rho_1": 0.73,
 7      "raw_mean_r": 1.4600000000000004
 8    },
 9    "2h": {
10      "D_at_rho_1": 0.73,
11      "raw_mean_r": 2.920000000000001
12    },
13    "h+h^3": {
14      "D_at_rho_1": 0.73,
15      "raw_mean_r": 1.4600000000000004
16    },
17    "log(1+h)": {
18      "D_at_rho_1": 0.73,
19      "raw_mean_r": 1.4600000000000004
20    },
21    "h^3 (invalid)": {
22      "D_at_rho_1": Infinity,
23      "raw_mean_r": 1.9589033626083181e-32
24    }
25  },
26  "transition": [
27    {
28      "rho": 0.5,
29      "D": 1.46,
30      "min_boundary_derivative": -0.45999999999999996,
31      "feasible_sampled": false
32    },
33    {
34      "rho": 0.65,
35      "D": 1.123076923076923,
36      "min_boundary_derivative": -0.15999999999999992,
37      "feasible_sampled": false
38    },
39    {
40      "rho": 0.72,
41      "D": 1.0138888888888888,
42      "min_boundary_derivative": -0.020000000000000018,
43      "feasible_sampled": false
44    },
45    {
46      "rho": 0.73,
47      "D": 1.0,
48      "min_boundary_derivative": 0.0,
49      "feasible_sampled": true
50    },
51    {
52      "rho": 0.74,
53      "D": 0.9864864864864865,
54      "min_boundary_derivative": 0.020000000000000018,
55      "feasible_sampled": true
56    },
57    {
58      "rho": 0.85,
59      "D": 0.8588235294117647,
60      "min_boundary_derivative": 0.24,
61      "feasible_sampled": true
62    },
63    {
64      "rho": 1.0,
65      "D": 0.73,
66      "min_boundary_derivative": 0.54,
67      "feasible_sampled": true
68    }
69  ],
70  "softsup_tau_0.02_rho_1": 0.6647435462271849,
71  "max_boundary_gradient_finite_difference_error": 1.3789791530882667e-10,
72  "valid_invariance_relative_spread": 0.0,
73  "invalid_h3_D": Infinity,
74  "notes": "For h^3, q_prime(0)=0, so the defining-function regularity assumption fails and the boundary gradient vanishes."
75}