1{
 2  "seed": 1524,
 3  "n_states": 12000,
 4  "base_failure_rate": 0.46058333333333334,
 5  "critic": {
 6    "bce": 0.3512498187459485,
 7    "mean_prediction": 0.4608653265895653,
 8    "mean_label": 0.46058333333333334
 9  },
10  "predictions": {
11    "enrichment": "rho_fail=E_q[y]/E_p[y]",
12    "ess": "ESS/B approaches 1/E_q[w^2]",
13    "gradient_identity": "E_q[w g]=E_p[g]"
14  },
15  "verification": [
16    {
17      "alpha": 0.0,
18      "predicted_enrichment": 0.9999999999999994,
19      "observed_enrichment": 1.00020354622761,
20      "predicted_ess_fraction": 0.9999999999999987,
21      "weighted_gradient_cosine": 0.9773100556001814,
22      "unweighted_gradient_cosine": 0.9773100556001814,
23      "weighted_gradient_l2_error": 1.5865122319069402,
24      "exact_identity_l2_error": 2.2216270818478592e-14
25    },
26    {
27      "alpha": 0.5,
28      "predicted_enrichment": 1.399414505771332,
29      "observed_enrichment": 1.4018681020445087,
30      "predicted_ess_fraction": 0.6955684305462502,
31      "weighted_gradient_cosine": 0.966974955423025,
32      "unweighted_gradient_cosine": 0.9592871973865706,
33      "weighted_gradient_l2_error": 1.7740178957343766,
34      "exact_identity_l2_error": 2.2023380273754356e-14
35    },
36    {
37      "alpha": 1.0,
38      "predicted_enrichment": 1.634298288820409,
39      "observed_enrichment": 1.6397344852542066,
40      "predicted_ess_fraction": 0.26766598629989596,
41      "weighted_gradient_cosine": 0.9166753899563264,
42      "unweighted_gradient_cosine": 0.9413258850208939,
43      "weighted_gradient_l2_error": 2.769184041820306,
44      "exact_identity_l2_error": 2.2727613731326205e-14
45    },
46    {
47      "alpha": 2.0,
48      "predicted_enrichment": 1.8312356246940125,
49      "observed_enrichment": 1.8383051384114346,
50      "predicted_ess_fraction": 0.017082705451833817,
51      "weighted_gradient_cosine": 0.8670712367326305,
52      "unweighted_gradient_cosine": 0.932892435467256,
53      "weighted_gradient_l2_error": 5.776019217121439,
54      "exact_identity_l2_error": 2.243090158935384e-14
55    },
56    {
57      "alpha": 4.0,
58      "predicted_enrichment": 1.945734722609935,
59      "observed_enrichment": 1.9507078885471318,
60      "predicted_ess_fraction": 2.8695367384982844e-05,
61      "weighted_gradient_cosine": 0.9218421287687226,
62      "unweighted_gradient_cosine": 0.9279067839672815,
63      "weighted_gradient_l2_error": 5.828636433710799,
64      "exact_identity_l2_error": 2.2262688202020137e-14
65    }
66  ],
67  "training": [
68    {
69      "alpha": 0.5,
70      "uniform_mse": 0.1651713471398834,
71      "weighted_mse": 0.16512279290884183,
72      "unweighted_mse": 0.19735122093968538
73    },
74    {
75      "alpha": 1.0,
76      "uniform_mse": 0.1651713471398834,
77      "weighted_mse": 0.16516038832137736,
78      "unweighted_mse": 0.29406721443241945
79    },
80    {
81      "alpha": 2.0,
82      "uniform_mse": 0.1651713471398834,
83      "weighted_mse": 0.18004326633012838,
84      "unweighted_mse": 0.38504488832931943
85    }
86  ],
87  "notes": "Predictions are finite-population exact; observed values are Monte Carlo.",
88  "importance_identity_check": {
89    "max_exact_l2_error": 2.2727613731326205e-14,
90    "criterion": "exact error should be numerical roundoff; finite-batch cosine degrades as ESS falls"
91  }
92}