1{
 2  "variance_ac_checks": [
 3    {
 4      "a": 0.2,
 5      "predicted_variance": 1.0416666666666667,
 6      "observed_variance": 1.039359809225965,
 7      "predicted_rho": 0.2,
 8      "observed_rho": 0.19712120713555553,
 9      "variance_relative_error": 0.002214583143073625,
10      "rho_abs_error": 0.0028787928644444793
11    },
12    {
13      "a": 0.5,
14      "predicted_variance": 1.3333333333333333,
15      "observed_variance": 1.3364053126316229,
16      "predicted_rho": 0.5,
17      "observed_rho": 0.49345963553197963,
18      "variance_relative_error": 0.0023039844737172133,
19      "rho_abs_error": 0.006540364468020365
20    },
21    {
22      "a": 0.7,
23      "predicted_variance": 1.9607843137254901,
24      "observed_variance": 1.9088560442163003,
25      "predicted_rho": 0.7,
26      "observed_rho": 0.7000817449041847,
27      "variance_relative_error": 0.026483417449686814,
28      "rho_abs_error": 8.174490418477731e-05
29    },
30    {
31      "a": 0.85,
32      "predicted_variance": 3.6036036036036028,
33      "observed_variance": 3.6107102987430446,
34      "predicted_rho": 0.85,
35      "observed_rho": 0.8516771310782592,
36      "variance_relative_error": 0.001972107901195112,
37      "rho_abs_error": 0.0016771310782591753
38    },
39    {
40      "a": 0.93,
41      "predicted_variance": 7.401924500370103,
42      "observed_variance": 7.482899020887075,
43      "predicted_rho": 0.93,
44      "observed_rho": 0.9308581868230037,
45      "variance_relative_error": 0.010939657721842917,
46      "rho_abs_error": 0.0008581868230036482
47    }
48  ],
49  "boundary_check": {
50    "predicted_boundary": 1.0,
51    "observed_grid_boundary": 1.005,
52    "grid_step": 0.0050000000000000044
53  },
54  "intervention": {
55    "trials": 120,
56    "baseline_rms": 3.6238904138142156,
57    "monitor_rms": 3.6295660483237375,
58    "baseline_danger_rate": 0.9666666666666667,
59    "monitor_danger_rate": 0.9666666666666667,
60    "trigger_rate": 1.0,
61    "mean_warning_lead_steps": 75.76666666666667,
62    "median_warning_lead_steps": 85.5,
63    "settings": {
64      "window": 40,
65      "a_c": 0.9,
66      "gamma": 1.8
67    }
68  },
69  "pass_criteria": {
70    "max_variance_relative_error_lt_0.10": true,
71    "max_rho_abs_error_lt_0.02": true,
72    "boundary_within_grid_step": true
73  },
74  "interpretation": "The first two checks test stationary AR(1) formulas; the intervention is a small illustrative safety simulation, not a trained controller benchmark."
75}