{
  "variance_ac_checks": [
    {
      "a": 0.2,
      "predicted_variance": 1.0416666666666667,
      "observed_variance": 1.039359809225965,
      "predicted_rho": 0.2,
      "observed_rho": 0.19712120713555553,
      "variance_relative_error": 0.002214583143073625,
      "rho_abs_error": 0.0028787928644444793
    },
    {
      "a": 0.5,
      "predicted_variance": 1.3333333333333333,
      "observed_variance": 1.3364053126316229,
      "predicted_rho": 0.5,
      "observed_rho": 0.49345963553197963,
      "variance_relative_error": 0.0023039844737172133,
      "rho_abs_error": 0.006540364468020365
    },
    {
      "a": 0.7,
      "predicted_variance": 1.9607843137254901,
      "observed_variance": 1.9088560442163003,
      "predicted_rho": 0.7,
      "observed_rho": 0.7000817449041847,
      "variance_relative_error": 0.026483417449686814,
      "rho_abs_error": 8.174490418477731e-05
    },
    {
      "a": 0.85,
      "predicted_variance": 3.6036036036036028,
      "observed_variance": 3.6107102987430446,
      "predicted_rho": 0.85,
      "observed_rho": 0.8516771310782592,
      "variance_relative_error": 0.001972107901195112,
      "rho_abs_error": 0.0016771310782591753
    },
    {
      "a": 0.93,
      "predicted_variance": 7.401924500370103,
      "observed_variance": 7.482899020887075,
      "predicted_rho": 0.93,
      "observed_rho": 0.9308581868230037,
      "variance_relative_error": 0.010939657721842917,
      "rho_abs_error": 0.0008581868230036482
    }
  ],
  "boundary_check": {
    "predicted_boundary": 1.0,
    "observed_grid_boundary": 1.005,
    "grid_step": 0.0050000000000000044
  },
  "intervention": {
    "trials": 120,
    "baseline_rms": 3.6238904138142156,
    "monitor_rms": 3.6295660483237375,
    "baseline_danger_rate": 0.9666666666666667,
    "monitor_danger_rate": 0.9666666666666667,
    "trigger_rate": 1.0,
    "mean_warning_lead_steps": 75.76666666666667,
    "median_warning_lead_steps": 85.5,
    "settings": {
      "window": 40,
      "a_c": 0.9,
      "gamma": 1.8
    }
  },
  "pass_criteria": {
    "max_variance_relative_error_lt_0.10": true,
    "max_rho_abs_error_lt_0.02": true,
    "boundary_within_grid_step": true
  },
  "interpretation": "The first two checks test stationary AR(1) formulas; the intervention is a small illustrative safety simulation, not a trained controller benchmark."
}