{
  "status": "PASS",
  "paths": 20000,
  "seed": 71037,
  "steps": 120,
  "moment_checks": 12,
  "gamma": 1.55,
  "old_asymptotic_mse": 0.006944444444444445,
  "new_asymptotic_mse": 0.004480286738351254,
  "checks": [
    {
      "step": 1,
      "design": "old",
      "exact_expected_mse": 0.5721,
      "empirical_mse": 0.5721257409409016,
      "monte_carlo_standard_error": 0.00037798751810606335,
      "z_discrepancy": 0.06809997597421268
    },
    {
      "step": 1,
      "design": "reinvested",
      "exact_expected_mse": 0.5712129032258065,
      "empirical_mse": 0.571231817185749,
      "monte_carlo_standard_error": 0.0003034889446257537,
      "z_discrepancy": 0.06232174277646858
    },
    {
      "step": 5,
      "design": "old",
      "exact_expected_mse": 0.10176181273600006,
      "empirical_mse": 0.10143675318173787,
      "monte_carlo_standard_error": 0.00024672748106688573,
      "z_discrepancy": 1.317484184804178
    },
    {
      "step": 5,
      "design": "reinvested",
      "exact_expected_mse": 0.09956224194890329,
      "empirical_mse": 0.09929757216988219,
      "monte_carlo_standard_error": 0.00019717284397655476,
      "z_discrepancy": 1.342323687599515
    },
    {
      "step": 10,
      "design": "old",
      "exact_expected_mse": 0.01712538184206992,
      "empirical_mse": 0.016946170911971488,
      "monte_carlo_standard_error": 9.570400476801216e-05,
      "z_discrepancy": 1.8725541374453576
    },
    {
      "step": 10,
      "design": "reinvested",
      "exact_expected_mse": 0.014689633940077704,
      "empirical_mse": 0.014553717283727244,
      "monte_carlo_standard_error": 7.353019806698887e-05,
      "z_discrepancy": 1.8484467596107186
    },
    {
      "step": 30,
      "design": "old",
      "exact_expected_mse": 0.00694579772314567,
      "empirical_mse": 0.0069583089362296475,
      "monte_carlo_standard_error": 4.965822518626531e-05,
      "z_discrepancy": 0.2519464406359357
    },
    {
      "step": 30,
      "design": "reinvested",
      "exact_expected_mse": 0.004481643793363177,
      "empirical_mse": 0.004489616274519852,
      "monte_carlo_standard_error": 3.203944510465887e-05,
      "z_discrepancy": 0.24883330939823836
    },
    {
      "step": 60,
      "design": "old",
      "exact_expected_mse": 0.006944444446518338,
      "empirical_mse": 0.006883983107604973,
      "monte_carlo_standard_error": 4.8744287257956794e-05,
      "z_discrepancy": 1.2403779461047577
    },
    {
      "step": 60,
      "design": "reinvested",
      "exact_expected_mse": 0.004480286740430935,
      "empirical_mse": 0.004441278898381988,
      "monte_carlo_standard_error": 3.144792166061923e-05,
      "z_discrepancy": 1.2403949128948446
    },
    {
      "step": 120,
      "design": "old",
      "exact_expected_mse": 0.006944444444444445,
      "empirical_mse": 0.006981443884194567,
      "monte_carlo_standard_error": 4.943752816817516e-05,
      "z_discrepancy": 0.7484079629600076
    },
    {
      "step": 120,
      "design": "reinvested",
      "exact_expected_mse": 0.004480286738351254,
      "empirical_mse": 0.004504157344641827,
      "monte_carlo_standard_error": 3.1895179463343226e-05,
      "z_discrepancy": 0.7484079629652859
    }
  ],
  "scope": "Linear Gaussian modal coefficient SGD; no neural benchmark or hardware"
}