{
  "paper": "GJblFvJcMb",
  "claim": 5,
  "arxiv": "2504.19043",
  "source_scope": "Section 3.2 (average case) and Section 3.4 (adversarial case)",
  "design": {
    "K": [
      5,
      10,
      20
    ],
    "n": [
      500,
      1500,
      3500,
      10000
    ],
    "n_reps": 50,
    "coef": "N(0,1)",
    "interactions_scaled_to_main_R2": 0.7,
    "noise_var": 0.1,
    "binary_factors": true,
    "true_pi": "Proposition 1 closed-form"
  },
  "average_case": [
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      "K": 5,
      "sweep": [
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          "K": 5,
          "n": 500,
          "rmse_mean": 0.006461795519609526,
          "rmse_median": 0.006441473842272505,
          "bias2_median": 1.925756012859587e-07,
          "var_median": 4.0604308635783115e-05,
          "variance_dominates": true,
          "coverage_pi": 0.9480000000000001,
          "rmse_Q": 0.041286964330342096,
          "lam": 1.6711055759427953
        },
        {
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          "bias2_median": 4.397210394640941e-08,
          "var_median": 1.528652881425369e-05,
          "variance_dominates": true,
          "coverage_pi": 0.968,
          "rmse_Q": 0.02456763127249781,
          "lam": 1.6711055759427953
        },
        {
          "K": 5,
          "n": 3500,
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          "bias2_median": 6.485479860845058e-08,
          "var_median": 5.278543139260377e-06,
          "variance_dominates": true,
          "coverage_pi": 0.952,
          "rmse_Q": 0.01693910751191979,
          "lam": 1.6711055759427953
        },
        {
          "K": 5,
          "n": 10000,
          "rmse_mean": 0.00155414240696854,
          "rmse_median": 0.0015758935848253172,
          "bias2_median": 1.870114581873225e-08,
          "var_median": 2.3437304364133936e-06,
          "variance_dominates": true,
          "coverage_pi": 0.924,
          "rmse_Q": 0.010912603985334978,
          "lam": 1.6711055759427953
        }
      ],
      "rmse_decreases": true,
      "variance_dominates_at_maxn": true,
      "coverage_pi_at_maxn": 0.924
    },
    {
      "K": 10,
      "sweep": [
        {
          "K": 10,
          "n": 500,
          "rmse_mean": 0.007013917440829284,
          "rmse_median": 0.006713439826552316,
          "bias2_median": 1.245846044718415e-06,
          "var_median": 4.321492669620198e-05,
          "variance_dominates": true,
          "coverage_pi": 0.938,
          "rmse_Q": 0.05363010429052456,
          "lam": 1.8314563277706923
        },
        {
          "K": 10,
          "n": 1500,
          "rmse_mean": 0.003702385909396305,
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          "bias2_median": 2.1797935534346663e-07,
          "var_median": 1.3950627130498467e-05,
          "variance_dominates": true,
          "coverage_pi": 0.942,
          "rmse_Q": 0.026396623410346952,
          "lam": 1.8314563277706923
        },
        {
          "K": 10,
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          "bias2_median": 3.448669052052663e-08,
          "var_median": 5.359381818842434e-06,
          "variance_dominates": true,
          "coverage_pi": 0.958,
          "rmse_Q": 0.013969799106910681,
          "lam": 1.8314563277706923
        },
        {
          "K": 10,
          "n": 10000,
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          "bias2_median": 8.603114480100907e-08,
          "var_median": 1.745040906126524e-06,
          "variance_dominates": true,
          "coverage_pi": 0.954,
          "rmse_Q": 0.011576389545590102,
          "lam": 1.8314563277706923
        }
      ],
      "rmse_decreases": true,
      "variance_dominates_at_maxn": true,
      "coverage_pi_at_maxn": 0.954
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    {
      "K": 20,
      "sweep": [
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          "bias2_median": 9.107464676598005e-07,
          "var_median": 0.00014098233892214615,
          "variance_dominates": true,
          "coverage_pi": 0.9460000000000001,
          "rmse_Q": 0.21505665313075278,
          "lam": 2.0007786273454538
        },
        {
          "K": 20,
          "n": 1500,
          "rmse_mean": 0.005311505346276954,
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          "bias2_median": 3.770463942592464e-07,
          "var_median": 2.737060116436915e-05,
          "variance_dominates": true,
          "coverage_pi": 0.9440000000000002,
          "rmse_Q": 0.10284634701539644,
          "lam": 2.0007786273454538
        },
        {
          "K": 20,
          "n": 3500,
          "rmse_mean": 0.003423300986658493,
          "rmse_median": 0.003327497302306002,
          "bias2_median": 9.342114747453597e-08,
          "var_median": 1.0773183248827142e-05,
          "variance_dominates": true,
          "coverage_pi": 0.9480000000000002,
          "rmse_Q": 0.0700078953986648,
          "lam": 2.0007786273454538
        },
        {
          "K": 20,
          "n": 10000,
          "rmse_mean": 0.0019198522807017907,
          "rmse_median": 0.0019239108847675613,
          "bias2_median": 7.217569374034592e-09,
          "var_median": 3.699654089227817e-06,
          "variance_dominates": true,
          "coverage_pi": 0.9530000000000001,
          "rmse_Q": 0.03621903868478622,
          "lam": 2.0007786273454538
        }
      ],
      "rmse_decreases": true,
      "variance_dominates_at_maxn": true,
      "coverage_pi_at_maxn": 0.9530000000000001
    }
  ],
  "adversarial": {
    "sweep": [
      {
        "n": 1000,
        "p_R": 0.5,
        "value_true": 0.4776537203230401,
        "value_hat_mean": 0.4701726775365815,
        "coverage_value": 1.0,
        "coverage_strategy": null,
        "piA_true_support": 2
      },
      {
        "n": 5000,
        "p_R": 0.5,
        "value_true": 0.536778094188713,
        "value_hat_mean": 0.5345057696807607,
        "coverage_value": 0.96,
        "coverage_strategy": null,
        "piA_true_support": 2
      },
      {
        "n": 10000,
        "p_R": 0.5,
        "value_true": 0.5659109787090211,
        "value_hat_mean": 0.5653511755528775,
        "coverage_value": 0.98,
        "coverage_strategy": null,
        "piA_true_support": 3
      }
    ],
    "coverage_pattern_n5000_approaches_nominal": true,
    "note": "single gender factor, two-party zero-sum game (paper's tractability choice)"
  },
  "claim5_passed": true
}