{
  "task_id": "F5-conf-03",
  "statement_true": false,
  "counterexample_provided": true,
  "counterexample_values": {
    "construction": "X ~ N(0,1); S ~ Rademacher (P(S=1)=P(S=-1)=1/2) independent of X; Y = S*X. Then Y ~ N(0,1) but X+Y = (1+S)X is 0 with prob. 1/2 and 2X otherwise (atom at 0, Var 2).",
    "n": 100000,
    "seed": 20261029,
    "mean_x": -0.0033187423835634258,
    "sd_x": 0.9982238690893596,
    "mean_y": -0.00024909222432809854,
    "sd_y": 0.9982293548745821,
    "mean_sum": -0.0035678346078915233,
    "sd_sum": 1.4058866469982523,
    "ks_sum_vs_normal": 0.2508475723268392
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  "statement_b_true": true,
  "feasibility": "complete",
  "feasibility_reason": null,
  "data_issues": [],
  "n_input_rows": {
    "propositions.csv": 2,
    "design.csv": 2
  },
  "n_analysed": 100000,
  "random_seed": 20261029,
  "supplementary_diagnostics": {
    "ks_x_vs_normal": 0.0020917798156042666,
    "ks_y_vs_normal": 0.0019518220846299617,
    "share_sum_exactly_zero": 0.50047,
    "ks_critical_value_5pct_approx": 0.0042943730625086595,
    "corr_xy": -0.008226889835527693
  },
  "baseline_b_indep_ks_sum_vs_normal": 0.0018749949107932373,
  "baseline_b_indep_sd_sum": 1.4152986579809257,
  "baseline_b_seed": 20261030
}