{
  "task_id": "F5-conf-03",
  "statement_true": false,
  "counterexample_provided": true,
  "counterexample_values": {
    "construction": "X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. Then Y ~ N(0,1) by symmetry of N(0,1), and X+Y = (1+S)X equals 0 with probability 1/2 and 2X ~ N(0,4) otherwise (non-degenerate, not normal).",
    "n": 100000,
    "seed": 20261029,
    "mean_x": -0.0033187423835634253,
    "sd_x": 0.9982238690893596,
    "mean_y": -0.0002490922243280974,
    "sd_y": 0.9982293548745821,
    "mean_sum": -0.003567834607891523,
    "sd_sum": 1.4058866469982523,
    "ks_sum_vs_normal": 0.2508475723268392
  },
  "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,
  "ks_x_vs_normal": 0.0020917798156042666,
  "ks_y_vs_normal": 0.0019518220846299617,
  "frac_sum_exactly_zero": 0.50047,
  "ks_critical_value_alpha_0_01": 0.00514818803075412,
  "baseline_ks_sum_independent": 0.0017646088927930625
}