{
  "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) by symmetry, but X+Y = (1+S)X equals 0 with probability 1/2 and 2X otherwise (Var = 2), so X+Y has an atom at 0 and is neither normal nor constant.",
    "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,
    "supplementary": {
      "share_sum_exactly_zero": 0.50047,
      "ks_x_vs_fitted_normal": 0.0020917798156042666,
      "ks_x_pvalue": 0.77318862336257,
      "ks_y_vs_fitted_normal": 0.0019518220846299617,
      "ks_y_pvalue": 0.8399489498054262,
      "corr_xy": -0.008226889835527693,
      "excess_kurtosis_sum": 2.9891322932407807
    }
  },
  "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
}