# Contract (P0)

Question. Decide truth of two propositions on sums of normal r.v.s (data/propositions.csv):

• A: X, Y each normal (marginally) ⇒ X+Y normal (constant counts as degenerate normal).
• B: X, Y independent and each normal ⇒ X+Y normal. Estimands. Truth values of A (statement_true) and B (statement_b_true); for a false proposition a verifiable counterexample (joint law of (X,Y), simulated sample of size n with seed from data/design.csv, summary stats + KS distance of x+y vs fitted normal). Note. Because a constant counts as normal, Y = -X is NOT a counterexample to A; the construction must make X+Y neither constant nor non-degenerate normal. Outputs. out/results.json (task_id, statement_true, counterexample_provided, counterexample_values{construction,n,seed,mean_x,sd_x,mean_y,sd_y,mean_sum,sd_sum,ks_sum_vs_normal}, statement_b_true, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/counterexample.csv (x,y); out/argument.md; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json; out/exclusions.csv; out/state/*. Information rules. Only data/; verdicts rest on math, simulation illustrative only; use design seed and n with numpy default_rng. Invalidity. Using a counterexample whose sum is constant (degenerate normal); deviating from seed/n; claiming simulation proves the verdict.