# 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 (constants count as degenerate normal).
• B: X, Y independent and each normal => X+Y normal. Estimands. Truth values of A and B (by mathematical argument); for a false proposition, a concrete, verifiable counterexample: joint law of (X,Y), plus a simulated sample (seed, n from data/design.csv) showing normal marginals and non-normal sum. 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. Availability rules. Only data/; verdicts from proof, simulation only illustrative; use design seed and n with numpy default_rng. Invalidity. Missing/inconsistent seed or n; a "counterexample" whose sum is actually normal (e.g. Y=-X gives a constant, which is explicitly allowed as normal, so it is NOT a counterexample); simulation treated as proof.