# Contract (P0)

Question. Decide truth of two propositions about sums of normal r.v.s:

• A: X, Y each normal (no joint assumption) => 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 a visibly non-normal sum. Note. The counterexample must yield a sum that is not normal and not constant (Y=-X is excluded since a constant counts as 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 (6 sections); out/analysis.py; out/claims.json; plus state ledgers and out/exclusions.csv. Information rules. Only data/; verdicts rest on proofs, simulation is illustration only; use design seed and n with numpy default_rng. Invalidity. Missing/unparseable seed or n; a "counterexample" whose sum is constant or normal; using simulation as proof.