# Contract (P0)
**Question.** Decide truth of two propositions on sums of normal r.v.s (data/propositions.csv):
- 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; 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 but non-normal sum.
Note: because constants count as normal, Y = -X is NOT a valid counterexample; the sum must be non-degenerate and non-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; out/analysis.py; out/claims.json; out/exclusions.csv; out/state/*.
**Information rules.** Only data/. Verdicts rest on mathematical proof; simulation only illustrates. Use seed and n from design.csv with numpy default_rng.
**Invalidity.** Counterexample whose sum is constant (degenerate normal) or whose marginals are not exactly normal; using a seed/n other than the design; claiming the simulation proves anything.