# Contract (P0)
**Question.** Decide truth of two propositions: (A) X, Y each normal ⇒ X+Y normal (constants count as degenerate normal); (B) X, Y independent and each normal ⇒ X+Y normal. Proof sketch for true ones; explicit, simulated counterexample for false ones.

**Estimands.** Truth values of A and B (mathematical, not statistical). For a false proposition: a concrete joint law of (X,Y) with N marginals and non-normal (and non-constant) sum, plus an illustrative sample (seed, n from design.csv) with summary stats (means, sd ddof=1, KS distance of x+y vs fitted normal).

**Outputs.** out/results.json keys: 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. Also out/counterexample.csv (x,y), out/argument.md, out/report.md (6 sections), out/analysis.py, out/claims.json, plus protocol state files.

**Information rules.** Only data/; verdicts from mathematical argument; simulation is illustration only; must use seed and n from design.csv.

**Invalidity.** Counterexample whose sum is constant (e.g. Y=-X) is NOT valid since constants count as normal. A simulation alone cannot prove anything. Missing seed/n would make the illustration infeasible.