# Contract (P0)
**Question.** Two propositions about sums of normal r.v.s (data/propositions.csv):
- A: if X and Y are each (marginally) normal, X+Y is normal (constants count as degenerate normals).
- B: if X, Y are independent and each normal, X+Y is normal.
Decide each by mathematical argument; for a false one give an explicit joint construction of (X,Y) and a simulated sample (seed, n from data/design.csv) showing normal marginals and a non-normal sum.

**Estimands.** Truth values of A and B (mathematical, not statistical); for A if false, a verifiable counterexample plus sample summaries (means, sds ddof=1 of x, y, x+y; KS distance of x+y vs fitted normal).
Note: because constants count as normal, the counterexample Y=-X is NOT valid; 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/ files; verdicts rest on proofs; simulation uses design seed and n with numpy default_rng.

**Invalidity.** Counterexample with degenerate sum; marginals not exactly normal; simulation not following seed/n; verdict based on simulation alone.