# Contract

• Question: decide truth of A (normal marginals ⇒ normal sum) and B (independent normal marginals ⇒ normal sum); proof sketch if true, explicit counterexample if false.
• Estimands: truth values (statement_true for A, statement_b_true for B); for a false proposition, a concrete joint construction plus a simulated sample (seed, n from data/design.csv) with summary stats and KS distance of x+y vs fitted normal. Meaningful as mathematical statements; simulation is illustration only.
• 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.
• Info rules: only data/; verdicts rest on math; use seed/n as given.
• Invalidity: missing seed/n; a counterexample whose sum non-normality is not visible at n; verdict based solely on simulation.