# Verification checks (P4)
| # | check | outcome |
|---|---|---|
| 1 | Delete results.json and counterexample.csv, re-run analysis.py; results.json byte-identical (cmp), counterexample.csv same SHA-256 | PASS |
| 2 | rows in counterexample.csv = counterexample_values.n = n_analysed = design n = 100000; columns x,y | PASS |
| 3 | mean_x and sd_sum recomputed from CSV match results.json | PASS |
| 4 | abs(y) == abs(x) row-wise (construction Y = S*X holds) | PASS |
| 5 | sd_x, sd_y, sd_sum > 0 | PASS |
| 6 | sd_sum = 1.4059 close to theoretical sqrt(2)=1.4142 (Var(X+Y)=2 since Cov(X,SX)=E[S]E[X^2]=0) | PASS |
| 7 | Marginal KS (0.0021 x, 0.0020 y) below approx 5% critical value 0.0043; sum KS 0.251 is ~58x that value; independent-sum baseline KS 0.0019 | PASS (consistent with theory) |
| 8 | share_sum_exactly_zero = 0.50047 vs theoretical 1/2 | PASS |
| 9 | seed 20261029 and n from design.csv used | PASS |
| 10 | Sum is non-degenerate (sd_sum>0), so it is not a "degenerate normal" exception | PASS |