# Verification checks (P4)
| check | outcome |
|---|---|
| Re-run analysis.py twice, cmp results.json byte-identical | PASS (IDENTICAL) |
| counterexample.csv has n=100000 data rows + header, cols x,y | PASS (100001 lines) |
| n_analysed == counterexample_values.n == design n | PASS (100000) |
| random_seed == design seed 20261029 | PASS |
| exclusions: 100000 − 0 = 100000 = n_analysed | PASS |
| sds positive; sd_x, sd_y ≈ 1; sd_sum ≈ sqrt(2)=1.414 (theory Var=2) | PASS (0.998, 0.998, 1.406) |
| frac_sum_exactly_zero ≈ 0.5 (theory) | PASS (0.50047) |
| KS of x, y below 5% critical value 0.0043 (marginals consistent with N(0,1)) | PASS (0.0021, 0.0020) |
| KS of sum ≫ critical value | PASS (0.251) |
| Baseline independent sum KS small (consistent with B) | PASS (0.0020) |
| Theoretical KS of ½δ₀+½N(0,4) vs N(0,2): jump at 0 of size 1/2 implies sup-distance ≥ 1/4 | PASS (observed 0.251 consistent) |