# Verification checks (P4)
| # | check | outcome |
|---|---|---|
| 1 | analysis.py re-run after deleting results.json & counterexample.csv; `cmp` with previous results.json | PASS (byte-identical) |
| 2 | counterexample.csv has n=100000 rows, columns x,y, no NaN | PASS |
| 3 | stats recomputed from counterexample.csv match results.json (mean_sum diff 1.7e-18, sd_sum diff 0, KS diff 0) | PASS |
| 4 | |x| == |y| for every row (construction Y = ±X respected) | PASS |
| 5 | Marginals: sample mean ≈ 0, sd ≈ 1 (sd_x 0.998, sd_y 0.998); KS of x, y vs N(0,1) ≈ 0.0028, 0.0016 < 0.0043 (approx 5% critical value) | PASS |
| 6 | Sum: fraction exactly zero 0.50047 ≈ 0.5 (theory); sd_sum 1.406 ≈ sqrt(2)=1.414 | PASS |
| 7 | KS(sum vs fitted normal) = 0.2508 vs population value 0.25 and vs baseline independent-sum KS 0.0020 | PASS (clear departure; baseline consistent with B) |
| 8 | n_input_rows 2 + 2 matches files; exclusions ledger 2−0=2 | PASS |
| 9 | Sum is not constant (atom has mass ~0.5, not 1) — so counterexample not defeated by the "degenerate normal" clause | PASS |