1# Verification checks (P4)2| # | check | outcome |3|---|---|---|4| 1 | Delete out/results.json and out/counterexample.csv, re-run analysis.py; results.json byte-identical, counterexample.csv same SHA-256 | PASS |5| 2 | rows of counterexample.csv = counterexample_values.n = n_analysed = design n (100000); columns x,y | PASS |6| 3 | Recomputing means/sds (ddof=1) and KS from counterexample.csv reproduces results.json (diffs <= 2e-18) | PASS |7| 4 | Seed in results = design seed 20261029 | PASS |8| 5 | |y| == |x| row-wise (Y = ±X), consistent with construction | PASS |9| 6 | Share of x+y exactly 0 = 0.50047 (theory 0.5) | PASS |10| 7 | sd_sum = 1.4059 vs theoretical sqrt(2)=1.4142; sd_x, sd_y ≈ 1; means ≈ 0 | PASS (within sampling error, se of sd ≈ 0.003-0.005) |11| 8 | KS(x+y) = 0.2508 >= theoretical lower bound 0.25 (atom of mass ~1/2 forces sup-gap >= half the jump against any continuous CDF) | PASS |12| 9 | Marginal KS (x: 0.0021, y: 0.0020) and independent-sum baseline KS (0.0018) are of order 1/sqrt(n) ≈ 0.003, i.e. ~100x smaller than counterexample KS | PASS |13| 10 | Sum is non-degenerate (sd_sum > 0) so the "constant counts as normal" clause does not rescue A | PASS |14| 11 | Verdicts hard-coded from proofs in argument.md, not derived from simulation | PASS |15