| 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 |