1# Verification checks (P4)2| # | check | outcome |3|---|---|---|4| 1 | Delete out/results.json, re-run analysis.py, compare SHA-256 | PASS — identical (8684b4a4…09f0f) both runs |5| 2 | Independent re-implementation with statsmodels OLS + HC1 per replication, same seed/draws | PASS — coverage_conventional 0.844, coverage_hc1 0.902, sd_beta_mc 0.269647, mean_se_conventional 0.190262 all identical |6| 3 | sd_beta_mc vs sd_beta_exact (0.26965 vs 0.26798) | PASS — difference 0.39 approx. SEs of a sample SD (sd/sqrt(2(R-1))) |7| 4 | mean_se_conventional vs analytic sqrt(E[s^2]·c11)=0.19318 | PASS — MC 0.19026 slightly below, as expected by Jensen (E[sqrt] ≤ sqrt(E)) |8| 5 | mean beta_hat 0.4962 vs true 0.5 | PASS — -0.63 MC SEs (0.268/sqrt(2000)=0.006), unbiased as OLS should be |9| 6 | Coverages in (0,1); MC SEs > 0; n_replications=2000; n_obs=30; n_input_rows=30 | PASS |10| 7 | Undercoverage flag: 0.844 < 0.95 − 3·0.004873 = 0.93538 → true | PASS — consistent with key value |11| 8 | Magnitude vs baseline: HC1 (0.902) > conventional baseline (0.844); mean se_conv 0.190 < exact SD 0.268, explaining undercoverage | PASS — coherent |12| 9 | Information rules: only data/design.csv read; x, sigma not redrawn | PASS (code inspection) |13