1# Verification checks (P4)2| # | check | outcome |3|---|---|---|4| 1 | Clean re-run (results.json deleted, script re-run) reproduces byte-identical results.json | PASS (cmp identical) |5| 2 | data/design.csv SHA-256 unchanged after runs | PASS |6| 3 | n_replications=2000, n_obs=30, n_input_rows=30; exclusions 30-0=30 | PASS |7| 4 | sd_beta_exact, sd_beta_mc, mean_se_conventional > 0 | PASS (0.2680, 0.2696, 0.1903) |8| 5 | sd_beta_mc vs sd_beta_exact: diff 0.0017 vs MC SE of SD ≈ 0.268/sqrt(2*1999)=0.0042 | PASS (within 0.4 SE) |9| 6 | mean_beta_hat 0.4962 vs beta=0.5: diff -0.0038 vs MC SE 0.0060 | PASS (unbiased as expected) |10| 7 | mean_se_conventional 0.1903 ≤ exact sqrt(E[s²]/Sxx)=0.1932 (Jensen) and close | PASS |11| 8 | se_conv and se_HC1 of replication 1 match statsmodels to 1e-10 | PASS |12| 9 | Coverages in [0,1]; t crit = t.975(28)=2.0484 | PASS |13| 10 | Undercoverage flag: 0.844 < 0.95-3*0.004873=0.9354 → true; same conclusion with MCSE at estimated p (0.00811) | PASS (robust to MCSE definition) |14| 11 | Magnitude vs baseline: mean se_conv / exact SD = 0.71, consistent with coverage well below 0.95; HC1 mean SE 0.241 closer to 0.268, coverage 0.902 higher than baseline 0.844 | PASS (coherent) |15