1# Verification checks (P4)2| check | outcome |3|---|---|4| Clean re-run (results.json deleted, script re-run) byte-identical to previous output | PASS |5| se_conv and se_HC1 match statsmodels OLS bse / HC1_se on replication 1 (0.159330, 0.153937) | PASS |6| All SE-type quantities positive | PASS |7| Coverages in [0,1] and coverage×R integer | PASS |8| sd_beta_mc (0.26965) within 5% of sd_beta_exact (0.26798); diff 0.6% < ~1.6% sampling sd | PASS |9| mean β̂ (0.49620) within 3 MC SE of 0.5 (unbiasedness) | PASS |10| mean_se_conventional (0.19026) ≤ exact sqrt(E[s²](X'X)⁻¹₁₁) (0.19318), Jensen | PASS |11| conventional_ci_undercovers equals rule cov < 0.95 − 3·sqrt(.95·.05/2000) = 0.93538 | PASS |12| R = 2000, n = 30, seed recorded | PASS |13| Magnitude vs baseline: HC1 coverage (0.902) > conventional (0.844); mean se_conv well below sd exact, explaining undercoverage | consistent |14