Verification checks (P4)
- Reproducibility: re-ran out/analysis.py; results.json byte-identical (cmp) — PASS.
- OLS formula cross-check: demeaned slope equals np.linalg.lstsq on (1, y_{t-1}) for replication 1 (|diff|<1e-10, asserted in script) — PASS.
- bias_mc = rho_hat_mean - rho: 0.67629 - 0.8 = -0.12371 — PASS.
- bias_mc_se = rho_hat_sd_mc/sqrt(20000) = 0.148913/141.42 = 0.001053 — PASS; positive SEs (bias_mc_se, rho_hat_sd_mc, se_asymptotic) — PASS.
- bias_analytical = -(1+2.4)/30 = -0.11333; se_asymptotic = sqrt(0.36/30) = 0.10954 — PASS.
- discrepancy_se_units = (-0.12371+0.11333)/0.001053 = -9.85 — PASS.
- Counts: n_input_rows 7; n_replications = n_analysed = 20000; exclusions remove 0 — PASS.
- Magnitude vs baseline: MC bias same sign and ~1.09x the analytical value; MC sd (0.149) > asymptotic SE (0.110), plausible for rho near 1 at n=30 — PASS.
- Design followed: seed 20261029, default_rng, stationary y_1, c=0, sigma=1 — PASS.