Verification checks (P4)
- Reproducibility: re-ran out/analysis.py; byte-identical out/results.json (cmp) — PASS.
- bias_mc = rho_hat_mean - rho: 0.676290 - 0.8 = -0.123710 — PASS.
- bias_mc_se = rho_hat_sd_mc/sqrt(20000) = 0.148913/141.42 = 0.001053 > 0 — PASS.
- discrepancy = (-0.123710+0.113333)/0.001053 = -9.85 — PASS.
- bias_analytical = -(1+2.4)/30 = -0.113333; se_asymptotic = sqrt(0.36/30)=0.109545 — PASS.
- n_analysed (20000) = n_replications (20000) - removed (0), consistent with exclusions.csv — PASS.
- Magnitude: bias_mc negative and same order as analytical (relative diff ~8%); |bias| ≈ 1.13 x asymptotic SE — plausible (known downward bias, larger than O(1/n) term near unit root) — PASS.
- rho_hat_sd_mc (0.149) > se_asymptotic (0.110): finite-sample dispersion larger than asymptotic, expected for rho near 1 with small n — noted, not an error.
- Gate run: see phases.json P4.