# Verification checks (P4)
1. Clean re-run: deleted results.json/figure/sensitivity CSV, re-ran analysis.py; `cmp` with previous results.json → IDENTICAL. PASS
2. Manual Bartlett NW SE equals statsmodels HAC SE (asserted |diff|<1e-10 in script). PASS
3. Hand computation of 1960Q1 (Δu=-0.4667, g=2.2237) and 2019Q4 (Δu=0, g=0.6796) from raw CSV rows matches script series. PASS
4. n_analysed=240, first 1960Q1, last 2019Q4; exclusion ledger 319-78-1=240. PASS
5. se_iid>0, se_hac>0; CI contains beta_hat; CI symmetric; half-width/se_hac=1.95996 (normal critical value). PASS
6. Magnitudes: beta_hat=-0.256 (HAC/iid SE ratio 1.80, consistent with positive residual autocorrelation 0.39 at lag 1); mean_growth 0.754%/q ≈ 3.0% annualised (plausible for 1960–2019); growth rate stabilising u = -alpha/beta ≈ 0.72%/q, near mean growth. PASS
7. okun_negative_5pct consistent: beta<0 and p_value_hac=9.5e-13<0.05; remains significant at every bandwidth 0–12 (max p 5.7e-12). PASS
8. Information rule: only 1959Q4–2019Q4 levels used (asserted window construction). PASS