# Verification checks (P4)
1. Reproducibility: deleted out/results.json, re-ran analysis.py, `cmp` against previous copy -> IDENTICAL. PASS
2. Closed form satisfies Bellman equation: residual V(y) - [ln c(y) + beta V((y-c)^alpha)] = 0.0 at y=0.3,1,3. PASS
3. Closed-form policy is the argmax of RHS: bounded scalar maximisation at y=1 gives c=0.65800002 vs 1-alpha*beta=0.658. PASS
4. max_abs_error_policy recomputed from the six c keys = 0.0064066 (matches). PASS
5. savings_rate_closed_form = 1 - c_closed_y1/1 = 0.342 = alpha*beta. PASS
6. Stopping rule: final_sup_change 9.9967e-9 < tol 1e-8; n_iterations=361 consistent with beta^n*||TV0-V0|| decay. PASS
7. Grid adequacy: VFI policy indices in [133,276] of [0,399] -> no boundary truncation. PASS
8. Magnitudes: value gap V_num(1)-V_closed(1) = -3.4e-4 (grid-wide max 4.8e-4), well above VFI tolerance bound beta*tol/(1-beta)=1.9e-7, so the residual is discretisation error, not iteration error. Policy relative errors -0.06%, +0.15%, -0.49%; consistent with discrete choice of y' on a log grid with step h=0.01154 (implied savings k=y'^(1/alpha) has relative error up to ~h/(2 alpha)≈1.6%). PASS
9. grid_points_used = n_analysed = 400 = grid_points in model.csv; n_input_rows=10 = rows in model.csv; exclusions ledger: 10 - 0 = 10. PASS
10. No uncertainty intervals (deterministic computation); nothing to check for CI containment. N/A