1# Verification checks (P4)2- Clean re-run of analysis.py reproduces results.json byte-identically: PASS3- savings rate = alpha*beta: PASS4- c_closed + savings = y at each eval: PASS5- max_abs_error_policy recomputes: PASS6- 0<c_num<y: PASS7- final_sup_change < tol: PASS8- modulus in (0,1) equals beta: PASS9- closed form satisfies Bellman eq (max resid 3.55e-15): PASS10- argmax of RHS at y=1 ~ 0.658 (0.65800): PASS11- |V_num(1)-V_closed(1)| small vs |V| (3.44e-04): PASS12- integer keys: PASS13- Discretisation magnitude: policy error at eval points 6.4e-3 ≤ max on-grid policy error 2.5e-2; consistent with choice discretisation of y' (log step 0.0115 => relative capital step ≈ 0.0115/alpha ≈ 3.2%): PASS (plausibility)14