# Verification checks (P4)

• Clean re-run of analysis.py reproduces results.json byte-identically: PASS
• savings rate = alpha*beta: PASS
• c_closed + savings = y at each eval: PASS
• max_abs_error_policy recomputes: PASS
• 0<c_num<y: PASS
• final_sup_change < tol: PASS
• modulus in (0,1) equals beta: PASS
• closed form satisfies Bellman eq (max resid 3.55e-15): PASS
• argmax of RHS at y=1 ~ 0.658 (0.65800): PASS
• |V_num(1)-V_closed(1)| small vs |V| (3.44e-04): PASS
• integer keys: PASS
• 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)