# Verification checks (P4) - Clean re-run of out/analysis.py: results.json byte-identical: PASS - exclusions: n_raw 10 - removed 0 = 10 rows parsed: PASS - closed c = (1-ab)y: PASS - max err recomputed: PASS - final_sup < tol: PASS - policy error <= on-grid max: PASS - value err small vs |V|: PASS - closed form satisfies Bellman eq (fine continuous check): PASS - savings rate = alpha*beta: PASS - modulus in (0,1): PASS - n_analysed == grid_points_used == 400: PASS - choices interior to grid: PASS