# Checks
- [PASS] Reproducibility: re-ran out/analysis.py; out/results.json byte-identical (cmp).
- [PASS] Closed form verified independently: for y in {0.5,1,2}, a continuous bounded optimiser (scipy) applied to the Bellman RHS with V=A+B ln y returns argmax = (1-alpha*beta)y to 1e-8 and T V - V = 0 (fixed point).
- [PASS] max_abs_error_policy equals max of the three |c_num - c_closed| (recomputed).
- [PASS] savings_rate_closed_form = 1 - c_closed_y1/1 = alpha*beta = 0.342.
- [PASS] VFI converged: final_sup_change 9.997e-9 < tol 1e-8 after 361 iterations; consistent with beta^n * initial gap (0.95^361 ~ 9e-9 x O(1) gap).
- [PASS] Policy never at grid bounds (0 bound hits) -> no truncation distortion.
- [PASS] Magnitudes: relative policy errors -0.06%, +0.15%, -0.48% at y=0.5,1,2, consistent with ln-grid step 0.0115 in y' (=> ~3.2% step in required investment, i.e. at most ~0.55% of y in consumption). |V_num(1) - V_closed(1)| = 3.4e-4, larger than the stopping-rule bound beta*tol/(1-beta)=1.9e-7, so the residual value gap is discretisation (and interpolation) error, not iteration error.
- [PASS] Units: consumption in output units, values in utils; contraction modulus = beta = 0.95 in (0,1).