# Contract (P0)
**Question.** Deterministic optimal growth, log utility, y' = (y-c)^alpha, full depreciation, A=1. Compare the closed-form policy/value with
value-function iteration (VFI) on the prescribed log-spaced grid.

**Estimands.** c_closed(y) at y=0.5,1,2; c_num(y) from VFI at same points (interpolated); max |c_num - c_closed| over the 3 points;
V_closed(1), V_num(1); closed-form savings rate (y-c)/y; sup-norm contraction modulus of the Bellman operator; plus VFI diagnostics
(grid points, iterations, last sup change). Meaningful under: log utility, Cobb-Douglas technology, full depreciation, interior solution,
0<alpha<1, 0<beta<1; the numerical comparison is valid only for this parameter point and grid.

**Outputs.** out/results.json (keys per TASK.md table: task_id, c_closed_y05/y1/y2, c_num_y05/y1/y2, max_abs_error_policy,
value_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used, n_iterations, final_sup_change,
feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/report.md (6 sections); out/analysis.py;
out/claims.json; out/exclusions.csv; state files.

**Information rules.** Use only data/model.csv; prescribed grid & parameters; deviations go to data_issues. Numerical policy must come
from VFI, never from the closed form; closed form derived by guess-and-verify and stated in report.

**Invalidity.** Missing/inconsistent parameters; VFI not converging; grid unable to contain the policy (y' leaving the grid); using the
closed form to build the numerical policy.