# Contract (P0)
**Question.** Deterministic optimal growth, log utility, y' = (y-c)^alpha, full depreciation, A=1. Compare the closed-form policy/value with VFI on the prescribed log-spaced grid.
**Estimands.** Closed-form c(y) at y=0.5,1,2; VFI c(y) at same points (interpolated if off-grid); max |c_num-c_closed|; closed-form and VFI V(1); closed-form savings rate (y-c)/y; Bellman contraction modulus (sup norm). Meaningful under: log utility, Cobb-Douglas, full depreciation, interior solution, 0<beta<1, 0<alpha<1.
**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; plus protocol files.
**Information rules.** Only data/model.csv; prescribed grid/params; deviations go to data_issues; numerical policy from VFI only, closed form derived in report.
**Invalidity.** Grid not containing feasible/optimal choices (truncation), VFI not converging, use of closed form inside VFI.