[
 {"id":"C1","text":"The closed-form optimal policy is c(y)=(1-alpha*beta)y, giving c=0.329, 0.658, 1.316 at y=0.5, 1, 2 and a savings rate alpha*beta=0.342.","results_keys":["c_closed_y05","c_closed_y1","c_closed_y2","savings_rate_closed_form"],"status":"supported","caveat":"Requires log utility, Cobb-Douglas technology, full depreciation and interior solution."},
 {"id":"C2","text":"VFI on the prescribed 400-point log grid reproduces the closed-form policy at the evaluation points with maximum absolute error 0.0064 (about 0.5% of consumption at y=2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy","grid_points_used"],"status":"supported","caveat":"Discrete-choice discretisation error; specific to this grid and parameter point; eval points interpolated in ln y."},
 {"id":"C3","text":"The VFI value function at y=1 (-19.5248) agrees with the closed form (-19.5244) to about 3e-4.","results_keys":["value_num_y1","value_closed_y1"],"status":"supported","caveat":"Interpolated between grid nodes."},
 {"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta=0.95, and VFI converged in 361 iterations to a sup change below 1e-8.","results_keys":["contraction_modulus","n_iterations","final_sup_change"],"status":"supported","caveat":"Contraction argument via Blackwell conditions on the bounded discretised problem."}
]