[
 {"id":"C1","text":"The closed-form 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 an interior solution."},
 {"id":"C2","text":"VFI on the prescribed 400-point log grid reproduces the closed-form policy at the evaluation points to within 0.0064 (max abs error, at y=2).","results_keys":["c_num_y05","c_num_y1","c_num_y2","max_abs_error_policy"],"status":"supported","caveat":"Error comes from discretising the control on the grid and grows with y; single grid and parameter point."},
 {"id":"C3","text":"The VFI value at y=1 (-19.52476) matches the closed form (-19.52441) to about 3.4e-4 utils.","results_keys":["value_num_y1","value_closed_y1"],"status":"supported","caveat":"Interpolated in ln y; 1.0 is not a grid node."},
 {"id":"C4","text":"The Bellman operator is a sup-norm contraction with modulus beta=0.95; VFI met the 1e-8 tolerance after 361 iterations.","results_keys":["contraction_modulus","n_iterations","final_sup_change"],"status":"supported","caveat":"The Blackwell argument applies to the bounded truncated-grid problem; log utility is unbounded on the full domain."}
]