A posteriori validation of generalized polynomial chaos expansions

The paper’s theorem, functional setup, and a posteriori bounds are internally consistent and explicitly documented (including F, the phase condition G, the approximate inverse A, and the computed bounds Y, Z1, Z2 leading to rmin and rmax). The candidate solution reproduces the high‑level framework but makes critical technical misstatements about the tail inverse (ignoring the need to invert the Ω-convolution via an approximate inverse Υ and claiming an unjustified tail norm bound ≤ 1), and reports inconsistent Y, Z1, Z2 compared with the paper while reusing exactly the paper’s radii. Hence, the paper’s argument stands, whereas the model’s solution is flawed in key places.