A nonuniform contraction example and a Caputo Green-function mismatch in polynomial F-contraction results

Independent technical comment on Hamza et al., Fixed Point of Polynomial F-Contraction with an Application, Mathematics 14(4) (2026), 589, doi:10.3390/math14040589. The note gives an exact off-diagonal calculation disproving Example 2’s logarithmic contraction verification, while showing that the same map is an ordinary F-contraction in the paper’s relaxed class for F(t)=-1/t. Constant-forcing tests identify a mismatch between the displayed Green function and the stated Caputo boundary-value problem. A two-point substitution disproves Example 4’s claimed nonlinear Lipschitz constant; a larger constant repairs the estimate. A separate discussion identifies unproved boundedness and product-limit steps in the abstract Cauchy argument without claiming a counterexample to the main abstract theorems. The corrected Caputo integral formulation retains a direct Banach contraction estimate, subject to a separate classical regularity justification. Version 1.1. Includes the complete PDF and a source ZIP with LaTeX source, a README, and auxiliary exact-arithmetic checks. AI assistance and author responsibility are disclosed in the note. This is an independent comment, not an author-issued corrigendum or a journal-endorsed correction.