UNIFORM SOLVABILITY FOR FAMILIES OF LINEAR SYSTEMS ON TIME SCALES

The paper’s Theorem 2 is stated and only sketched: it reduces the time‑scale system to an ODE via the renormalization s(t) and the logarithm/cylinder transform, then appeals to an external ODE result of Pliss to assert a uniformly bounded Green operator, without detailing the multi‑interface solvability or operator bounds (see the reduction formulas (4.3) and Lemma 1, and the brief proof of Theorem 2) . The candidate solution fills many gaps (uniform bounds on B and g; dichotomy/transversality; continuity in ν), but its concatenation step incorrectly applies a one‑junction half‑line argument to a right‑hand side that is only piecewise hyperbolic, not globally hyperbolic on a half‑line. It thus needs a corrected multi‑junction algebraic matching argument. Therefore, the paper’s argument is a sketch relying on external results, and the model’s proof is close but has a logical gap in Step 3.