Robust high-order low-rank BUG integrators based on explicit Runge-Kutta methods

The paper gives a complete, self-contained proof of the global error bound ||Y_N − A(t_N)||_F ≤ C′(δ_r + ε_r + γ_r + h^p) under the stated assumptions (Lipschitz F, smoothness for RK order p), via a local error bound (Theorem 1) and Lady Windermere’s fan (Theorem 2). By contrast, the model’s proof pivots on treating G(t,Y)=P_Y F(t,Y) as a Lipschitz (and sufficiently smooth) right-hand side and invoking RK stability and order on G, but it neither justifies the required Lipschitz and smoothness of G on V_r nor keeps the argument within the paper’s hypotheses. Thus the model’s reasoning is incomplete under the paper’s assumptions, even though it reaches the same bound.