<p>Rivers shape their floodplains through meander growth and cutoffs, which reorganize channel geometry. Such threshold events are thought to limit geomorphic predictability, yet whether cutoffs alone are sufficient to generate deterministic chaos remains unresolved. We test this question using a kinematic meander model formulated at fixed spatial resolution to track the divergence, measured by the Hamming distance, between trajectories that begin from infinitesimally perturbed initial channel conditions. Using a counterfactual numerical experiment that disables cutoffs, we find that trajectories with cutoffs exhibit sustained exponential divergence, whereas those without cutoffs do not. The inferred growth rate, measured by the finite-time Lyapunov exponent, converges with grid resolution, is insensitive to perturbation magnitude, and is consistent across diverse initial planforms. Notably, we find that the Lyapunov exponent scales with migration rate but remains effectively invariant to the cutoff threshold, whereas the cutoff threshold regulates the frequency of topological resets. Thus, in kinematic models, cutoffs alone produce sensitive dependence on initial conditions and define a finite predictability horizon that is bounded by the mode of cutoff formation.</p>