A finite-network lower bound

If $a_n=\ell /n$, the bound is linear in $n$ for a fixed nonzero target once ${\delta }_n\to 0$. At a fixed scale it is linear in distance. The choice $a_n=\ell /n$, however, is an additional realization prescription.

The ratio $a_n/h_n$ is a model-dependent propagation ceiling. No invariant physical speed is derived by naming that ratio.