Corollary: Same-task coherent/adaptive separation

In the streaming model that forbids destruction of any delivered carrier until all $n_h$ have arrived, the optimal peak for ${\mathcal{D}}_h$ is $n_h=3^h$. The adaptive module construction implements that same channel with peak $h+1$.

Proof. The retained-coherent convention forces all input carriers to remain live at the last arrival. The unitary $U_h$ and terminal syndrome readout attain that peak. The adaptive bound is Theorem thm:tree. Channel uniqueness prevents a change of the off-code task.