Lemma: Finite traffic without junction conflicts

Any fixed finite collection of planned logical routes can be run on the same schedule with the preceding per-route timing bounds, provided finite reserved interfaces are large enough. Routes and storage plans are chosen before the unknown input is supplied.

Proof. Assign a distinct register colour to each logical connection. Reserve a slot of the appropriate type for that colour at the sites it may use, together with hub-memory slots. During transport phases, swap the corresponding slots across each pair block. During junction phases, perform all prescribed colour permutations and memory operations inside the one junction block.

Different colours are distinct tensor factors. An arbitrary finite permutation of them is a legal local block channel; its internal gate depth is not separately charged in this model. No hub site belongs to more than one block. A finite collection uses only finitely many colours and slots at each site.