Theorem: Legal global scheduling without long-route serialization

For every fixed finite future-causal network, all sufficiently large target scales admit one deterministic legal partition schedule implementing all its routes and hub frames.

Long wire routes execute in parallel. Only the finite local access operations at each hub are serialized. The schedule is independent of the input state, payload values, outcomes, and external reference.

Proof. At each tick, a moving edge requests at most one pair, whose two sites lie in its assigned residue class. Different edge routes have disjoint residue classes, so their requested pairs are disjoint.

A hub-frame access pair joins its private hub residue to an incident private edge residue. An incoming route has ended before its gathering swap; an outgoing route begins after its dispersal swap. Thus an access pair never competes with movement on that same edge.

Different hub frames use different hub residues. An edge cannot be undergoing access at both endpoints at the same tick: Lemma lem:slack leaves at least one route tick between the two frames. Therefore all active pairs at a tick form a matching. Payload singleton ticks cannot compete with access at their own hub because the local frame serializes them.

Complete the matching by singleton identities at all remaining used sites. The experiment uses finitely many sites and factors. The unused lattice may equivalently be completed by singleton identities without constructing an infinite active tensor product.

Every decision was determined by the graph, assigned residues, rounding rules, and clock. No quantum or classical outcome was consulted.