Proposition: Heisenberg commutation in a fixed reversible run

Take fixed site tensor interfaces and a unitary partitioned run with one-step physical reach at most $c\Delta t_n$. If local observables $A$ at tick $s$ and $B$ at tick $t\ge s$ have spatial supports at distance greater than $c(t-s)\Delta t_n$, their Heisenberg representatives on the common initial Hilbert space commute.

Proof. Let $U(t,s)$ be the product unitary between the ticks. The one-layer adjoint support proof shows that $U(t,s{)}^{†}BU(t,s)$ lies in the backward support region of $B$. The reach bound makes this region disjoint from the support of $A$. They commute on the tick-$s$ tensor interface. Conjugate both by the common initial-to-$s$ unitary.