Finite realizations and one-layer ticks

A two-site block $\{u,v\}$ is permitted precisely when

Singleton channels include the identity and local state replacement. A circuit may use arbitrary finite $X$, but no physical register outside $X$ is available during that realization.

The phrase “one tick” is important. A sequence of overlapping two-site gates is not silently included inside one tick. If such gates require successive layers, each layer is charged its own ${\delta }_j$.