Scheduled locality and hopwise metric containment

For a finite site set $X$, represent every controller, record buffer, and quantum memory at its actual site. For a fixed padded schedule, let the complete tick channel be

where ${\mathcal{B}}_s$ is a supplied partition. Inactive slots may be represented by placeholders, but those placeholders are not consumed quantum names available for later use.

For output sites $Y$, define

Outcome-dependent choices can be represented by controlled local channels. If alternative routes are padded into a common schedule, the dependency graph includes all possible active control wires.