Model specification: Bounded-step realizing networks

The following lower bounds concern finite acyclic networks of complete channels, not arbitrary process matrices. Assume:

1. an external message $M\cong {\mathbb{C}}^d$ is introduced at a source; other initial resources are fixed independently of that message;

2. all quantum wires, classical controls, routing choices, and retained records occur in the dependency graph;

3. source and receiver interfaces have specified spatial coordinates in the chosen extracted frame;

4. every spatially nonzero dependency hop advances by at most $a_n>0$;

5. execution has $N_n$ rounds and every source–receiver dependency path contains at most $N_n$ such hops;

6. no undeclared communication or decoder access bypasses this graph.

The step bound and round convention are additional realization premises. They are not supplied by (eq:lorentz).