Residue lanes inside one ordinary lattice

Fix a finite causal graph. First merge vertices joined by zero-duration edges into local macrovertices. Such vertices occur at the same spacetime point. Retain their original payload mapsgical order inside the macrovertex. Distinct unrelated vertices at the same spacetime point may also be placed in one macrovertex.

After this operation, every remaining wire edge has positive duration. Write $E$ for the number of remaining edges and $V$ for the number of macrovertices. Choose an integer

Assign a different residue $r\in \{0,\dots ,L-1\}$ to every edge and every macrovertex.

For each assigned residue, define

These are pairwise disjoint subsets of $h_n{\mathbb{Z}}^D$. Let $Q_{r,n}$ be a fixed nearest-point rounding map onto ${\Lambda }_{r,n}$, with deterministic tie breaking. Then