Device closure remains separate and withdrawn in its strong form

For $\phi :\Lambda \to \mathbb{Z}$, define

It is $r$-compatible if $|\phi (x)-\phi (y)|\le 1$ whenever $d(x,y)\le r$. An ordinary one-tick edge has new coordinate duration $1+\phi (y)-\phi (x)$.

One coordinate bijection preserves the dependency graph. Corrections telescope on a spatial round trip. A zero or negative coordinate duration is not itself a new device.