The causal midpoint replacement

For a pair block, use its spatial midpoint; for a singleton, use its site. The event time is the midpoint of its firing interval. Thus a block $B=\{x,y\}$ during tick $k$ has midpoint

Connect consecutive uses of each logical register by a straight segment between the corresponding midpoint events. Add the initial and terminal port events and their half-tick connecting segments. Let $F^{\mathrm{mid}}$ be the resulting finite geometric graph.