Example: Local writes need not commute

Let $x,y\in \{0,1\}$ initially both be zero. One map writes $x:=1-y$ and leaves $y$ fixed; the other writes $y:=1-x$ and leaves $x$ fixed. Their write footprints are disjoint, but both read the other's cell. The two orders give $(1,0)$ and $(0,1)$.

Similarly, a collection of individually acyclic edge insertions may form a cycle when combined. A global acyclicity guard is therefore not automatically stable under disjoint writes. These are new counterexamples to insufficient geometric hypotheses, not inherited quantum counterexamples.