CO phase selection for a stirred catalytic surface model

We consider a catalytic surface model on \(\Z^2\) with CO adsorption, diatomic oxygen adsorption, finite-rate reaction and finite-rate stirring. If the CO arrival rate \(p\) exceeds the oxygen parameter \(q\), we prove that every site is eventually occupied by CO almost surely, from every iid initial law with positive CO density. This gives CO poisoning on every finite set. The density estimate of Durrett and Swindle controls the total time spent vacant. An additional reaction count then controls all state changes, including stirring. Spatial independence of the initial states and driving clocks determines the limiting phase.