CARBON PROCESSING AND CYCLING: THE RISE AND STABILIZATION OF ATMOSPHERIC OXYGEN
An important additional factor that must be considered in any realistic model is the amount of reducing power at the earth's surface and its time variation. There are some values of reducing power that will prevent evolution of the atmosphere to a free oxygen state. That free oxygen has been present for somewhat more than the last 2Ga constrains the size and evolution of the reducing reservoir.
Ultimately there must be processes controlling the overall average oxidation state of surface carbon if the level of free oxygen in the surface environment is to stabilize. Several mechanisms, including some that have been previously proposed, can help regulate carbon cycling and speciation. The details of the relatively recent (geologically speaking) stabilization of free oxygen in the atmosphere (assuming that it is, in fact approximately stabilized), may well involve as complicated a model as the earlier transition from reducing to oxidizing.