I was looking over the conversation in the comments (which mentions things like "revision counters" and "reverse-hysteresis"), and then it struck me:
Doesn't the universe work like that anyway?
Think about causality. "Every action proceeds from another", as my high-school philosophy teacher used to say. Now, I get that philosophy is rather outdated, but the basic concept applies here: Everything has a past, which has effected its current present.
For example, consider the soot in a chimney. At one point that soot was some combination of wood, paper, and other flammable substances. If it had been left alone, it would stay exactly the way it was due to Newton's first law of motion.
However, that's not what happened. At some point in its history the constituent components had excessive heat applied to them. As a result, the carbon, tar, and a few other components sublimated, becoming the soot in that chimney.
I argue that our universe does, in fact, work that way; the current state of each and every thing is derived from the events in its past.
That being said, I don't have a physics degree, so I could be misunderstanding the question.