I think it depends on what is doing the observing. If it's humans or conscious beings or something like that, then the admins could be keeping the precision per

I think it depends on what is doing the observing. If it's humans or conscious beings or something like that, then the admins could be keeping the precision perpetually out of our reach. If it's atoms or photons doing the observing, though, they're affected by the gravitational pull of every mass in their light cone. So an atom can distinguish between universes in which another atom 1000ly away moved by 0e or 1e (where e is the distance between two lattice points). But, it wouldn't have to know until 1000 years later. There does seem to be some computation-resource saving mechanic at play, but I don't think it has to do with discretization.