A fun variant of this is that the log can be taken at variable intervals and as long as it is sufficiently detailed, it can still capture all salient details.
Similarly a simulation run at some "tick rate" can also be run at 2x the rate while taking 1/2 the step per tick. Within the universe nobody would notice, as long as the steps were fine enough to begin with.
I think it was in Diaspora (or Permutation City?) that Greg Egan proposed that any tick rate would be unnoticable to that simulated beings, including "none".
In other words, the movie Top Gun will continue to exist as-is, no matter how many copies are made of it, including none. Encoded as a digital file it is just a number, a pure timeless concept, it doesn't have to be written down to exist. It always existed on the number line, even before Tom Cruise was born. In fact, every encoding of Top Gun exists on the number line, in every compression format, in every resolution, even a future 16K resolution that was never filmed and has no display devices made for it yet. Its encoding as a 400GB long number is there, already, and will always be there.
In other words, and simulation, an log of events, any experience already exists in mathematics, in every encoding... somewhere on the number line. This includes the entire physical universe. This isn't hypothetical, it's necessarily true! Anything that can be represented by a finite amount of information must be on the number line.
Even if you assume the Universe lasts forever, you can break its history up into a sequence of states, each of which is finite. Then the series will exists on the number line as a set of points heading off to infinity.