I'm not an expert on these matters. That is why I wrote my post as I did. So you say the information content of the universe is not equal to the information required to reproduce it? That makes intuitive sense. But you have to wonder, if two non-identical universes were informationally identical, in what sense their differences would matter. In the scope of the op, I would say they are irrelevant.

But anyway, this is not relevant to the larger point. I was saying, even if the universe could be represented merely by an integer, the op still would not hold . I have zero stake in the interesting but here irrelevant question of whether the universe can actually be represented by an integer, real, or whatnot.