As a corollary to some of Tegmark's theory I believe it will be possible to prove that the level 4 multiverse is "accounted for" by a mathematical structure.. It's a project I've been working on which assumes that the reality hypothesis implies the mathematical universe hypothesis.

Bruno Marchal wrote:

... and if you believe that the universe can be accounted for by a some consistent mathematical structure. Which is an open problem. Assuming mechanism, physical universes have no real existence at all, except as first person sharable experience by machines (mathematical digital machines).

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