Oh Boy, you are well on the way to full scale wolframing. At the moment I would argue its not even a theory
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Yes, I think that it is mostly a framework, albeit one with theoretical elements, both a priori: complexity theory, information theory, universality, learning etc. and predictions that can be empirically addressed. Digital physics is still largely a stub, but a promising one.
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Aah! Okay. So, provably total functions then.
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Well, otherwise your universe gets stuck, but of course you wouldn't notice if you are inside. Obviously, for as long as we can discuss our observations (and bring forth all the physical, biological etc. conditions under which we can) it must have never gotten stuck.
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....for us....does that mean it works for others ?
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No, just from the perspective of a god, or a set of constructive principles, a computer programmer or a foundational physicist.
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