I've been on the same trip as this guy for the last couple of decades. I haven't tried to write it up as scientific papers, but I've been actively looking for refutation of some of the key insights that lead down this path of thinking and haven't found any yet.

I think that the key premise here is assuming that consciousness can be a feature of a turing machine. If you accept that premise then all objections to reality being purely mathematical fall away, and Conway's Game of Life (GoL) provides a perfect substrate for thought experiments around this. Because we know that GoL is turing complete, and GoL is obviously purely mathematical... its phenomena exist without our simulating them, simply because they are mathematically possible. We simulate them in order to help us discover their existence, but their existence is "Platonic", independent of our simulations. So if consciousness can be a feature of any turing complete system, then an infinitude of consciousnesses exist in the space of GoL phenomena; consciousnesses from whose perspective their respective (from our perspective purely mathematical) GoL Universes are "material".

The main obstacle to accepting this view is insisting on dualism between the material and the purely mathematical, giving a special status to materialism. But materialism also tends to lead one to accept that consciousness can be a property of turing machines, which would then imply a mathematical reality. I call this paradox "the poverty of materialism", and I'd love to see a convincing refutation.

I see the author also has some newer papers as well on the broad topic.

The reader may also enjoy this survey report on multiverse theories which I generated just this morning:

https://html-preview.github.io/?url=https://github.com/impre...

Anyone making an absolute claim of knowledge of the nature of self-awareness needs to demonstrate how qualia arises by making a testable way to disable qualia in humans or to demonstrate qualia in a non-human system. The latter is preferred.

(2016)

This is 8 years old, and as far as I can tell, has never been cited by anyone other than the author.

This person is making a mistake with Everettian mechanics, assuming there is branching, which is precisely not what is happening.