Under construction. I am currently writing a new paper on this (being clearer on the conceptual aspects than the paper below), and also working more on the open mathematical points. Over the next few months, I will put some of the material here.
In the meantime, you might like to have a look at a talk from 2021 (video on the right), and at the following quite technical paper:
M. P. Müller, Law without law: from observer states to physics via algorithmic information theory, Quantum 4, 301 (2020). DOI:10.22331/q-2020-07-20-301.
One motivation for this approach is a feature called “Restriction A” that is described in this paper with Caroline Jones:
C. L. Jones and M. P. Müller, Thinking twice inside the box: is Wigner’s friend really quantum?, arXiv:2402.08727.