Max Tegmark answers the question Is the physical world isomorphic to some mathematical structure? with the claim that "The physical world is completely mathematical" and "Everything that exists mathematically exists physically." (page 1)
This would be a claim than any physics model, as a mathematical structure, exists in some universe or somewhere physically. So any physics model would illustrate Tegmark's hypothesis. Finding a physics model would not help justify it.
Bertrand Russell commented on bare mathematical structure in The ABC of Relativity (page 138):
The theory of relativity has accomplished a very great deal in this respect, and in doing so has taken us nearer and nearer to bare structure, which is the mathematician's goal - not because it is the only thing he is interested in as a human being, but because it is the only thing he can express in mathematical formulae.
Russell suggests there is more going on with reality than what can be expressed by this mathematical structure and illustrates this by comparing the structure present in a musical score with the actual music played by an orchestra: "you can infer the music from the score and the score from the music". However, if you were stone-deaf from birth would you be able to enjoy the music?
The value of the music would be completely unimaginable to you, but you could infer all its mathematical characteristics, since they are the same as those of the score. (page 137)
What Tegmark needs to find to justify his hypothesis is not whether there exists a physical model that fits his hypothesis (they all do), but rather does an argument exist justifying the claim that mathematical structure is all there is to reality. That is a philosophical question and it is something Russell suggests is worth doubting.
Russell, B. (1958). The ABC of relativity https://archive.org/details/in.ernet.dli.2015.187959/page/n1
Tegmark, M. (1998). Is “the theory of everything” merely the ultimate ensemble theory?. Annals of Physics, 270(1), 1-51. https://arxiv.org/abs/gr-qc/9704009