I mean we are discussing it so it's certainly logically possible.

> In principle continuous values cannot be physically manifested with certainty or arbitrary precision regardless of what world we are in.

Why would they need to be physically manifestable? Again how can you make assertions about what parts of physicality are maintained by the machine that is computing physicality? How can you make assertions about the world containing our own?

> Positing such a super-Turing machine is like saying "I have a square circle in my pocket".

Except it isn't. It's more like "I launched my square circle beyond the observable universe". If it was in my pocket I could take it out and show it to you.

Positing a "super-Turing" machine is pointless because it isn't testable. But it is possible. I feel like that distinction is important which is why I commented. Which is much how I feel about super-determinism in general, sure it's possible, but how do we test it? It's pointless because whether not it exists doesn't change anything. The issue of the discrete values is an interesting facet of that, one that might lead to something testable, like those "is the universe a hologram" experiments. Establishing what would be required of such a system is useful, but it doesn't dismiss it out of hand.

I guess my issue is that your arguments don't fully embrace the theory so they are bit like trying to disprove the existence of a different god using the holy book of your own god. There are valid reasons to disagree with superdeterminism, but arguing from the lens of physicality misses the issue at hand.