It's not a matter of computability though, it's a matter of exact precision not being physically possible in a continuum.
You are right that in modern information theory exact precision on a continuum is physically impossible (for others: as we continue to subdevide the precision we require more bits of information, which has known physical limits).
But what I think the other posters was getting at is that if the universe runs on a machine that is not bound by those rules, say rules where arbitrary precision on a continuum can be stored as a value (which again violates physicality as we know it but such a machine is "outside" the universe so physicality is moot already), then that is possible.
Which is to say the universe is a machine which can compute things a Turing machine can't (a Turing machine can compute everything that can be computed that we are aware of, ergo if the universe can compute things it can't then the assertion being made - albeit somewhat clumsily - is that the universe doesn't follow the asserts we know).
However, I would argue that such a super-Turing machine is logically impossible. In principle continuous values cannot be physically manifested with certainty or arbitrary precision regardless of what world we are in.
Positing such a super-Turing machine is like saying "I have a square circle in my pocket".
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.
Ugh. Is information theory mathematics or physics? Nature is analog and doesn't work in terms of bits, it's more similar to Euclidean geometry than Cartesian.
Both are absurd concepts! When probing the ultimate depths of reality like this there are no good answers.