That seems true, but unsatisfying. If you only consider a finite time, you can only use a finite number of digits is the idea? Or can infinite time also work, b

That seems true, but unsatisfying. If you only consider a finite time, you can only use a finite number of digits is the idea? Or can infinite time also work, because laws of thermodynamics? Either way though, then doesn't your model of the universe just need an extra parameter, the number of digits to care about? Seems like everything else being equal, the fewer unmotivated parameters in your model, the better. Especially because this would rely on internal details of what happens in the universe, seems unlikely to be true unless this is a simulation.