Is the universe discrete or continuous?

What proof is there that the universe is discrete and what proof is there that the universe is continuous?

You can never know if the universe is discrete for certain since even if it appears so there may still be some undetectable phenomena you are unaware of.

You can never find evidence to suggest the universe is continuous as there can never be a scientific instrument capable of infinite accuracy.

You know, the reality here is that you can still get your PhD on the basis of such a question as long as you mathematically model the characteristics of a discrete universe.

After all, we mint PhDs for string theory CONSTANTLY, and there's not a shred of evidence that's been produced from any experiment to support string theory.  These so-called physicists are just mathematicians.  So, why not a "discrete brane" physicist?  We're all making this up as we go along, and don't bother with the Old Way of setting up experiments to test theories.  So, why not?