> Has this been actually proven?
Neither proven nor disproven in any capacity.
Also I have no clue how anyone could assert that the universe being "continuous" (whatever that means) could be casually claimed by anyone to have any link to our universe being "a simulation" (whatever that means) or not.
>Simulations are usually vastly simpler than the substrate they run on.
So to simulate continuum you need a transfinite VM. It will be more efficient to just run the universe bare metal.