Edit: I just realized that they edited their post. Originally it said "empirical math". Now that it says "empirical measurements" my question is void.

That's not my question... Unless I am completely misunderstanding what is being said.

What does empirical math, specifically, have to do with simulation theory.

I'm not advocating for simulation theory here for what it's worth. I just don't understand what "empirical" math has to do with it. The statement that "empirical math needs to be demonstrated first" is just super weird to me.

I don't know what to do with it. It feels like it's claiming that all math is theoretical... Or that math is a tautology... Or that they think math is incapable of doing something that simulation theory posits or...

So, instead of guessing at some general conclusion of what they are talking about I asked.

If you didn't edit it then I must have transformed some things in my brain... I apologize.

I think math is a process. The discovery of math is at least. Consider the origin of the incompleteness theorem. Mathematicians (Hilbert primarily) sought to prove that math is purely a construction of interpreted symbols that was wholly self-contained (primarily that everything provable within math only requires math to prove). Godel later proved, using only math, that math is incomplete. That is to specifically say, that there are things in math that are true, that you cannot prove with math. This means that there are more true things in math than you can prove. Simultaneously Godel demonstrated that this is also true for everything outside of math.

Deep in this proof is this seemingly magical thing that proves that the process of science can't prove all true things... Because the process of science is math.