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I think it isn't falsifisble.

But some people seemingly like to pretend with enough "can do attitude" they can prove or disprove anything in a paper, no matter how unconvincing the line of reasoning.

This. The main issue with how people approach the simulation hypothesis is by thinking that the beings that made our VMs are just like us.

It is hard to even disprove that we aren't a Boltzmann brain that hallucinated entire reality. Assuming the simulation is perfect(or at lest consistent) the only way to falsify it is to get some impossible estimates for required CPU/memory/storage. I think the whole "if simulations are possible, multiple ones will be created" falls apart when 1 second of running simulation requires several years of compute.

IMHO, it likely isn't even falifiable.

for the article: "the fundamental nature of reality operates in a way that no computer could ever simulate"

Yes, no computer in our universe, with our physical laws. In "a totally different level of existence", all bets are off regarding the fundamental nature of reality there. It could be utterly different. So, speculation is nonsensical, it's unfalifiable.

There are no irrational numbers measurable in the universe. Irrational numbers as far as we encounter are computable via straightforward algorithms.

Indeed, simulating God himself will have to wait a little bit

Yes, this is exactly my problem with claims about the 'real' universe if we are, in fact, in a simulation. It might be literally, programmatically, impossible for us to infer anything about it. The analogy I like to use is Pac-Man believing that the entire universe exists within the confines of a blue-walled maze.

I would imagine the hand-wavey response might not be far away from "God is not algorithmic".

Just for reference, the main author's stance on god : https://youtu.be/k_VBzweMIlM?t=125

That example is particularly fishy. The truthiness of a statement is not part of the statement itself, so any explicitly stated truth value is not inconsistent with truthiness, rather it is meaningless.

It’s like saying

    bool isTrue = true;
    bool isProvable = false;
    bool isTrueAndProvable = isTrue && isProvable; // false

It rests on magical conspiracy theories with an imaginary "them" hobgoblins. Changelings with more dimensions.

Do you necessarily need to compute anything in order to perform a simulation? Suppose whenever some weird undecidable statement quantum gravity situation comes up inside the simulation, you pause it, recreate the scenario on a lab bench, and then copy the data into your simulation. You didn't compute what would happen, you don't even necessarily understand how it works, but as long as its the same quantum gravity stuff inside and out, the simulation can proceed faithfully. This makes some assumptions about locality I guess.

Of course the whole affair seems a little moot since you obviously only have to be accurate enough that it doesn't disrupt the ancestor simulation or whatever, but that's less fun to think about I suppose.

The paper's core claim is wrong even before you get into any quantum gravity stuff. The other HN thread contains a number of comments explaining why.