Didn't expect to see a PhilPapers link on HN! I liked your paper, definitely gave me something to chew on. I've never given much thought to attempting to falsify the simulation hypothesis in any meaningful way (on account of a general apathy to its oft "contrived" nature that you elude to). However, your thought experiment regarding this supposed
x-x' property is quite clever. Now my mind is buzzing...
P.S. I appreciated your reference to Popper in the abstract. It prompted me to take my copy of The Open Society & Its Enemies off the shelf and peruse it for nostalgia's sake. :)