What is a "rational subdivision"? Last I checked any reasonable screen doesn't have overlapping pixels, so I can't think of any reasonable definition of pixel

What is a "rational subdivision"? Last I checked any reasonable screen doesn't have overlapping pixels, so I can't think of any reasonable definition of pixel that does what you say they should do. If your pixels disjointly cover almost the whole screen, you've got to have finitely many pixels or pixels of varying size. (Or uncountably many of them.)