I guess the (crazy, I know) assumption that I made is that I have some analytical, symbolic expression for a function that describes the state of the universe a

I guess the (crazy, I know) assumption that I made is that I have some analytical, symbolic expression for a function that describes the state of the universe at every point. This "state" describes some fundamental quantity (not necessarily a quantity we have a name for yet). Then we express the value of any particle field at every point as a (potentially very complex) symbolic expression that only uses the state function from my previous paragraph. All of these expressions need only finite memory to store. They describe functions with domain R^n to some co-domain of operators or whatever. Then I can calculate the value of this complex function at any point with any precision I like, with finite memory, although unbounded - I need to allocate more memory when I want more precision. Point is, I delay the process of "latticization" (calculating the numerical values at each point of a chosen lattice) to the very end - only then I have to choose how fine-grained my lattice is.