Well but (I think) what you're talking about now is the complexity of the 'wrapper' function I posed, not the complexity of the hypothetical algorithm I started out with. Yes you can add an indirection that converts it back into O(1) but the original, but that wasn't the point. I think. But then again, maybe what your second paragraph is saying is exactly that? I'll admit that I lost track of things somewhere between writing my original comment, switching back and forth to my code between compiles and now being back here :)
Also, I don't understand what you mean by 'mathematically pure', but that's on my end.
Also, I don't understand what you mean by 'mathematically pure', but that's on my end.