Since you don't know what parity of Q is, you can't refer to the class of worlds where it's "the same" or "different", in particular because it can't be different. So again, I don't know what you describe here.

I'm merely trying to exclude a possible misunderstanding that would mean both of us being correct in the version of the problem we are talking about. Here's another attempt. The only difference between the world Omega shows up in and the counterfactual worlds Omega affects regarding the calculator result is whether or not the calculator malfunctioned, you just don't know on which side it malfunctioned. Is that correct?