You are not, because you are ignoring them when they say centres don't exist.

I don't agree that I am.

In which case SH is not implied to exist. But I knew that it is a fictitious story. The point was that "the number the 3 is prime" doens't imply that 3 exists, since properties can be correctly or incorrectly ascribe to fictive entities. There is no obvious implication from a statement being true to a statement involving entities that actually exist. Mathematical formalism and fictivism hold 3 to be no more existent than SH, and are not obviously false.

I don't understand what you're trying to accomplish with this line of reasoning. Obviously, "truths" about fictitious stories do not imply the existence of the entities they quantify over. A fiction is a sort of mutually agreed upon lie. (I don't agree, btw, that a statement about Sherlock Holmes is true in the same way that "There are white Swans" is true). But it is none the less the case that the assertion "Sherlock Holmes is a bachelor" implies the existence of Sherlock Holmes. It just so happens that everyone plays along with the story. But unlike the stories of Sherlock Holmes I really do believe in quantum mechanics and so take the theory's word for it that the entities it implies exist actually do exist.

I'm obviously aware there are alternatives to Platonism and that there is plenty of debate. I presumably have reasons for rejecting the alternatives. But instead of actually asserting a positive case for any alternative you seem to just be picking at things and disagreeing with me without explaining why (plus a decent amount of misunderstanding the position). If you'd like to continue this discussion please do that instead of just complaining about my position. It's unpleasant and not productive.