In reference to something "physical." Or maybe we could say a "genuine phenomenon." I mean, I get it. Physical things are there in a way that we can't really deny their being there. But certain invisible realities exist. Laws of nature for example. Do Newton's laws of motion count as physical things? And what exactly ARE laws of nature? Are they forces in their own right? Are they "realities" that compel the universe to behave in a certain way? OR are they simply things that have never been (and possibly will never be) observed to be otherwise. I don't know if it is even possible to settle this issue one way or the other, but I know one thing: the laws of nature are real. Whatever they are, they exist and every physical thing is (apparently) beholden to them.
You are explaining yourself perfectly well. And I agree that the issue of mathematical realism vs. fictionalism is a natural place to take this debate. I find the debate on the subject fascinating. We have Plato's ideas that "numbers are just as real as physical things." Great idea, I think. But, I see why people have issues with it. Mathematical fictionalism is one of those ideas that is just "out there"... seems very implausible. But fictionalism has yet to be refuted and probably never will be.
@Polymath257 argues for a "middle theory" between these two. And I forget exactly how it goes. But I find it to be a highly practical and plausible theory. I used to know the theory and what its merits and objections were, but it's been a while since I've thought about it. But when I was thinking a lot about philosophy of mathematics I was stuck between Platonism and Polymath's favorite theory. Fictionalism, while intriguing, just seems too implausible on account of math describing things so accurately. Even incredibly useful fictions usually aren't THAT useful.