There seems to be a piece of this that's missing. Why would a realist use "discovered" while an anti-realist would use "invented?" To appreciate this, definitions of each word, and a synopsis of the philosophies, would need to be provided. Without understanding that, it's difficult to understand the distinction.
But from looking at the two words, and the "classification" of some suggested synonyms, it at least appears to me that realists concern themselves with with verbs divorced from intention. To "discover" something could also be to "stumble upon" something. Meanwhile, anti-realists concern themselves with verbs associated with intention. To "invent" implies deliberate effort.
Therefore, if I can use such expressions, realists are objectively passive, while anti-realists are subjectively active.
What you're looking for, then, is a verb that either combines both qualities or neither quality. But I'm not sure if that's possible. Especially if you want something that applies to all subjects. There may be no choice but to use a verb that comes down on one side or the other.
(I could propose any number of additional synonyms—identified, determined, expressed—but all of the things that make the other synonyms inappropriate would apply to these as well.)
My intuition tells me that, in order to use something that really distances itself from either perspective, a rephrasing may be necessary:
Who is considered to be the founder of X?
Who is the most famous for X?
Neither of these necessitates an explicit chain of events. While the meaning between the two differs, and neither means the same as "discover" or "invent," I don't think there can be something exactly the same as "discover" or "invent," that is completely neutral across all usage.