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According to conventional wisdom, the relationship between P and NP must be one of two possibilities: either P=NP or P≠NP. Unlike traditional approaches that base mathematical concepts on equivalent transformations—and, by extension, on the principle that correspondence remains unchanged—my theory is founded on non-equivalent transformations. By constructing a special non-equivalent transformation, I will demonstrate that for a problem Pa in the complexity class P and its corresponding problem Pb in the complexity class NP, Pa is a P non-equivalent transformation of Pb, and Pb is an NP non-equivalent transformation of Pa. That is, the relationship between Pa and Pb is neither P=NP nor P≠NP.