Abstract This paper provides a unified resolution to the $P$ versus $NP$ problem by establishing the derivation $P \leftarrow NP$. We leverage the concept of NP-completeness, formulated by Stephen Cook, to demonstrate that the higher-dimensional quantum morphism $\{0, 1\}$ inherently contains the solutions to all NP-complete problems. By redefining the problem through Neo-Logicism and Morphic Derivation, we show that $P = NP$ is a logical necessity, bypassing the non-constructive barriers previously suggested by classical computation.