Resolution via Quantum $P \leftarrow NP$

Discussion & Validation:

• • Participation in Global Discourse at Communications of the ACM (CACM): I have actively participated in the discussion regarding Lance Fortnow’s article, "Fifty Years of P vs. NP and the Possibility of the Impossible." (Reference: https://cacm.acm.org/research/fifty-years-of-p-vs-np-and-the-possibility-of-the-impossible/)

  • Inverting the Meaning of P vs NP: This paper provides the structural and physical foundation to transition from viewing P vs NP as a barrier to seeing it as a gateway. By integrating Frege's Bijectivity Principle and strengthening the Law of Excluded Middle from a quantum perspective, I demonstrate that the "impossible" becomes possible. By identifying NP as the Cause and P as the Effect through the 18203364 bias, this research effectively inverts the traditional understanding of the problem, offering a simultaneous resolution to both P vs NP and the Collatz Conjecture.

• For further discussion, peer validation, and formal recommendations regarding the findings of this paper, please visit the ResearchGate project page: https://www.researchgate.net/publication/399762283_RESOLUTION_VIA_QUANTUM_P_N_P

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.