ARigorous Proof of 𝑃 ≠ 𝑁𝑃: Integrating Category Theory, Quantum Simulation, and Combinatorial Analysis
Year: 2025
Type: article
Abstract: This paper presents a rigorous proof that P≠NP P \neq NP P=NP, leveraging category theory, quantum simulation, and combinatorial analysis. By modeling P P P and NP NP NP as categories and demonstrating their non-isomorphism via Hom-set analysis, alongside quantum complexity bounds and expander graph-based lower bounds, we conclusively separate these complexity classes. Formal Coq verification, edge case analysis, and third-party reproducible computations ensure robustness, addressing theoretical barriers and prior attempts' limitations.
Author: Rahbar Matak, Mehdi
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893349388
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