THE INDEPENDENCE OF P VS NP FROM ZFC

THE INDEPENDENCE OF P VS NP FROM ZFCA Formal Proof Christopher Michael PompetzkiThe Caravan of Linear Algebraic TruthJanuary 18, 2026 AbstractWe prove that the statement “P = NP” is independent of Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). The proof proceeds by establishing two lemmas: (1) ZFC cannot prove P = NP because every constructive path to such a proof encounters provable obstructions, and (2) ZFC cannot prove P ̸= NP because every such proof would relativize, contradicting Baker-Gill-Solovay. The independence follows directly.