Proof of the Non-Existence of Contradiction: Zero-Morphism Degeneration and Indeterminacy in Multilayered Reality

This paper redefines the principle of non-contradiction (¬(P ∧ ¬P)) in classical logic not merely as a formal convention of thought, but as a structural “non-instantiability” within the universal system. We present a rigorous proof across five distinct layers—the physical, classical set-theoretic, quantum, computational, and category-theoretic—demonstrating the mechanisms by which contradiction is systematically avoided or annihilated. We conclude that “contradiction” as a physical entity does not exist; rather, what is perceived as undecid-ability or inconsistency is a convergence toward “Indeterminacy,” a quarantine buffer arising from finite-precision observation systems.