P vs. NP as a Computational Boundary: A Derivation from the Metric Lag Potential

We propose a novel derivation of the P ≠ NP conjecture from first principles of the MetricLag Potential framework (Trautwein 2026). Building on the identification of mass ascomputational overhead and the physical prohibition of Φ_L > 1 in any finite-capacitycomputational manifold, we demonstrate that P ≠ NP is not merely a mathematicalconjecture but a physical necessity of the universal substrate. Specifically, we identify:- P-problems as computational processes whose operational complexity Σ_Opsscales polynomially — maintaining Φ_L < 1 and remaining physically realizable- NP-problems as computational processes whose verification complexity Σ_Opsscales exponentially — pushing Φ_L toward or beyond 1, the physical boundaryof the manifoldA hypothetical algorithm solving NP-problems in polynomial time would require theuniversal manifold to process exponential Σ_Ops in polynomial steps — equivalent toΦ_L > 1, which we show is physically forbidden by the same constraint that producesquark confinement in Yang-Mills theory. This provides the first information-theoreticproof concept for P ≠ NP, requiring no circuit complexity arguments and no relativizationbarriers. The result follows from three postulates, is internally consistent with the fullTrautwein framework, and suggests a deep connection between computationalcomplexity, physical realizability, and quantum consciousness.