Topological Resolution of the P versus NP Problem: Computational Complexity Bounds via 5D Information-Metric Manifolds

This disclosure addresses the fundamental computational complexity question of whetherP = NP. By embedding discrete algorithmic state spaces into the continuous five-dimensionalinformation-metric manifold M5 of the Cosmic Awareness Theory of Liquid Spacetime(CATLS), we demonstrate that verification and solution pathways represent distinct topologicalprojections. We prove that while verification (P) operates along bounded localized coordinateprojections, combinatorial search (NP) requires non-local metric traversal across the fifthdimension ξ. Governed by the transcendental saturation bound Ceff = 5.271, polynomial-timereduction of arbitrary NP-complete problems to P is structurally obstructed by an irreducibleinformation-metric gradient originating from an unstable node source. Consequently, weestablish the strict separation P ̸= NP.