The Topological Uniqueness Theorem: Energetic Entanglement, Fractal Asymmetry, and the Principle of Least Action in the Infinite Substratum

The material diversity of the universe is not the result of chaos, but a topological necessity of the infinite Substratum. This paper establishes the “Topological Uniqueness Theorem,” asserting that the existence of two absolutely identical quantum systems is physically impossible. Using Substratum Hydrodynamics (Papers I-XVI), we demonstrate that any two objects experience distinct “mutual pressures” due to phase delays (Δt) and spatial asymmetry. We link hydrodynamic stability to Ilya Prigogine's principle of Minimum Entropy Production and offer a mechanical derivation of the Pauli Exclusion Principle. We conclude that energy is not a substance, but the geometric entanglement of Substratum flow, creating an infinite, non-repeatable fractal structure.