PFUSRC-114: The Theory of Boundaries——Self-Limitation and Hierarchical Attribution of Steady-State Structures

Every steady-state structure inherently possesses an intrinsic boundary; without a clear boundary, the logical distinction between interior and exterior collapses, and the very concept of steady state loses its ontological ground. This paper delivers methodological closure for the full PFUSRC theoretical framework. It first distinguishes the Universal Universe as an all-inclusive complete set with logically undefinable boundaries, thus excluded from valid physical discourse. The Topological Universe (Mother Universe) is defined as a locally self-sustained steady-state structure bounded by the 55-Closure, a closed anchor-point system composed of 19+17+19 topological nodes dynamically sustained by the 45° triple coaxial bicone, fixed prime anchor nodes and the universal β₁ driving field. Within this boundary alone do all physical laws and three categories of mathematics hold self-consistently. Two core methodological principles are established: the Principle of Boundary Correspondence, requiring every boundary claim to specify its ontological level, matching topological structure and measurable observational data; and the Principle of Boundary-Crossing Degeneration, stating any theory transgressing its intrinsic boundary must degrade into local approximations with its symmetries, dualities and mapping relations redefined. The paper diagnoses the core flaw of mainstream physics as static descriptive frameworks mismatching dynamically evolving objective reality, originating from universal neglect of explicit boundary definition. General Relativity and Quantum Mechanics are repositioned as scale-limited effective approximations valid only under specific degenerating limits within the 55-Closure, rather than ultimate logically closed systems. This paper further reinterprets the logical ambiguity introduced by equating zero to absolute nothingness, clarifies hidden boundary barriers embedded in terminology such as antimatter, dark matter and dark energy, and correlates the scope of instrumental, abstract and ontological mathematics to distinct boundary constraints. It extends boundary analysis to artificial intelligence research and academic economic costs caused by boundary vagueness, concluding that the Theory of Boundaries constitutes the sole guarantee of the PFUSRC system’s falsifiability, internal self-consistency and rigorous valid discourse.