The Determination Principle of the Maximum Cosmic Scale in Hierarchical Universes / 階層宇宙における最大スケールの決定原理

Short Abstract This paper proposes a determination principle for the maximum cosmic scale within the framework of the Black Hole Fractal Steady-State Universe (BFSSU) and Dynamic Mass Flow (DMF) cosmology. While the standard ΛCDM model successfully describes the observable universe, it provides no theoretical mechanism for determining the total physical size of the universe itself. The present study argues that this limitation arises from the absence of a global framework connecting conservation laws, information conservation, and cosmic structure. Within the BFSSU/DMF framework, black holes are reinterpreted as hierarchical boundary interfaces through which Dynamic Mass Flow is exchanged between parent and child universes. Assuming global conservation of mass, energy, and information together with hierarchy-invariant DMF flow equilibrium, the maximum growth scale of black holes becomes universal across all hierarchical levels. From this structural principle, the governing relation Rₘₐₓ = k/ρ is derived, demonstrating that the maximum cosmic scale is determined by the global mean density and the universal DMF boundary constant. The derived relation naturally reproduces the observed scale of the observable universe while providing consistent interpretations of critical density, spatial near-flatness, supermassive black hole mass limits, and the holographic principle. Rather than replacing standard cosmology, the BFSSU/DMF framework introduces a complementary structural architecture that connects global conservation laws with cosmic-scale determination and provides testable predictions for future observational cosmology.