The global spatial structure of the universe remains underdetermined by standard cosmological dynamics. While general relativity and contemporary cosmological models tightly constrain local geometry, expansion, and matter evolution, they do not select a unique global topology. In particular, they leave open whether space is infinite, finite but unbounded, or globally identified, and they provide no principled criterion for excluding one possibility over another.This paper introduces a Tier-0 admissibility framework in which physically realized universes are selected as stable fixed points of a recursive global constraint. The framework operates as a selection principle on global configurations rather than as a new dynamical law, and it preserves all established local physics, including cosmic expansion, causal structure, and the standard resolution of the darkness of the night sky.Within this framework, global closure arises naturally as equivalence or identification, not as a physical boundary or termination of space. Finite-but-unbounded spatial structures emerge as admissible global configurations, while infinite spatial extent remains compatible with closure at the level of admissible state space. Physical boundaries are shown to be generically inadmissible due to instability under recursive constraint.The paper further identifies concrete, in-principle observable consequences of global closure, including constraints on large-scale correlation structure and global mode spectra, particularly in cosmological observables sensitive to the largest scales. These effects provide a clear route to empirical falsification without modifying local cosmological dynamics.This work is part of a broader Tier-0 program that applies recursive admissibility and structural stability as foundational principles across quantum theory, probability, and cosmology. The present paper functions as a self-contained application of that framework to the problem of global spatial topology.https://doi.org/10.5281/zenodo.18073598