Finite Distortion Capacity in a Non-Zero Substrate: Global Admissibility Closure

Finite Distortion Capacity in a Non‑Zero Substrate: Global Admissibility Closure develops the global admissibility layer of a continuous‑substrate framework. Building on prior results establishing continuity, bounded deformation, local saturation behavior, and finite local distortion capacity, this paper introduces the configuration‑level structure required to close the admissibility branch of the program. This work builds directly on four upstream analyses: The Displacement Framework: Horizon‑Bounded Accounting in a Timeless 4D Manifold (Partin, 2026a), DOI: https://doi.org/10.5281/zenodo.19039477 Toward a Formal No‑Tear Theorem in a Continuous Substrate Framework (Partin, 2026b), DOI: https://doi.org/10.5281/zenodo.19422745 The Charged Fabric: A Substrate Framework for Continuity, Compression, and Gravitational Response (Partin, 2026c), DOI: https://doi.org/10.5281/zenodo.19477118 Saturation Limits of the Displacement Field: Bounded Deformation, Admissibility Under Limits, and the Exclusion of Singular Collapse (Partin, 2026d), DOI: https://doi.org/10.5281/zenodo.19487818 These papers establish, respectively, the displacement‑level structural framework, continuity‑based exclusion of rupture, microphysical deformation response, and bounded‑deformation analysis excluding singular collapse. The present paper introduces a notion of global boundary approach, a boundary‑response functional that diverges near the admissibility boundary, and a global redistribution requirement governing admissible continuation. A global admissibility discriminator theorem is proven, showing that admissible evolution cannot attain the admissibility boundary and must instead proceed through redistribution within the admissible class. To connect the earlier finite‑capacity analysis with the global closure result, the paper introduces a capacity function measuring remaining admissible headroom, a qualitative deformation‑regime structure, and the concept of distributed configurations as the admissible alternative to point‑like singular concentration. These additions clarify how bounded local capacity scales into global admissibility structure without introducing dynamics or constitutive assumptions. As the fifth and final paper in the admissibility branch of the substrate‑framework program, this work completes the structural closure of admissible configurations in a continuous substrate. Together with the upstream results, it establishes continuity, bounded deformation, finite distortion capacity, and global non‑attainability as the full set of structural constraints governing admissible configurations.