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‑closure layer of a continuous‑substrate framework. Building on four upstream analyses establishing observer‑relative accounting, continuity of induced geometry, local deformation structure, and bounded local deformation, this paper identifies the configuration‑level continuation structure compatible with finite local deformation capacity. The central result is structural rather than dynamical: admissible continuation near finite‑capacity exhaustion cannot remain arbitrarily point‑supported while preserving finite local deformation capacity. As residual capacity collapses within a localized region, admissible continuation requires redistribution of deformation burden across an extended, non‑zero‑volume domain. Distributed continuation therefore emerges as the admissible continuation class compatible with continuity and bounded deformation. The analysis does not introduce a constitutive law, microscopic mechanism, evolution equation, or replacement gravitational dynamics. It characterizes the admissible continuation structure internal to the admissible class and completes the admissibility branch of the substrate program at the configuration level. Upstream papers in the program include: The Displacement Framework (Partin, 2026a) Toward a Formal No‑Tear Theorem (Partin, 2026b) The Charged Fabric (Partin, 2026c) Saturation Limits of the Displacement Field (Partin, 2026d) Together with these results, the present work establishes continuity, bounded deformation, finite local deformation capacity, and distributed continuation near finite‑capacity exhaustion as the structural constraints governing admissible configurations in a continuous substrate.