Gamma-DG Core II: Structural Completion, Stabilization, and Geometry-Side Coherence

27-Mar-2026(v2.0) Gamma-DG Core II develops the next central structural layer of Gamma-DG from the temporal nucleus established in Core I. Whereas Core I isolated minimal temporal organization through order, barriers, monotonicity, and lift–descent structure, this Version 2 formalizes the completion-oriented layer in which structural completion, stabilization, transfer-compatible organization, and geometry-side coherence are treated as intrinsic components of the theory. This revised version strengthens the manuscript by replacing stronger global formulations with finite and structurally controlled ones. In particular, stabilization is reformulated through finite stabilizing observation layers that contain all sufficiently late completed observation values on a stabilized tail. Transfer-compatible organization is then expressed through finite transfer layer maps preserving the finite joins realized by the stabilized tail. Geometry-side coherence is correspondingly formulated through finite geometry-side models, so that coherent geometric interpretation is asserted only under explicit finite realization conditions rather than as a universal global consequence. These revisions preserve the overall architecture of Core II while improving mathematical caution, internal coherence, and compatibility with application-neutral structural transfer. Core II is thus presented as a reusable theoretical layer linking the temporal nucleus of Gamma-DG to stabilized structural coherence, transfer-compatible organization, and finite geometry-side interpretability. 22-Mar-2026(V1.0) Gamma-DG Core II develops the next central structural layer of Gamma-DG from the temporal nucleus established in Core I. Whereas Core I isolated minimal temporal organization through order, barriers, monotonicity, and lift–descent structure, the present paper formalizes the completion-oriented layer in which structural completion, stabilization, transfer-compatible organization, and geometry-side coherence are treated as intrinsic components of the theory. The purpose is to identify the internal conditions under which ordered Gamma-DG structures become completed, stabilized, and coherently transferable beyond the minimal nucleus. Core II is thus proposed as a reusable and application-neutral theoretical layer linking temporal organization to stabilized structural coherence.