Structural Conditions for Semantic Termination in Statistical Systems

This paper defines the formal structural requirements for the Invariant Constraint Kernel (ICK), the constraint-governed substrate required for semantic termination in AI inference architectures. Building directly on the Taxicab Condition and the τ-operator introduced in Termination as a Condition for Semantic Resolution in Statistical Systems (Zenodo: 10.5281/zenodo.20034316), this paper specifies the internal geometry of the ICK as a constrained structural space composed of three primitive classes: Invariant Equivalence Classes, Relational Constraint Structures, and Terminal Invariant Subsets. The central result is a formal proof of the categorical distinction between local admissibility and global admissibility—showing that a dependency path may terminate relative to a local anchor while failing global admissibility. A second result establishes that global admissibility requires convergence of all terminating dependency paths to a unique invariant anchor. These results define the boundary conditions for any architecture seeking to enforce structural admissibility by design rather than by behavioral tuning. Builds on the Modal–Dependence Calculus (MDC): 10.5281/zenodo.19704166.