Physics of Difference VII: Global Persistence of Realization-Dependent Distinction under Local Reduction

This work investigates obstruction to globally compatible reduction within realization accessibility semicategories equipped with locally defined reduction systems.The central problem addressed is whether locally compatible reduction necessarily eliminates realization-dependent distinction under global transition accessibility composition. The analysis shows that, in general, it does not.To investigate this phenomenon, the framework introduces:• realization accessibility semicategories,• accessibility patches,• local reduction tolerance systems,• transition accessibility relations,• and relational cocycle compatibility conditions.Unlike conventional quotient constructions, reduction organization is formulated locally without assuming globally transitive equivalence compatibility. Consequently, locally admissible reduction systems may fail to remain globally compatible under successive transition accessibility composition.A global relational consistency criterion is established showing that globally compatible reduction exists if and only if relational cocycle compatibility holds globally. Failure of this condition generates residual accessibility obstruction under closed accessibility composition.Explicit finite realization accessibility systems exhibiting:• local reduction compatibility,• relational cocycle incompatibility,• and globally persistent residual accessibility structureare constructed concretely.The resulting framework exhibits formal similarities to cocycle obstruction theory, sheaf-type gluing failure, and holonomy-like residual organization while remaining entirely relational and pre-geometric.The central conceptual consequence is therefore the following:realization-dependent distinction need not disappear globally even when every local accessibility patch individually admits compatible reduction.Residual accessibility organization may survive reduction as a genuinely global compositional phenomenon arising directly from incompatibility between local reduction organization and global accessibility composition.