Constructive Organizational Coupling Theory: Toward Interacting Frozen Organizational Architectures

This paper develops a constructive theory of coupling between frozen organizational architectures as Paper X of the Organizational Field Theory research program. The inherited forward and inverse layers are held fixed: coupling may extend relational structure, but it may not rewrite the configuration spaces, dependency records, genealogies, observation maps, or admissibility conditions of either parent. The construction begins with a compatibility domain and proceeds through realizable interfaces, coupling configurations, parent-preserving coupling maps, joint dependency and genealogy structures, coupled observation, exact and tolerance recovery fibres, and structural stability. Existence and uniqueness statements are formulated only under explicit realizability, factorization, and perturbation assumptions; compatibility alone is not treated as sufficient for a physical or mathematical interaction. A finite directed-graph example demonstrates how an admissible cross-parent relation can be added while preserving both ancestral subgraphs and how observational degeneracy can remain after coupling. The resulting framework separates compatibility, realized coupling, observation, reconstruction, and stability, and it identifies the audit data required at each layer. The theory is representation-independent in the stated constructive sense and is deliberately restricted to frozen organizations. Time-dependent coupling, bifurcation, reorganization, and emergence are reserved for Paper XI.