The Boundary-Transition Domain INTERFACE, THRESHOLD, AND LAWFUL PASSAGE IN THE ONTOLOGY OF COHERENT CLOSURE

This paper develops the boundary-transition domain within the Ontology of CoherentClosure and argues that boundary and transition must be understood jointly rather than inisolation. Boundary concerns the lawful conditions of separation, interface, containment,threshold localization, and differentiated structure. Transition concerns the lawful conditions ofpassage, crossing, bifurcation, transfer, and regime change relative to such boundaries. The paper proposes that these two aspects form a unified ontological field: the boundary-transition domain.Within this framework, the paper distinguishes two principal wings of the domain. The boundarywing includes threshold boundaries, interface boundaries, containment boundaries, topologicalboundaries, and ontological boundaries. The transition wing includes threshold transitions,scaling transitions, symmetry transitions, phase transitions, basin transitions, and ontologicaltransitions. The paper further argues that each wing contains its own internal hierarchy ofdescriptor types: parameters, invariants, and constants. This internal hierarchy mirrors thebroader constants ontology and suggests that major ontological domains may locally reproducethe structure of the whole. A central claim of the paper is that boundary constants govern where lawful passage becomespossible, while transition constants govern how lawful passage occurs relative to such boundaries.Feigenbaum structure is treated as the clearest initial exemplar of a transition-constant family,while the Coulomb barrier is reinterpreted as the atomic appearance of a more general coherencediscontinuity. This reinterpretation allows a familiar physical barrier to be understood as a localexpression of a deeper ontological boundary condition. The aim of the paper is not merely classificatory. It is to show that structured separation andlawful passage are universal features of generative reality, and that their parameters, invariants,and constants belong to a distinct domain within the ontology of coherent closure. In this sense,the boundary-transition domain becomes the field in which differentiated structure and regimepassage first become jointly intelligible.