Domains, Boundaries, and Transition Functions: On the Domain-Relative Validity, Migration, and Coupling of Models under Finite Conditions

Models are often treated as though they were generally valid or readily transferable to other contexts. This leads to misapplications, apparent contradictions, and forms of model overextension. By contrast, this paper develops a domain-based perspective within Epistemics as model management under finite conditions. Domains are not presupposed as given regions but are understood as functionally reconstructed spaces of order with their own functional logic, their own conditions of stability, and their own criteria of validity.Against this background, the paper investigates how models encounter stability problems at domain boundaries, under what conditions they can be transferred between domains, and why such transfers require adaptation. Transition functions are thereby determined as conditions of functional connectivity. Model migration accordingly appears as a process of transformation, and model overextension as a boundary violation.Moreover, the paper shows that the viability of a model depends not only on its internal structure but also on its domain coupling. A model can be stable within one domain and simultaneously fragile across domains. Falsification therefore appears not only as an intra-domain test of a model but also as an indication of transition problems, unstable domain couplings, or insufficiently specified domain boundaries.The theoretical contribution of the paper lies in an integrated architecture of domain-relative model validity. Domains, boundaries, transition functions, model migration, model overextension, domain coupling, and falsification are related to one another within a common framework. In this way, model validity becomes determinable not as general or universal, but as domain-relative, boundary-dependent, and transition-bound.