Open-Set Constraints on Ontology in Continuum Theories

This paper establishes a general semantic constraint on physical ontology in continuum theories under explanatory realism and finite-information access. Working in the framework of represented state spaces, we show that ontic predicates must define open stability regions in the representation topology. Predicates defined by exact equalities, lower-dimensional subspaces, digit-level conditions, or algorithmic properties are therefore structurally non-denoting, even though they are mathematically well defined. Ontic structure in continuum physics must take the form of robust stability regions rather than sharp boundary conditions. The result is theory-agnostic and applies to any physical framework whose states are modeled in continuum spaces and accessed through finite procedures. Bounded input dependence emerges as the operational manifestation of this topological constraint.