Bounded Input Dependence and the Non-Observability of Computability

We formalize a general semantic constraint on physically admissible procedures: discrete outcomes must exhibit bounded input dependence, meaning that determinate outcomes are supported by finite stability margins in the underlying state space. We prove that any such procedure can discriminate only properties corresponding to open regions of state space. Properties whose truth sets are topologically thin, having empty interior with dense complement, are operationally unresolvable under admissible physical semantics. This limitation is structural rather than computational. It arises from topological constraints induced by stability at the semantic interface and applies uniformly across continuum ontologies. Stability is shown to be preserved under lawful continuous dynamics, implying that thin distinctions cannot be amplified into operational differences by finite physical evolution followed by admissible readout. Computability provides a canonical representative example. Computable and noncomputable elements form interwoven dense subsets of continuum domains, so computability is not a topological property of states but a property of representation structure. As such, it cannot be operationally extracted by bounded-input-dependent procedures. Restrictions motivated by bounded input dependence thus express ontological parsimony: they eliminate distinctions incapable of supporting stable physical discrimination. The result provides a semantic foundation for aligning ontological commitments with structurally admissible distinctions in realist physical theories.