Abstract

We formalize a general semantic constraint on physically admissible procedures, namely, that discrete outcomes must exhibit bounded input dependence, meaning that each outcome is certified by a finite stability margin in the underlying real valued state. 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 and dense complement, are operationally unresolvable under admissible physical semantics. Computability of real numbers provides a canonical example. The sets of Type-2 computable and noncomputable real numbers are both dense in the real line, so computability is not an operationally extractable property of a real magnitude. At the same time, every open neighborhood of the real line contains computable real numbers. Thus computable values form an operationally complete set of representatives for the continuum under bounded-input-dependent interfaces. Restricting ontic magnitudes to computable values therefore removes no distinctions that can participate in admissible physical readout. The result provides a semantic and operational motivation for aligning ontic commitments with computable magnitudes in realist physical theories.