Forced Extensional Totalization in Linear Continuum Dynamics

Continuum physical theories represent states as real- or complex-valued fields and dynamics as linear operators on infinite dimensional spaces. When interpreted ontically under explanatory realism, such theories are committed to a semantic closure requirement: admissible physical magnitudes must be denoted, and physical evolution must preserve denotation. The work of Pour-El and Richards shows that even well-posed linear continuum dynamics can violate effective uniformity and computability. In this paper we identify a more elementary semantic obstruction. We present a self-contained construction showing that linear continuum evolution, when coupled to an entirely standard localized averaging readout, can force the aggregation of countably many independent contingencies into a single demanded real-valued magnitude. The resulting scalar is extensionally equivalent to the halting real. Under any admissible semantics, its specification is non denoting, since approximating it to arbitrary precision requires forced extensional resolution of a non-total predicate. The construction uses only smooth, compactly supported, finite-energy initial data for the three-dimensional wave equation and does not rely on function-space semantics, regional statehood assumptions, or modulus-of-continuity arguments. It therefore establishes a minimal semantic obstruction for ontic readings of continuum dynamics, isolating forced extensional totalization as the operative mechanism behind failures of semantic closure.