Forced Extensional Totalization in Linear Continuum Dynamics

Continuum physical theories model states as real- or complex-valued fields and dynamics as linear operators on infinite dimensional spaces. Under explanatory realism, an ontic interpretation incurs two semantic commitments: (i) real-valued physical magnitudes must denote relative to the theory’s admissible state interface, and (ii) the theory must be semantically closed under its own evolution and readout rules. Denotation is interface-relative: it requires the existence of a total continuous witness on names. Equivalently, it requires bounded input dependence at each fixed finite precision. Failure of bounded input dependence is captured by forced extensional totalization (FET), in which even coarse output precision cannot be stabilized by any finite prefix of a state name. We give a physics-facing construction of FET for the three-dimensional wave equation with Kirchhoff point readout. We construct a countable family of smooth, compactly supported, finite-energy initial states localized on pairwise disjoint shrinking latitude belts on the Huygens sphere, and restrict the admissible domain to states containing at most one localized contingency. Each nonzero belt perturbation is normalized to contribute the same order-one amount to the readout, while the zero state contributes none. Under any non oracular state interface satisfying a minimal locality-of-access condition, no finite prefix can rule out activation of some sufficiently deep belt. The induced point readout therefore behaves like the existential predicate "some belt is active'', exhibits FET at the zero state, and fails to denote. Semantic closure fails: the evolution-readout pipeline yields a localized point magnitude that is non-denoting relative to the fixed state interface. The result isolates a semantic obstruction to ontic readings of continuum dynamics. It is independent of computability, predictability, or measurement feasibility, and it holds despite smooth compact support, finite energy, and classical well-posedness.