Abstract
Whether observation dynamics can leave distinct matter records under identical physical initial conditions and subsequent external forcing depends on three questions: whether observation initial states have a well-defined identity, whether they can be prepared, and whether their evolution satisfies the common field equations. We construct a local realization within the existing five-dimensional response space and quadratic common action of PODA. With spatial and temporal references fixed, primitive response transport yields nonzero mixed curvature and identifies the observation coordinate through distinguishable comparison records; the image of its field data is an invariant subspace of the transverse dynamics. The field restoring force and a nonzero current overlap allow a single matter input to prepare arbitrary sufficiently small joint initial states. An explicit eighth-degree polynomial protocol carries the state initially at rest to two final states with identical matter position, matter velocity, and observation configuration, but opposite observation velocities. The input vanishes continuously at both endpoints, and the net work equals the stored energy. After release, the two-frequency displacement and the observation comparison probability obey a common integral identity. We also derive propagation relations for initial-state mismatch, finite readout precision, and control-waveform errors, and retain the complete calculations for matter sources, the one-loop relativistic response, and indirect tests involving common parameters. The result is an existence theorem for preparation and response in the specified local realization, within the stated quadratic dynamics and external matter-source model.