Abstract

We develop a local spacetime-Enter adaptation of the fixed-time scalar-response problem of Manuscript V. The central analytical finding is an exact separation between two obstructions: the complete distributional Ward defect controls raw compact-current representability, whereas its causal propagation controls representability after a harmonic prescription. Initial-surface terms are retained explicitly. A compact-Cauchy residual wave makes the obstruction nonzero on an open dense family of smearings, while compact curvature currents nevertheless interpolate the same response on every declared two-dimensional transverse-traceless plane whose separating region is admitted.

A separate calculation constructs the first retarded coefficient of the compactly switched minimal scalar vertex. Its external-metric version is linear in the scalar field, has coefficientwise scaling degree below four, and has no minimal-extension ambiguity. The one-oscillator version is a mixed quadratic operator with a proved essentially self-adjoint real polynomial realization. A distinct Newton–wave composition has a symmetric cubic Wick form with a joint ultraviolet, transfer, and initial-edge cutoff limit. A regular-region witness distinguishes states agreeing on all polynomial forms of degree at most two.

The operational contribution is an exact, reference-preserving finite instrument obtained by compressing the represented responses and cubic forms before destructive clock readout. For the cubic witness this gives an explicit qubit experiment. This connects admissibility and form-level distinctions to a complete finite readout without identifying them with a continuum field apparatus. Its potential value is methodological: it prevents classical descent, operator representation, and recorded response from being conflated.

The cone, external schedule, flat continuation, vacuum, and Newton prescription are declared inputs. No global conical Green theorem, intrinsic Newton inverse, derived spacetime, Einstein dynamics, or inherited characteristic quantum coefficient is claimed.