Abstract

We formulate prescription independence at the response level and complete the three-stage construction for one explicitly declared free-field benchmark. The source and readout are the vacuum-centred Wick square of a massless scalar on four-dimensional Minkowski spacetime. At first order in a compact external source, the complete connected vacuum susceptibility has a punctured retarded kernel $\hslash \Theta (t){\delta }^{\prime }(t^2-|\mathbf{x}{|}^2)/(4{\pi }^3)$.

A locally integrable logarithm gives an explicit retarded extension. Reality, translation covariance, agreement away from coincidence, and scaling degree at most four imply that every admissible normalization differs by exactly $\hslash c{\delta }_0$. Thus the complete response ambiguity is determined, rather than inferred from two regulators. We construct an admissible annular test whose pairing is exactly $-\hslash t_0/(2{\pi }^2)$ for every prescription, and provide a single delayed source/readout experiment with a rigorously nonzero response.

We also prove the general observable-descent criterion, its test-determined topological separation condition, reconstruction descent, and a finite-bank certificate that remains valid when the underlying ambiguity is infinite-dimensional. Calibration, minimum-variance weights, regulator smoothing, and imperfect annihilation are treated separately.

The benchmark is not the reflected triangle of VII-D and is not the unresolved gravitational characteristic coefficient. The latter construction remains open on the supplied data. Classical admission, the nonzero auxiliary remainder of XII-F, and finite instruments in VII-G are not substituted for that missing quantum response.