Manuscript V@1 · V.tex · section · e7ddf37d

Contrast: the Newton–wave cubic form

Contrast: the Newton–wave cubic form · lines 3035–3079

The object in this section is not a retarded product. It is obtained by first inserting a classical scalar stress into a specified nonlocal metric inverse, then applying the fixed-time scalar response, and finally fully Wick ordering the resulting cubic kernel.

	External or finite-mode $R_{1, 1}$	Newton–wave $C_{f}^{(3)}$
Metric	Prescribed $h$ or $Q e + Π r$	Reconstructed $R^{A}_{t_{0}} T (ϕ)$
Quantum degree	One, or mixed two	Three
Kernel issue	Two-point contractions, $sd \leq 3$	Newton transfer $1/∣ q ∣^{2}$
Extension	Unique coefficientwise minimal extension	Locally integrable fully Wick kernel
Witness	Vacuum–one-particle or coherent displacement	Vacuum–three-particle away from transfers
Time control	Compact switch $g$	Sharp $t_{0}$ ; separate response-edge regulator
Bilinear comparison	Mixed coefficient equals switched bilinear	A different composed observable

We provide the definitions and kernel estimates needed for this contrast, rather than invoking a result from a companion manuscript.