Meaning of the example

On this specially chosen harmonic family, the classical coefficient reduces to a cubic source-response expression:

This restricted reduction is a consequence of the explicit vanishing of $w,v,h,{\varphi }_1$ in the calculation. It is not a universal identification of a relational second-order observable with a Newton-inverse cubic.

In particular, it does not identify:

1. a classical coefficient with a Wick-ordered composite;

2. a scalar-source reconstruction with an independent graviton field;

3. the displayed coefficient with a complete interacting second-order quantum field;

4. a nonzero classical value with a scheme-independent radiative response.

If the source is replaced by zero while the prescribed homogeneous metric data and scalar correction data are also set to zero, then $j={\varphi }_2=0$. This is the exact source-off control for the family. Removing an interaction switch in another model is not this operation.

Figure fig:VI-sourced-positive displays the nonzero classical coefficient and its exact source-off control.