Definition and normalization

The response (eq:k1) follows from (eq:vertex) and (eq:grgreen); its factor $-2$ is not adjusted by a Wick convention. The tree is the isolated order-${\hslash }^0$ retarded contraction along the graviton slot of the first observable coefficient. It is not a definition of the full retarded product.

The polynomial $\tau$ is background independent. No free graviton letter survives in it.