Off-origin product

Let

On $z\ne 0$, direct Fourier evaluation gives

At a nonzero null point, $Q_{\mathrm{geom}}$ is a submersion. The boundary value in (eq:rational) has one, rather than both, conormal orientations. Consequently its wavefront covectors at that point cannot cancel pairwise. This is the usual off-diagonal Feynman relation; the product criterion and that relation are described in BDH (Theorem 13 and Proposition 26).