The correct charged ordering identity

For the neutral real scalar, this reduces to

The sign agrees with the spectral convention in the supplied I-B-G and I-B-VP records CheungIBG,CheungIBVP.

Let ${\mathcal{G}}^{-}=-{\mathcal{G}}^{+}$ and ${\mathcal{D}}_{\mathrm{ap}}^{-}=-{\mathcal{D}}_{\mathrm{ap}}^{+}$, where the minus sign negates cotangent fibers without changing base points.