Proposition: Sign audit

The inherited coefficients (eq:ordered-coefficients) give

Proof. The classical terms cancel. The scalar tests and smooth configuration factors in ${{\mathcal{Q}}^{\mathcal{R}}}_{g,f}$ commute, so their order may be changed without exchanging singular distributions. Subtracting the two order-$\hslash$ coefficients gives the factor $-2$ multiplying $K-\overline{K}$. The definition of the imaginary part then gives the factor $-4i$.