The restricted graph statement

Suppose the remaining operations are constructed in a fixed flat graph prescription, and their normalized coefficients preserve the background independence of Proposition prop:inventory. Suppose also that the normal-ordering and finite insertion terms are specified.

Then the loop coefficient has the form

where $\ell$ depends on the observation, switches, mass, ordering data, and normalization constants, but not on $(h_{\mathrm{cl}},k_{\mathrm{cl}})$.