dominates, then the dependence of eq.  on $k$ and ${p_\text{typ}}$ is indeed indicative of the order $Q^{n+1}$. If subsequent terms dominate, the slope may be larger than $n+1$ – but never smaller.

[**Necessary but Not Sufficient**]{} This shows that a slope smaller than $n+1$ conclusively demonstrates failure of the PC to be consistent. However, the criterion is necessary rather than sufficient: Slopes $\ge n+1$ are proof neither of failure, nor of success. Indeed, a PC may be inconsistent but the coefficient of the terms with slope $<n+1$ may be anomalously small, leading to a “false positive”.

[**Estimating the Expansion Parameter**]{} When the cutoffs $\Lambda_1$ and $\Lambda_2$ are both varied over a wide range[^1], the analysis also gives a practical way to find the size of the expansion parameter as a function of $k$. Ratios between different orders estimate $Q(k,{p_\text{typ}})$, and hence residual theoretical uncertainties as function of $k$. This is of course only one way to assess $Q(k)$; within reason, the least optimistic and hence most conservative of several methods should be picked. For example, Ref. [@Griesshammer:2011md] combined this with the convergence pattern of the EFT series; see also [@Furnstahl:2015rha].

[**Choice of Expansion Parameter**]{} In Sect. \[sec:application\], $k$ is varied 