Notes of Note {#sec:notesofnote}
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With this example in mind, let us consider assumptions, strengths, extensions, features, caveats and limitations of such an analysis to assess the consistency of a PC proposal.

Matters of Principle {#sec:principle}
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[**Renormalisation Group Evolution**]{} Multiply eq.  by $(\Lambda_1-\Lambda_2)/\Lambda_1$ and take $\Lambda_2\to\Lambda_1$: $$\label{eq:rge} \frac{\Lambda}{{\mathcal{O}}}\;\frac{{\mathrm{d}}{\mathcal{O}}}{{\mathrm{d}}\Lambda}=
  \left(\frac{k,{p_\text{typ}}}{{\overline{\Lambda}_\text{EFT}}}\right)^{n+1}
  \;\frac{{\mathrm{d}}\ln{\mathcal{C}}_n(\Lambda)}{{\mathrm{d}}\ln\Lambda}\;\;.$$ This is Wilson’s Renormalisation Group Equation for the observable ${\mathcal{O}}$. Note that eq.  features a *total* derivative: LECs in ${\mathcal{O}}$ are readjusted as $\Lambda$ changes.

In practise, an EFT at finite order $n$ and with finite cutoff tolerates cutoff artefacts which are parametrically small, i.e. at least of order $n+1$. This also limits the rate of change in the residual ${\mathcal{C}}_n$: I call an observable “perturbatively renormalised” when the right-hand side of eq.  is smaller than any term on the left-hand side. To some, this condition implies $\Lambda$ can only be varied in a range around ${\overline{\Lambda}_\text{EFT}}$; the functional dependence on $k$ and $n$ is then still a quantitative prediction. A double-logarithmic plot reveals quantitative aspects of the Renormalisation Group evolution and can be utilised to falsify claims of consistency in an EFT.

[**Extending the Expansion**]{} The order $n$ is not counted relative to LO. It is not even 