order $Q^n$ in an EFT: $$\label{eq:observable}
  {\mathcal{O}}(k,{p_\text{typ}};\Lambda;{\overline{\Lambda}_\text{EFT}})=
  \sum\limits_i^n\left(\frac{k,{p_\text{typ}}}{{\overline{\Lambda}_\text{EFT}}}\right)^i
  {\mathcal{O}}_i(k,{p_\text{typ}};{\overline{\Lambda}_\text{EFT}})\; +\;{\mathcal{C}}_n(\Lambda;k,{p_\text{typ}},{\overline{\Lambda}_\text{EFT}})\left(\frac{k,{p_\text{typ}}}{{\overline{\Lambda}_\text{EFT}}}\right)^{n+1}$$ \[Non-integer $n$ and non-integer steps from one order to the next will be discussed in Sect. \[sec:principle\].\] The notation indicates that numerators may depend on both $k$ and ${p_\text{typ}}$. In a properly renormalised result, effects attributed to a regulator $\Lambda$ appear only at orders which are higher than the last order $n$ which is known in full. The residual ${\mathcal{C}}_n(\Lambda;k,{p_\text{typ}},{\overline{\Lambda}_\text{EFT}})$ may still depend on ${\overline{\Lambda}_\text{EFT}}$, $k$ and ${p_\text{typ}}$, but it should be of natural size for all $k,{p_\text{typ}}<{\overline{\Lambda}_\text{EFT}}$, so that its contribution is parametrically suppressed by $\left(\frac{k,{p_\text{typ}}}{{\overline{\Lambda}_\text{EFT}}}\right)^{n+1}$ relative to the known terms of the series. If not, cutoff variations produce corrections which are comparable in size to the regulator-independent terms ${\mathcal{O}}_i(k,{p_\text{typ}};{\overline{\Lambda}_\text{EFT}})$ and contradict the EFT assumption that higher-order corrections are parametrically small.

The relative difference of ${\mathcal{O}}(k,{p_\text{typ}};\Lambda)$ at any two cutoffs is then: $$\label{eq:master}
  \frac{{\mathcal{O}}_n(k,{p_\text{typ}};\Lambda_1)-{\mathcal{O}}_n(k,{p_\text{typ}};\Lambda_2)}
  {{\mathcal{O}}_n(k,{p_\text{typ}};\Lambda_1)}=\left(\frac{k,{p_\text{typ}}}{{\overline{\Lambda}_\text{EFT}}}\right)^{n+1}
  \times\;\frac{{\mathcal{C}}_n(\Lambda_1;k,{p_\text{typ}},{\overline{\Lambda}_\text{EFT}})-
    {\mathcal{C}}_n(\Lambda_2;k,{p_\text{typ}},{\overline{\Lambda}_\text{EFT}})}
  {{\mathcal{C}}_n(\Lambda_1;k,{p_\text{typ}},{\overline{\Lambda}_\text{EFT}})}\;\;.$$ One can now vary $k$ or ${p_\text{typ}}$ to read off both the order $n$ to which the calculation is complete and the breakdown scale ${\overline{\Lambda}_\text{EFT}}$ – if the cutoff behaviour cannot be eliminated in its entirety, i.e. ${\mathcal{C}}_n(\Lambda_1)\ne{\mathcal{C}}_n(\Lambda_2)$ for at least some cutoff pairs, and if the residuals ${\mathcal{C}}_n$ vary more 