on $n$ and ${\overline{\Lambda}_\text{EFT}}$ do not depend on $\Lambda_1$ and $\Lambda_2$. While any two cutoffs $\Lambda_1,\Lambda_2\gtrsim{\overline{\Lambda}_\text{EFT}}$ will do in principle, small leverage may lead to numerical artefacts. The larger $\Lambda_2-\Lambda_1$, the clearer the signal should be. For our example, Fig. \[fig:nonLepage900MeV\] shows that an upper cutoff of $900\;{\ensuremath{\mathrm{MeV}}}$ instead of $600\;{\ensuremath{\mathrm{MeV}}}$ leads to different curves but very similar slopes. Infinities, zeroes and oscillations of ${\mathcal{O}}$ with $k$ for any pair $\Lambda_1,\Lambda_2$ can lead to problems (see “*Observables: Accidental Zeroes and Infinities*” below) which are readily avoided by choosing a cutoff pair such that ${\mathcal{O}}(\Lambda_1)-{\mathcal{O}}(\Lambda_2)>0$ for all $k$. Even when one does not choose to take one of the cutoffs to infinity[^2], a reasonable range of allowed cutoffs exists. If $\Lambda_1\approx\Lambda_2$, one may of course directly consider the numerical derivative of eq.  – over a range of cutoffs. \[To reiterate: exact cutoff independence ${\mathcal{O}}(\Lambda_1)\equiv{\mathcal{O}}(\Lambda_2)$ for any cutoff pair is not considered.\]

![\[fig:nonLepage2\] \[fig:nonLepage900MeV\] \[fig:EREvsZ\] *Left*: Thick coloured lines: Z-parametrisation of the $\mathrm{NN}$ amplitude as in Fig. \[fig:nonLepage\], but for $\Lambda_1=900\;{\ensuremath{\mathrm{MeV}}}$, not $600\;{\ensuremath{\mathrm{MeV}}}$; thin gray lines: Bethe’s Effective Range Parametrisation; from Ref. [@improve3body]. \[fig:toB3\] *Right*: Test when the leading $3N$ interaction is determined not by the $Nd$ scattering length as in Fig. 