perturbatively renormalised in the EFT sense. There is no decrease from NLO to [N${}^{2}$LO]{} when $H_2\equiv0$. That by itself could be accidental – after all, would one not expect better convergence with one more parameter to tune?

More informative is a look at the slopes. Lines at different orders are near-parallel for small $k$ because there are additional natural low-energy scales ${p_\text{typ}}$, namely the binding momenta of the deuteron ($\gamma_t\approx45\;{\ensuremath{\mathrm{MeV}}}$) and of the virtual singlet-S state ($\gamma_s\approx8\;{\ensuremath{\mathrm{MeV}}}$). For $k\lesssim\gamma_{t,s}$, eq.  is not very sensitive to $k$, so all slopes should be small and near-identical. However, when $k\gg\gamma_{t,s}$ (but of course still $k\ll{\overline{\Lambda}_{\slashed{\pi}}}$, so that the EFT converges), they converge towards one region.

Indeed, the fits of $n$ to the nearly straight lines in the momentum range between $70$ and $100$ to $130\;{\ensuremath{\mathrm{MeV}}}<{\overline{\Lambda}_{\slashed{\pi}}}$ compare well to the PC prediction when $H_2$ is added at [N${}^{2}$LO]{} [@improve3body]: $$\label{eq:3Ntab}
  \begin{tabular}{c@{{\hspace{0.5ex}}}|@{{\hspace{0.5ex}}{\hspace{0.5ex}}}c@{{\hspace{0.5ex}}{\hspace{0.5ex}}}c@{{\hspace{0.5ex}}{\hspace{0.5ex}}}c@{{\hspace{0.5ex}}{\hspace{0.5ex}}}|@{{\hspace{0.5ex}}{\hspace{0.5ex}}}c}
    & LO&NLO&{N\ensuremath{{}^{2}}LO\xspace}&{N\ensuremath{{}^{2}}LO\xspace} {without $H_2$}\\    \hline
    {$n+1$} fitted &${\sim 1.9}$&{$2.9$}&{$4.8$} [\emph{sic!}]&${3.1}$\\    {$n+1$} predicted &${2}$&{$3$}&{$4$}&not renormalised
  \end{tabular}$$ Without $H_2$ at [N${}^{2}$LO]{}, the slope does not improve from NLO. This is a clear signal that the PC is inconsistent without a momentum-dependent $3N$ interaction at [N${}^{2}$LO]{}: Its assumptions do not bear out in the functional behaviour 