[Force softening]{} & $N_{halo,{\textsc{subfind}}}$ & $N_{halo,{\textsc{hbt}}}$ & $N_{halo,{\textsc{ahf}}}$ & [$N_{sub,{\textsc{subfind}}}$]{} & [$N_{sub,{\textsc{hbt}}}$]{} & [$N_{sub,{\textsc{ahf}}}$]{}\
& [$h^{-1}{\rm Mpc}$]{} & [$h^{-1}{\rm M_\odot}$]{} &[$h^{-1}{\rm kpc}$]{}& $\ge300$ & $\ge300$ & $\ge300$ & $\ge300$ & $\ge300$ & $\ge300$\
BoxLo &8 &$2.1\times10^{6}$ &1.25 &1136 &- &- &213 &- &-\
\
BoxA\_S1&8 &$2.6\times10^{5}$ &0.04 &6589 &6698 &6775 &1934 &2169&1460\
BoxA &8 &$2.6\times10^{5}$ &0.63 &6651 &6587 &6798 &1651 &1899&1216\
BoxA\_S2&8 &$2.6\times10^{5}$ &1.25 &6585 &6476 &6529 &1388 &1618&944\
\
BoxB &20 &$4.1\times10^{6}$ &1.56 &8923 &8785 &9139 &2111 &2494&1302\
BoxC &50 &$6.5\times10^{7}$ &3.91 &12791 &12533&12874&2687 &3325&1597\
BoxD &100&$5.2\times10^{8}$ &7.81 &17562 &17053&16901&3072 &3949&1737\
&&&&$\ge2400$ & $\ge2400$ &$\ge2400$ & $\ge2400$ & $\ge2400$ & $\ge2400$\
BoxA&&&& 1132 &-&-&215&-&-\

This higher particle number threshold is used to compare with BoxLo over the same halo mass range.

Theory {#sec:theory}
======

The dimensionless spin parameter indicates how much a collection of particles is supported by the angular momentum against gravitational collapse assuming gravitational equilibrium, where a negligible spin parameter represents minimal support, while the value for a completely supported system depends on the chosen parametrisation. There are two standard parametrisations defined by @peebles_1969 and @bullock_2001, respectively, that we describe in the following two sections.

@hetznecker_2006 showed that Bullock’s parametrisation is less dependent on redshift evolution than 