down-spin fermion, the crystalline FFLO ground state is the most stable out of these, in line with previous results [@fflorevision1; @fflorevision2], with the condensate fraction equally shared by all symmetry related pair momentum vectors at this magnitude, as seen in [Fig. \[cfractan\]]{}. In the specific system studied here, $q^{}_{\mathrm{FFLO}}=2G$, as seen in Fig. \[cfraccomp\]. To make a fair comparison between the DMC and exact diagonalisation results, we have normalized the condensate fraction obtained from exact diagonalisation so that the weighted squared deviation from the DMC results is minimized.

![Plot of normalised condensate fraction $f^{}_{\mathrm{norm}}$ obtained using DMC averaged over $q$ (red) and condensate fraction predicted using exact diagonalisation of the states beneath the respective Fermi surfaces assuming $({N_\uparrow},{N_\downarrow})=(2,1)$ (blue), $({N_\uparrow},{N_\downarrow})=(3,1)$ (green) and normal FFLO pairing with $({N_\uparrow},{N_\downarrow})=(1,1)$ (grey) against $q$. The dashed black line marks out $q=q^{}_{\mathrm{FFLO}}$, the optimal magnitude of pairing momentum as predicted by FFLO theory and the only point on the FFLO curve where $f^{}_{\mathrm{norm}}\neq0$.[]{data-label="cfraccomp"}](cfraccompmin3){width="0.9\linewidth"}

If instead communal pairing is considered, the results obtained from exact diagonalisation of both $({N_\uparrow},{N_\downarrow})=(2,1)$ and $(3,1)$ are quantitatively similar to those obtained from DMC, with both sets of results exhibiting three key features. First and foremost, both have a nonzero condensate 