fraction at many values of $q$ including $q=0$, an essential feature of communal pairing theory that is in contrast to the predictions of FFLO theory. This is a direct consequence of considering non-exclusive communal pairing. Secondly, both DMC and communal pairing have a global maximum at $q=q^{}_{\mathrm{FFLO}}$ as this corresponds to the paired fermions being at their respective Fermi levels and thereby minimising their kinetic energy. Finally, both DMC and communal pairing curves exhibit a decay in the condensate fraction for $q>q^{}_{\mathrm{FFLO}}$ which is due to the increasing kinetic energy cost of the fermion pairs.

The quality of agreement between the communal pairing exact diagonalisation results and the DMC data can be quantified by the ratio of the weighted sum of squared deviations of the DMC results from either set of exact results in Fig. \[cfractan\] (azimuthal) or Fig. \[cfraccomp\] (radial), where the weights are the sample variances of the DMC data. This test statistic shows that the DMC results obtained are 27 times better described by an underlying $({N_\uparrow},{N_\downarrow})=(3,1)$ communal state and 38 times better described by an underlying $({N_\uparrow},{N_\downarrow})=(2,1)$ communal state than by FFLO pairing. This provides strong evidence that the state observed in DMC is not only 