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tokens: TESTING <sc>binulator</sc>+<sc>gravsphere</sc> ON MOCK DATA In Section 4.1 , we introduced an updated version of the gravsphere code (Read Steger 2017 ; Read et al. 2018 ) with a new reworked binning method, the binulator . In this Appendix, we present tests of the new code on mock data drawn from the Gaia Challenge 2 spherical and triaxial suite (Read et al. 2021 ). We focus on two mocks that were particularly challenging for the previous version of gravsphere : PlumCuspOm and PlumCoreOm. The former is a Plummer sphere embedded in a spherical, cuspy dark matter halo; the latter is the same embedded in a dark matter halo with a central constant density core. In both cases, the velocity dispersion profile is isotropic at the centre and maximally radially anisotropic at large radii. Both mocks are described in detail in Read et al. ( 2021 ). Here, we model both assuming Gaussian velocity errors on each star of 2 km s −1 for 100, 1000, and 10 000 randomly sampled kinematic tracers. We assume that the photometric light profile is in all cases well sampled with 10 000 stars, similarly to the situation with real data for nearby dsPh galaxies (e.g. Read et al. 2019 ). Previously, gravsphere struggled on these mocks. For both PlumCoreOm and PlumCuspOm with 1000 tracers, it returned a dark matter density that was systematically low for , shifting, however, to for 10 000 tracers. The velocity anisotropy was well recovered in all cases, except PlumCoreOm for which 1000 tracers were insufficient to detect the radial anisotropy at large radii (Read et al. 2021 ). In Gregory et al. ( 2019 ), gravsphere was tested on mock data for fewer tracers (20, 100, and 500 tracer stars). There, a similar bias towards low densities at large radii was reported. We show results applying the updated gravsphere with its new binulator binning module to the PlumCoreOm and PlumCuspOm mocks in Fig. A1 . In all cases, we obtain an unbiased recovery of both the dark matter density profile, , and the symmetrized stellar velocity anisotropy, . The code is no longer biased to low density at large radii. This owes to a combination of the improved data binning, the proper inclusion of the full error PDF for the virial shape parameters, and to our switch to using the coreNFW profile (recall that the non-parametric power-law-in-bins profile used previously by default in gravsphere biases models towards falling very steeply at large radii in the absence of data). Notice that now, even with just 100 tracers, we are able to detect that the PlumCuspOm is denser and falls more steeply than PlumCoreOm. For PlumCuspOm, we are also able to weakly detect that the velocity distribution is radially anisotropic at large radii. As we move to 1000 and 10 000 tracers, we obtain an increasingly high-fidelity recovery of both the density profile and the velocity anisotropy. Figure A1. Testing the updated gravsphere code and its new binulator module on spherical mock data from the Gaia Challenge suite.