stark difference between the proper motions of the two populations in Fig. \[fig:sgr\_pms\].

We also show the heliocentric distances of the Sgr stars as a function of Sgr Longitude in the top panel of Fig. \[fig:sgr\_pms\]. Again, there is excellent agreement with the [@law10] models. This figure shows that we can probe the Sgr proper motions out to $D \sim 50$ kpc, and thus we can accurately trace halo proper motions out to these distances (see Section \[sec:res\]).

In Fig \[fig:pm\_comp\] we zoom in on the regions along the Sgr stream where proper motions have been measured previously in the literature. Here, the agreement with the other observational data is even clearer. In particular, our Sgr leading arm proper motions at $ 240^\circ \lesssim \Lambda_\odot \lesssim 360^\circ$ are in excellent agreement with the *HST* proper motions measured by [@sohn15]. This is a wonderful validation of two completely independent astrometric techniques! Note that the Sgr stream is not the focus of this study, but the proper motion catalog we present here is a useful probe of the stream dynamics. For example, the slight differences between the [@law10] model predictions and our measurements could be used to refine/improve models of the Sgr 