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As mentioned previously, the argument that the disk model fails to adequetely describe the data depends on the extent to which the selection cuts adequately exclude edge-on and out-of-phase disks from our SDSS sample, if such things exist. This argument can be summarized by the claim that it would be difficult to observationally distinguish an edge-on rotating disk from an oppositely-aligned pair rotating in the line-of-sight direction. Previously, we had assigned a charactaristic velocity of 100 km/s to the satellites and only cut on satellites that have 1D velocity offset less than $\sqrt{2} \times 25$ km/s. Since the toy model is essentially scale-free, this is equivalent to cutting on satellites that have a 1D velocity offset less than $\sqrt{2} \times 25\%$ of the charactaristic 3D velocity for satellites of the host, i.e. a velocity threshold of $0.25 \times V_0$ is applied, where $V_0$ is the charactaristic 3D velocity of the satellites.   Figure \ref{fig:cuts} shows how the shape of the 90\% isotropic disk sample changes when this velocity threshold changes. The lines in the figure span from cutting on 10\% of the 3D velocity to cutting on 80\% of the 3D velocity. Overplotted is the SDSS data; it is apparent that reproducing the lack of signal at $\sim 20^{\circ} \, \lt \alpha \, \lt \sim 60^{\circ}$, or correspondingly the sharpness of the upturn at very small $\alpha$, requires a very high velocity threshold, cutting on 60-80\% of the characteristic velocity. Since we impose a cut of $\sqrt{2} \times 25$ km/s on our data, this would lead us to hypothesize a characteristic 3D velocity of $\sim 60$ km/s or lower for the SDSS satellite population. If this were to be the case, then we would expect the systems selected to be sufficiently edge-on to account for the lack of signal detected at $\alpha \sim 30^{\circ}$, however the figure indicates that this is not the case. Rather, the mean 1D velocity of the SDSS satellites is 111.4 km/s and the mean 1D velocity of the 25 (?) 22  pairs with $\alpha \lt 10^{\circ}$ is 109.4 km/s, consistent with the overall sample. This seems to indicate that a velocity cut of $\sqrt{2} \times 25$ km/s would be insufficient to isolate only edge-on planes, and if such systems existed, planes of moderate inclination would be seen in the data. Since they are not, we disfavor the idea that the data supports the ubiquity of corotating planes in SDSS in satellites brighter than r = -16.