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\subsubsection{COP model}  Figure \ref{fig:bells} shows the same information as Figure \ref{fig:disks} with the disk model being replaced by the COP model. Due to the strong constraints of the model, the pure COP corotation fraction model is undefined over much of the regime (satellite pairs separated by e.g. 60 degrees $60^{/circ}$  simply do not exist no matter how the model is rotated), therefore we do not plot it. Instead, we plot only the 50\% isotropic and 90\% isotropic cases, both of which are in quite good agreement with the SDSS data. This agreement is particularly notable at small $\alpha$, where the sharp dropoff in corotating fraction at $\alpha \sim 10^{\circ}$ is captured by the model. Whether or not the COP model is physical will be discussed at length in \ref{sec:Discuss}; we claim that the COP model is the better fit to the kinematic data than the disk model. \subsection{Velocity Modeling and Cuts}