Graphic showing the connection between the free parameters and the constrained quantities in this study. The free parameters (shown in red) describe the pre-collapse orbit and the CC itself. The constrained quantities (shown in black) are either directly measured or are derived from auxiliary quantities (shown in blue), in which case they need to be treated carefully. The auxiliary post-CC system velocities v_f are directly measured but unconstraining on their own. As a proxy for the inaccessible initial velocity components v_i, we assume that these are consistent with (and can thus be drawn from) the measured velocity dispersion of the birth association V_env of the binary. The components of the net velocity vector Δv are constrained quantities. In the best-case observing scenario, we can obtain 10 distinct parameter constraints from the observations, but there are still 12 free parameters. If we further assume that the pre-collapse orbit was circular (which nullifies the true anomaly ν_i), we reduce the number of free parameters to 10, and the solution can be uniquely determined.