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Jet resolution variables The small-angle behaviour of the resolution variables $d_{kB}$ and $d_{kl}$ given in equations 1 and 2 controls the behaviour of the $K_\perp~$algorithm in the soft and collinear limits. Away from the collinear limit, the user has a choice of angular definitions, controlled by the parameter angle. Note that the resolution variables are defined such that they remain monotonic functions of angle at large angles. Here, and throughout this paper, we use $\eta$ to denote true rapidity, i.e. $\eta = \frac{1}{2}\ln\frac{E+p_z}{E-p_z}$.