Flow chart of our routine described in Section 3.2.3. The central sketch shows the overall setup of the three-body encounters; a binary (m₁, m₂) on an orbit at a distance of d_• around the SMBH (M_SMBH) interacting with a tertiary (m₃). To the right of this sketch we show the possible outcomes from a three-body interaction. Group C contains interactions in which the binary remains intact and bound to the SMBH and as a consequence will experience continued evolution. Conversely, the evolution is terminated by outcomes in group T. To the left of the sketch we illustrate how a binary is evolved. A timestep, ∆t, is set by the shortest timescale of ZLK (quadrupole approximation), encounters, and circularisation (tides). The secular process with the shortest timescale min[τ_quad, τ_circ] is then run for ∆t. At every step 0.1 ∆t, a three-body encounter is sampled with the accept-reject method described in Appendix A. If accepted, the three-body encounter is carried out with tsunami. If rejected, we proceed to the next 0.1 ∆t and sample again. After a time, ∆t, has passed or after a three-body encounter, a new ∆t is calculated. In this example, the encounter occurs after ∆t₁ + 0.1 ∆t₂ + t_enc. This process is then continued until an outcome in group T occurs or until the simulation time exceeds 10 Gyr.