the gluino mass itself [14]. An important question to then consider is whether a BSM triple-top signal could be faked by SM four-top production with one top going unidentified. In Figure 5(b), we compare the triple-top cross sections predicted by each model with the corresponding four-top cross sections calculated at LO. Both the Z ′ and MSSM triple-top cross sections lie well above the SM four-top cross sections at all energies. This reduces the chance that a SM four-top signal could fake the larger BSM triple-top one. Each model also lies above its own four-top cross sections, which are themselves enhanced from the SM prediction. It should be noted, however, that these conclusions are not generic features of the models; slightly different values of ϵ$_{U}$ and the gluino branching fractions can flip the relative importance of the three- and four-top channels. It should be understood, therefore, that the triple-top signal is most valuable in its relation to top signals of other multiplicities. Means of distinguishing between two-, three-, and four-top final states are then critical to properly utilizing these signals. Direct reconstruction of every top quark in a multi-top event, after including detector cuts, background, and showering, can be extremely difficult due to large combinatorics [14]. Other methods have been developed for tagging high- p$_{T}$ top quarks at the LHC by investigating the jet substructure of the decay products [17–21]. These studies have focused on top-pair signals but perhaps could find applicability to three- and four-top events as well. While there are certainly practical challenges involved, the results presented here indicate that new physics may be inferred from the triple-top signal and therefore warrant further, more detailed simulations. The authors would like to thank the referee for valuable comments that have contributed to quality of this manuscript and also Y. Gao, I. Lewis, and M. McCaskey for helpful discussions. This work was supported in part by the U.S. Department of Energy under grants Nos. DE-FG02-95ER40896 and DE-FG02-84ER40173 and in part by the Wisconsin Alumni Research Foundation. V. ACKNOWLEDGEMENTS 11