KOI-872. Top panel: χ² vs. period ratio (N_dof  =  65). The 5:3 solution provides the best fit, although the 2:5, 5:2, and 3:5 solutions are also good. Second panel: TTVs from this work (Section 3.1). The gray curve is a GP model, used as a smooth interpolant to separate long- and short-timescale variations. Third panel: high-pass-filtered TTVs obtained by subtracting the GP. The red curve shows the best variant of the 5:3 solution (D. Nesvorný et al. 2012); the blue curve shows the 2:5 solution, which is second-best. Fourth panel: residuals of the 5:3 solution (rms  =  1.8 minutes) and the 2:5 solution (rms  =  4.2 minutes). Fifth panel: TDVs and predictions of the 5:3 and 2:5 models. By eye, it is difficult to declare a winner, although quantitatively, KOI-872’s TTV solution does appear unique.