Extracted parameter variation series and MCB detection analysis for system simu 21 (P_m = 1.196 d, P_b = 30 d) over a four-year baseline (49 epochs), (a–c) Residual series for the mid-transit time (t_c,TTV), total transit duration (t_T, TDV), and flat-bottom duration (t_F, TFV). The vertical axes display the deviations in minutes (for t_c and t_T) or the residual value (for t_F). Blue dots connected by solid lines represent the T×Vs from the three-body simulation, exhibiting clear periodic modulations induced by the presence of exomoon. Gray dots represent 100 random T×V series generated from the two-body MCB resamples. The red dashed line denotes zero variation, (d) Histogram of 5000 var₂ values (variance of the two-body residuals for t_F) with a Gaussian fit (red curve). The vertical solid blue line indicates the observed variance (var₃) from the three-body simulation, which lies far beyond the 99.7th percentile threshold (orange dashed line), confirming a robust detection. Black dotted and green dash-dotted lines denote the mean and median of the distribution, respectively.