Top panel: periodogram of the radial velocities of GJ 3543. The horizontal lines represent the same false-alarm levels as in Fig. 2. The two peaks at 1.1 and 9.2 d have an FAP lower than 0.3%. Bottom panel: periodograms for three independent subsets of observation epochs (BJD–2 400 000 = 55 500–55 750, first row; 55 850−56 050, second row; 56 340−56 380, third row). The 1.1 and 9.2 d peaks (marked by vertical dash-dotted lines) are both unstable over time.