Stability analysis of the TOI-421 planetary system. For fixed initial conditions (Table 6), the parameter space of the system was explored by varying the orbital period P_b and the eccentricity e_b of planet-b (left panel) and the eccentricities of both planets (right panel). The step size was 10⁻³ day in orbital period and 0.0025 in eccentricity. For each initial condition, the system was integrated over 5000 yr and a stability indicator was calculated, which involved a frequency analysis of the mean longitude of the inner planet. The chaotic diffusion was measured by the variation in the frequency (see text). Red points correspond to highly unstable orbits, while blue points correspond to orbits which are likely to be stable on a billion-years timescale. The black dots show the values of the best fit solution (Table 6).