Probability density of the inclination proper modes of the HIP 41378 system with and without the candidate planet h. Histograms are built from 10⁶ realisations of the Lagrange-Laplace system with the mass and semi-major axis uncertainties listed in Table 2. For planets g and h, the minimum mass is taken as the true mass. The histograms for frequencies s₃ and s₇ peak above the top border of the graph. Frequency s₅ is identically equal to zero from the conservation of angular momentum. The upper axis shows the minimum moon mass needed for planet f to be fully tilted through a resonance with a given frequency value s.