Probability density of the inclination proper modes of the HIP 41378 system. Histograms are built from 10⁶ realisations of the Lagrange-Laplace system with the mass and semi-major axis uncertainties in Table 1. The histogram for frequency s₄ has a long tail extending beyond the left border of the figure (with 99.7% occurrences above −1850″ yr⁻¹ and 95.4% above −1000″ yr⁻¹). The histogram for frequency s₃ peaks above the top border of the figure. Frequency s₅ is identically equal to zero from the conservation of angular momentum. The upper axis shows the minimum moon mass needed for HIP 41378 f to be fully tilted through a resonance with a given frequency value (see Sect. 4).