Left: results of our 2891 N-body integrations of the three-planet systems with Q′ _* = 10 ⁷ and Q′ _p = 5 × 10 ⁶. The total integration time was set to T = 10 ⁸ yr. Right: extension to T = 10 ⁹ yr using the semi-analytical model. We stopped the simulation if a hot Jupiter formed and acquired a nearly circular orbit (defined as e < 0.01). In both cases the stellar obliquity θ ₀ shows no significant deviation from the orbital inclination of the inner planet.