Top panel: illustration of the behaviour of the function from Eq. (F.1), when averaged on 32 different realisations for particles numbers N ∈ {8, 12, 16, 24, 32, 48, 64 } × 10⁵, along with the associated linear fits. To compute , we used the same binning of the action-space (J_φ,J_r) as in Fig. 5. As obtained in Eq. (F.3), one recovers that for a fixed value of N, the function is linear. The horizontal dashed line illustrates the threshold value for which the threshold time t_thold is determined. Bottom panel: illustration of the behaviour of the function N → t_thold(N). As derived in Eq. (F.5), one recovers a linear dependence of t_thold with N.