of generality, we fix the smoothing low-rigidity break parameter $s_{\rm l}=0.05$, which amounts to consider a fast transition. This is however not critical to the fit. Hence, we are left with 7 free parameters.

From these 7 parameters, we design three different benchmark propagation models which may be related to quite different limiting regimes of the underlying microphysics. The first, most generic, model includes the whole setup introduced above: let us name it the  model. The second one is much simpler as it is free of convection and reacceleration, hence with much less free parameters, while providing fits to the data comparable to the previous one (see ); let us call it the  model. The third and last one includes both reacceleration and convection, but relates the possible change in the propagation at low rigidities to a change originating specifically in the non-relativistic regime ($\eta$), instead of a more generic low-rigidity break in the diffusion coefficient. This scenario provides a slightly worse fit to the data compared to the previous ones, at the expense of a large reacceleration $V_{\rm A}$. However, it allows us to connect the current analysis to the strong reacceleration models that were popular in the past; 