The connection between the pre-stellar core mass function (CMF) and the stellar initial mass function (IMF) lies at the heart of all star formation theories. In this paper, we study the earliest phases of star formation with a series of high-resolution numerical simulations that include the formation of sinks. In particular, we focus on the transition from cores to sinks within a massive molecular filament. We compare the CMF and IMF between magnetized and unmagnetized simulations, and between different resolutions. We find that selecting cores based on their kinematic virial parameter excludes collapsing objects because they host large velocity dispersions. Selecting only the thermally unstable magnetized cores, we observe that their mass-to-flux ratio spans almost two orders of magnitude for a given mass. We also see that, when magnetic fields are included, the CMF peaks at higher core mass values with respect to pure hydrodynamical simulations. Nonetheless, all models produce sink mass functions with a high-mass slope consistent with Salpeter. Finally, we examine the effects of resolution and find that, in isothermal simulations, even models with very high dynamical range fail to converge in the mass function. Our main conclusion is that, although the resulting CMFs and IMFs have similar slopes in all simulations, the cores have slightly different sizes and kinematical properties when a magnetic field is included. However, a core selection based on the mass-to-flux ratio alone is not enough to alter the shape of the CMF, if we do not take thermal stability into account. Finally, we conclude that extreme care should be given to resolution issues when studying sink formation with an isothermal equation of state.
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