  The separation distribution for M-dwarf binaries in the ASTRALUX survey is
narrower and peaking at smaller separations than the distribution for
solar-type binaries. This is often interpreted to mean that M-dwarfs constitute
a continuous transition from brown dwarfs (BDs) to stars. Here a prediction for
the M-dwarf separation distribution is presented, using a dynamical population
synthesis (DPS) model in which "star-like" binaries with late-type primaries
($\lesssim1.5 M_{\rm sun}$) follow universal initial distribution functions and
are dynamically processed in their birth embedded clusters. A separate
"BD-like" population has both its own distribution functions for binaries and
initial mass function (IMF), which overlaps in mass with the IMF for stars.
Combining these two formation modes results in a peak on top of a wider
separation distribution for late M-dwarfs consistent with the late ASTRALUX
sample. The DPS separation distribution for early M-dwarfs shows no such peak
and is in agreement with the M-dwarfs in Multiples (MinMS) data. We note that
the latter survey is potentially in tension with the early ASTRALUX data.
Concluding, the ASTRALUX and MinMS data are unable to unambiguously distinguish
whether or not BDs are a continuous extension of the stellar IMF. Future
observational efforts are needed to fully answer this interesting question. The
DPS model predicts that binaries outside the sensitivity range of the ASTRALUX
survey remain to be detected. For application to future data, we present a
means to observationally measure the overlap of the putative BD-like branch and
the stellar branch. We discuss the meaning of universal star formation and
distribution functions.
