  Results from direct detection experiments are typically interpreted by
employing an assumption about the dark matter velocity distribution, with
results presented in the $m_\chi-\sigma_n$ plane. Recently methods which are
independent of the DM halo velocity distribution have been developed which
present results in the $v_{min}-\tilde{g}$ plane, but these in turn require an
assumption on the dark matter mass. Here we present an extension of these
halo-independent methods for dark matter direct detection which does not
require a fiducial choice of the dark matter mass. With a change of variables
from $v_{min}$ to nuclear recoil momentum ($p_R$), the full halo-independent
content of an experimental result for any dark matter mass can be condensed
into a single plot as a function of a new halo integral variable, which we call
$\tilde{h}(p_R)$. The entire family of conventional halo-independent
$\tilde{g}(v_{min})$ plots for all DM masses are directly found from the single
$\tilde{h}(p_R)$ plot through a simple rescaling of axes. By considering
results in $\tilde{h}(p_R)$ space, one can determine if two experiments are
inconsistent for all masses and all physically possible halos, or for what
range of dark matter masses the results are inconsistent for all halos, without
the necessity of multiple $\tilde{g}(v_{min})$ plots for different DM masses.
We conduct a sample analysis comparing the CDMS II Si events to the null
results from LUX, XENON10, and SuperCDMS using our method and discuss how the
mass-independent limits can be strengthened by imposing the physically
reasonable requirement of a finite halo escape velocity.
