  We demonstrate precisely what particle physics information can be extracted
from a single direct detection observation of dark matter while making
absolutely no assumptions about the local velocity distribution and local
density of dark matter. Our central conclusions follow from a very simple
observation: the velocity distribution of dark matter is positive definite,
f(v) >= 0. We demonstrate the utility of this result in several ways. First, we
show a falling deconvoluted recoil spectrum (deconvoluted of the nuclear form
factor), such as from ordinary elastic scattering, can be "mocked up" by any
mass of dark matter above a kinematic minimum. As an example, we show that dark
matter much heavier than previously considered can explain the CoGeNT excess.
Specifically, m_chi < m_Ge} can be in just as good agreement as light dark
matter, while m_\chi > m_Ge depends on understanding the sensitivity of Xenon
to dark matter at very low recoil energies, E_R ~ 6 keVnr. Second, we show that
any rise in the deconvoluted recoil spectrum represents distinct particle
physics information that cannot be faked by an arbitrary f(v). As examples of
resulting non-trivial particle physics, we show that inelastic dark matter and
dark matter with a form factor can both yield such a rise.
