  We consider a broad class of supersymmetric theories in which dark matter
(DM) is the lightest superpartner (LSP) of a hidden sector that couples very
weakly to visible sector fields. Portal interactions connecting visible and
hidden sectors mediate the decay of the lightest observable superpartner (LOSP)
into the LSP, allowing the LHC to function as a spectacular probe of the origin
of hidden sector DM. As shown in a companion paper, this general two-sector
framework allows only for a handful of DM production mechanisms, each of which
maps to a distinctive window in lifetimes and cross-sections for the LOSP. In
the present work we perform a systematic collider study of LOSP candidates and
portal interactions, and for each case evaluate the prospects for successfully
reconstructing the origin of DM at the LHC. If, for instance, DM arises from
Freeze-Out and Decay, this may be verified if the LOSP is a bino or
right-handed slepton decaying to the LSP through a variety of portal
interactions, and with an annihilation cross-section within a narrow range. On
the other hand, the Freeze-In mechanism may be verified for a complimentary set
of LOSP candidates, and within a narrow range of LOSP lifetimes. In all cases,
the LOSP is relatively long-lived on collider time scales, leading to events
with displaced vertices. Furthermore, scenarios with a charged or colored LOSP
are particularly promising.
