(VEV) does not introduce proton decay at tree level. In addition, this model has several potentially testable and interesting predictions:

-   $R$-parity violation is manifest though lepton number violating operators, which could lead to lepton number violating signatures at the LHC, *e.g.* [@FileviezPerez:2012mj; @Perez:2013kla].

-   The existence of two neutral light fermions (sterile neutrinos), in addition to the usual three neutrinos [@Mohapatra:1986aw; @Ghosh:2010hy; @Barger:2010iv]. These may play a role in cosmology [@Ghosh:2010hy; @Ade:2013zuv; @Perez:2013kla].

-   A $B-L$ neutral gauge boson, $Z'$, whose mass is proportional to the soft mass of the right-handed sneutrino. This gauge boson must be at the TeV scale and, therefore, detectable at the LHC.

-   The right-handed sneutrino VEV directly links the neutrino sector to lepton number violation by one unit. This generates tree-level Majorana contributions to the neutrino masses.

This last statement is significant, since it specifies the size of the RPV. It follows from the upper bound placed on this contribution by the neutrino masses that the RPV is only relevant for the decay of the LSP, which would otherwise be stable under RPC. All other SUSY processes will effectively be $R$-parity conserving. The last bullet point is also crucial because it relates neutrino 