  We present an exactly-solvable $p$-wave pairing model for two bosonic
species. The model is solvable in any spatial dimension and shares some
commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a
third order quantum phase transition. However, contrary to the fermionic case,
in the bosonic model the transition separates a gapless fragmented singlet pair
condensate from a pair Bose superfluid, and the exact eigenstate at the quantum
critical point is a pair condensate analogous to the fermionic Moore-Read
state.
