  We study a recently proposed quantum integrable model defined on a lattice
with N sites, with Fermions or Bosons populating each site, as a close relative
of the well known spin-1/2 Gaudin model. This model has 2N arbitrary
parameters, a linear dependence on an interaction type parameter x, and can be
solved exactly. It has N known constants of motion that are linear in x. We
display further constants of motion with higher Fermion content, that are are
linearly independent of the known conservation laws. Our main result is that
despite the existence of these higher conservation laws, the model has only N
functionally independent conservation laws. Therefore we propose that N can be
viewed as the number of degrees of freedom, in parallel to the classical
definition of integrability.
