  It has been recently shown that in order to have Dirac eigenvalues as
observables of Euclidean supergravity, certain constraints should be imposed on
the covariant phase space as well as on Dirac eigenspinors. We investigate the
relationships among the constraints in the first set and argue that these
relationships are not linear. We also derive a set of equations expressing the
linear dependency of the constraints in order that the second set of
constraints be linearly independent.
