  We prove the equivalence in the covariant phase space of the metric and
connection formulations for Palatini gravity, with nonmetricity and torsion, on
a spacetime manifold with boundary. To this end, we will rely on the
cohomological approach provided by the relative bicomplex framework. Finally,
we discuss some of the physical implications derived from this equivalence in
the context of singularity identification through curvature invariants.
