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

Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables