We show that it is possible to distinguish between different off-shell completions of supergravity at the on-shell level. We focus on the comparison of the ``new minimal formulation of off-shell four-dimensional N=1 supergravity with the ``old minimal formulation. We show that there are 3-manifolds which admit supersymmetric compactifications in the new-minimal formulation but which do not admit supersymmetric compactifications in other formulations. Moreover, on manifolds with boundary the new-minimal formulation admits ``singleton modes which are absent in other formulations.
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