  In a broad class of gravity theories, the equations of motion for vacuum
compactifications give a curvature bound on the Ricci tensor minus a multiple
of the Hessian of the warping function. Using results in so-called
Bakry--\'Emery geometry, we put rigorous general bounds on the KK scale in
gravity compactifications in terms of the reduced Planck mass or the internal
diameter. We reexamine in this light the local behavior in type IIA for the
class of supersymmetric solutions most promising for scale separation. We find
that the local O6-plane behavior cannot be smoothed out as in other local
examples; it generically turns into a formal partially smeared O4.
