A uniqueness theorem for warped $N>16$ Minkowski backgrounds with fluxes

We demonstrate that warped Minkowski space backgrounds, $\mathbb{R}^{n-1,1}\times_w M^{d-n}$, $n\geq3$, that preserve strictly more than 16 supersymmetries in $d=11$ and type II $d=10$ supergravities and with fields which may not be smooth everywhere are locally isometric to the $\mathbb{R}^{d-1,1}$ Minkowski vacuum. In particular, all such flux compactification vacua of these theories have the same local geometry as the maximally supersymmetric vacuum $\mathbb{R}^{n-1,1}\times T^{d-n}$.