  For an arbitrary $\infty$-topos, we classify the smashing localizations in
the $\infty$-category of sheaves valued in derived vector spaces: Any of them
is the restriction functor to a (unique) closed subtopos. Our proof is based on
the existence of a Boolean cover.
  This result in particular gives us the first example of a nonzero presentably
symmetric monoidal stable $\infty$-category whose smashing spectrum has no
points.
  Combining this with the sheaves-spectrum adjunction, we obtain a Tannaka-type
categorical reconstruction result for locales.
