  The question of tensor-triangular rigidity concerns whether it is possible to
recover the higher homotopical information of a presentable stable symmetric
monoidal $\infty$-category from its tensor-triangulated homotopy category
alone. We prove that tensor-triangular rigidity interacts well with
recollements, and as an application we obtain new results about the rigidity of
$E(n)$-local spectra.
