  We study norm functors in the sense of Bachmann--Hoyois for various
$\infty$-categories of correspondences occurring in motivic homotopy theory. We
show in particular that the symmetric monoidal structure on the
$\infty$-category of framed correspondence can be refined to a norm monoidal
structure, and that the resulting norm monoidal structure on the
$\infty$-category of motivic spectra with framed transfers is compatible with
the Reconstruction Theorem of Elmanto--Hoyois--Khan--Sosnilo--Yakerson. This
yields a recognition principle for normed motivic spectra. We show similar
results for various other flavors of transfer, e.g. finite syntomic and
oriented finite Gorenstein.
