  The purpose of this note is introduce a new axiom (called the Descent Axiom)
in the theory of $r$-spin cohomological field theories. This axiom explains the
origin of gravitational descendants in this theory. Furthermore, the Descent
Axiom immediately implies the Vanishing Axiom, explicating the latter (which
has no a priori analog in the theory of Gromov-Witten invariants), in terms of
the multiplicativity of the virtual class. We prove that the Descent Axiom
holds in the convex case, and consequently in genus zero.
