  The purpose of this paper is to prove a conjecture on reciprocity sheaves by
Kahn-Saito-Yamazaki. This is accomplished by extending Voevodsky's fundamental
results on homotopy invariant (pre)sheaves with transfers to its
generalizations, reciprocity sheaves and cube-invariant sheaves in the context
of theory of modulus (pre)sheave with transfers. The main results of this paper
is expected to play a crucial role in deducing the main properties of the
triangulated category of motives with modulus, which is a new triangulated
category enlarging Voevodsky's triangulated category of motives to encompass
non homotopy invariant motivic phenomena.
