  We seek the inverse formulas for the cosmological unifying relation between
gluons and conformally coupled scalars. We demonstrate that the weight-shifting
operators derived from the conformal symmetry at the dS late-time boundary can
serve as the inverse operators for the 3-point cosmological correlators.
However, in the case of the 4-point cosmological correlator, we observe that
the inverse of the unifying relation cannot be constructed from the
weight-shifting operators. Despite this failure, we are inspired to propose a
"weight-shifting uplifting" method for the 4-point gluon correlator.
