  We first prove that, in Vasiliev's theory, the zero-form charges studied in
1103.2360 and 1208.3880 are twisted open Wilson lines in the noncommutative $Z$
space. This is shown by mapping Vasiliev's higher-spin model on noncommutative
Yang--Mills theory. We then prove that, prior to Bose-symmetrising, the
cyclically-symmetric higher-spin invariants given by the leading order of these
$n$-point zero-form charges are equal to corresponding cyclically-invariant
building blocks of $n$-point correlation functions of bilinear operators in
free conformal field theories (CFT) in three dimensions. On the higher spin
gravity side, our computation reproduces the results of 1210.7963 using an
alternative method amenable to the computation of subleading corrections
obtained by perturbation theory in normal order. On the free CFT side, our
proof involves the explicit computation of the separate cyclic building blocks
of the correlation functions of $n$ conserved currents in arbitrary dimension
$d>2$, using polarization vectors, which is an original result. It is shown to
agree, for $d=3$, with the results obtained in 1301.3123 in various dimensions
and where polarization spinors were used.
