  We explore the conjectured duality between the critical O(N) vector model and
minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free
theory, the conformal partial wave expansion (CPWE) of the four-point function
of the scalar singlet bilinear is reorganized to make it explicitly
crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge
fields. We are able to analytically establish the factorized form of the fusion
coefficients as well as the two-point function coefficient of the HS currents.
We insist in directly computing the free correlators from bulk graphs with the
unconventional branch. The three-point function of the scalar bilinear turns
out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be
precisely related to the CPWs of the boundary dual scalar and its shadow. The
flow in the IR by Legendre transforming at leading 1/N, following the pattern
of double-trace deformations, and the assumption of degeneracy of the hologram
lead to the CPWE of the scalar four-point function at IR. Here we confirm some
previous results, obtained from more involved computations of skeleton graphs,
as well as extend some of them from d=3 to generic dimension 2<d<4.
