  We study the holographic duality between the free $O(N)$ vector model and
higher spin gravity. Conserved spinning primary currents of the conformal field
theory (CFT) are dual to spinning gauge fields in the gravity. Reducing to
independent components of the conserved CFT currents one finds two components
at each spin. After gauge fixing the gravity and then reducing to independent
components, one finds two components of the gauge field at each spin.
Collective field theory provides a systematic way to map between these two sets
of degrees of freedom, providing a complete and explicit identification between
the dynamical degrees of freedom of the CFT and the dual gravity. The resulting
map exhibits many features expected of holographic duality: it provides a valid
bulk reconstruction, it reproduces insights expected from the holography of
information and it provides a microscopic derivation of entanglement wedge
reconstruction.
