  We revisit AdS/CFT at finite radial cut-off, specifically in the context of
double trace perturbations, $\mathbb{O}_n$= $\mathbb{O}(x) (\partial^2)^{n}
{\mathcal O}(x)$, with arbitrary $n$. As well-known, the standard GKPW
prescription, applied to a finite radial cut-off, leads to contact terms in
correlators. de Haro et al (arXiv:hep-th/0002230) introduced bulk counterterms
to remove these. However, this prescription yields additional terms in the
correlator corresponding to spurious double trace deformations. Further, if we
view GKPW prescription coupled with the prescription in arXiv:hep-th/0002230,
in terms of a boundary wavefunction, we find that it is incompatible with
radial Schrodinger evolution (in the spirit of holographic Wilsonian RG). We
consider a more general wavefunction satisfying the Schrodinger equation, and
find that generically such wavefunctions generate both (a) double trace
deformations and (b) contact terms. However, we find that there exist special
choices of these wavefunctions, amounting to a new AdS/CFT prescription at a
finite cut-off, so that both (a) and (b) are removed and we obtain a pure power
law behaviour for the correlator. We compare these special wavefunctions with a
specific RG scheme in field theory. We give a geometric interpretation of these
wavefunctions; these correspond to some specific smearing of boundary points in
the Witten diagrams. We present a comprehensive calculation of exact
double-trace beta-functions for all couplings $\mathbb{O}_n$ and match with a
holographic computation using the method described above. The matching works
with a mapping between the field theory and bulk couplings; such a map is
highly constrained because the beta-functions are quadratic and exact on both
sides. We generalize standard double-trace Wilson-Fisher flow to the space of
the infinite number of couplings.
