  Clarifying the locality properties of higher-spin gravity is a pressing task,
but notoriously difficult due to the absence of a weakly-coupled flat regime.
The simplest non-trivial case where this question can be addressed is the
quartic self-interaction of the AdS scalar field present in the higher-spin
multiplet. We investigate this issue in the context of the holographic duality
between the minimal bosonic higher-spin theory on AdS$_4$ and the free
$O\left(N\right)$ vector model in three dimensions. In particular, we determine
the exact explicit form of the derivative expansion of the bulk scalar quartic
vertex. The quartic vertex is obtained from the field theory four-point
function of the operator dual to the bulk scalar, by making use of our previous
results for the Witten diagrams of higher-spin exchanges. This is facilitated
by establishing the conformal block expansions of both the boundary four-point
function and the dual bulk Witten diagram amplitudes. We show that the vertex
we find satisfies a generalised notion of locality.
