  In the ${\rm AdS}_3/{\rm CFT}_2$ setup we elucidate how gauge invariant
boundary patterns of entanglement of the CFT vacuum are encoded into the bulk
via the coefficient dynamics of an $A_{N-3}$, $N\geq 4$ cluster algebra. In the
static case this dynamics of encoding manifests itself in kinematic space,
which is a copy of de Sitter space ${\rm dS}_2$, in a particularly instructive
manner. For a choice of partition of the boundary into $N$ regions the patterns
of entanglement, associated with conditional mutual informations of overlapping
regions, are related to triangulations of geodesic $N$-gons. Such
triangulations are then mapped to causal patterns in kinematic space. For a
fixed $N$ the space of all causal patterns is related to the associahedron
${\mathcal K}^{N-3}$ an object well-known from previous studies on scattering
amplitudes. On this space of causal patterns cluster dynamics acts by a
recursion provided by a Zamolodchikov's $Y$-system of type $(A_{N-3},A_1)$. We
observe that the space of causal patterns is equipped with a partial order, and
is isomorphic to the Tamari lattice. The mutation of causal patterns can be
encapsulated by a walk of $N-3$ particles interacting in a peculiar manner in
the past light cone of a point of ${\rm dS}_2$.
