  We advance the exploration of cluster-algebraic patterns in the building
blocks of scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory. In
particular we conjecture that, given a maximal cut of a loop amplitude, Landau
singularities and poles of each Yangian invariant appearing in any
representation of the corresponding Leading Singularities can be found together
in a cluster. We check these adjacencies for all one-loop amplitudes up to 9
points. Along the way, we also prove that all (rational) N$^2$MHV Yangian
invariants are cluster adjacent, confirming original conjectures.
