Cluster patterns in Landau and leading singularities via the amplituhedron

We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in 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 invari-ant 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) N2MHV Yangian invariants are cluster adja-cent, confirming original conjectures.