  We clarify the natural cluster algebra of type A that exists in a residual
and tropical form in the kinematical space as suggested in 1711.09102 by the
use of triangulations, mutations and associahedron on the definition of
scattering forms. We also show that this residual cluster algebra is preserved
in a hypercube (diamond) necklace inside the associahedron where cluster
sub-algebras $(A_1)^n$ exist. This result goes in line with results with
cluster poligarithms in 1401.6446 written in terms of $A_2$ and $A_3$ functions
only and other works showing the primacy of $A$ cluster sub-algebras as data
input for scattering amplitudes.
