Yangian invariants and cluster adjacency in N $$ \mathcal{N} $$ = 4 Yang-Mills

We conjecture that every rational Yangian invariant in $$ \mathcal{N} $$ = 4 SYM theory satisfies a recently introduced notion of cluster adjacency. We provide evidence for this conjecture by using the Sklyanin Poisson bracket on Gr(4, n) to check numerous examples.