Indecomposability of Newton polytopes of F-polynomials as shard polytopes

Let a finite-type cluster algebra be given, and let an $F$-polynomial be one of its cluster-algebra $F$-polynomials. Its Newton polytope is the convex hull of the exponent vectors of its monomials. Newton-polytope shard conjecture. In any finite-type cluster algebra, Newton polytopes of $F$-polynomials are indecomposable shard polytopes. The source notes that the analogous statement is known in simply-laced types and relates the claim to type $B$ shard polytopes; the full finite-type assertion is presented as an expected extension and remains open.