Finite monomorphic decomposition sibling conjecture

Let $R$ be a relational structure with a finite monomorphic decomposition, and let siblings be counted up to isomorphism. Finite monomorphic decomposition conjecture. Under this assumption, $R$ has either one sibling or infinitely many siblings.

The source presents this as a strengthening of the preceding theorem. Its relationship with Thomassé's broader sibling-number conjecture is that it supplies the one-or-infinite alternative for structures with finite monomorphic decomposition.