Convergence of multidimensional scaling embeddings under Gromov–Wasserstein convergence

Let $(X_n,d_n,\mu_n)$ for $n\in\mathbb{N}$ be a sequence of metric measure spaces that converges to $(X,d,\mu)$ in the Gromov–Wasserstein distance. The associated multidimensional scaling (MDS) embeddings map these spaces into a common Euclidean space according to their metric-measure structure. MDS convergence conjecture. The MDS embeddings converge. This conjecture proposes stability of multidimensional scaling under Gromov–Wasserstein convergence of metric measure spaces; the supplied source does not specify the mode of convergence or provide evidence resolving the claim.