Dao–Takahashi's finite-radius conjecture for resolving subcategories

Let $R$ be a Cohen–Macaulay local ring. Let $\operatorname{\mathcal{X}}$ be a resolving subcategory of finitely generated $R$-modules with finite radius. Dao–Takahashi's conjecture. Then $\operatorname{\mathcal{X}}$ is contained in the category $\operatorname{CM}(R)$ of maximal Cohen–Macaulay $R$-modules. Dao and Takahashi proposed this conjecture in connection with the radius of resolving subcategories; it is known to hold when $R$ is a complete intersection, while the statement in general remains open.