The τ-perpendicular subcategory inheritance conjecture

Let $\Lambda$ be a finite-dimensional algebra. Let $\mathcal W\subseteq\mathsf{mod}\Lambda$ be a $\tau$-perpendicular subcategory of $\mathsf{mod}\Lambda$, and let $\mathcal V\subseteq\mathcal W$ be a wide subcategory of $\mathcal W$. Inheritance conjecture. Then $\mathcal V$ is a $\tau$-perpendicular subcategory of $\mathsf{mod}\Lambda$ if and only if $\mathcal V$ is a $\tau$-perpendicular subcategory of $\mathcal W$. The converse to the preceding composition result is known in several cases, including $\tau$-tilting finite algebras and hereditary algebras; the conjecture proposes that it holds for arbitrary finite-dimensional algebras.