Gromov's $(\alpha,\beta,\lambda)$-convergence conjecture for scalar curvature

Let $X$ and $X_i$ be closed oriented Riemannian manifolds, and let $W_{\alpha_i,\beta_i,\lambda_i}\colon X_i\to X$ denote Riemannian $(\alpha_i,\beta_i,\lambda_i)$-cobordisms, meaning $(\alpha_i,\beta_i)$-cobordisms equipped with a $\lambda_i$-Lipschitz retraction onto $X$. Assume there is a sequence of such cobordisms with $\beta_i\to 0$ and $\lambda_i\to 1$. Gromov's $(\alpha,\beta,\lambda)$-convergence conjecture. If each $X_i$ has non-negative scalar curvature, then so does $X$. This asks whether non-negative scalar curvature is preserved under a cobordism-based convergence with controlled volume and retractions; its resolution is not specified in the source.