Perfectness criterion for flop-functor equivalence

Let $X\to X_{\mathrm{con}}$ be a flopping contraction of $3$-folds, with $X$ having at worst Cohen–Macaulay rational singularities. Let the universal sheaf of the noncommutative deformation functor associated to the contracted curves be the corresponding complex, and let $\Lambda$ and $\Lambda_{\mathrm{con}}$ be the algebras in the contraction setup. A complex is perfect if it has finite projective dimension; in the stated equivalent formulation this is $\operatorname{pd}_{\Lambda}\Lambda_{\mathrm{con}}<\infty$. Perfectness criterion for flop-functor equivalence. The flop functor is an equivalence if and only if the universal sheaf is perfect, equivalently, if and only if $\operatorname{pd}_{\Lambda}\Lambda_{\mathrm{con}}<\infty$. The criterion would recover the known Bridgeland and Chen results for Gorenstein terminal singularities, where the universal sheaf is known to be perfect; the extension to the stated Cohen–Macaulay rational setting is open.