Topological and algebraic perfection conjecture for the formal punctured neighborhood of a coherent derived category

Let $X$ be a proper scheme over a perfect field $\mathrm k$. Write $\operatorname{Perf}_{\mathrm{top}}(\widehat{{\mathfrak D}^b_{coh}(X)}_{\infty})$ and $\operatorname{Perf}_{\mathrm{alg}}(\widehat{{\mathfrak D}^b_{coh}(X)}_{\infty})$ for the topological and algebraic perfect subcategories of the formal punctured neighborhood at infinity of ${\mathfrak D}^b_{coh}(X)$. Topological-algebraic perfection conjecture. One has

$$\operatorname{Perf}_{\mathrm{top}}(\widehat{{\mathfrak D}^b_{coh}(X)}_{\infty})=\operatorname{Perf}_{\mathrm{alg}}(\widehat{{\mathfrak D}^b_{coh}(X)}_{\infty}).$$

The conjecture asserts that the topological and algebraic notions of perfect objects coincide in this formal categorical neighborhood; the paper has established the corresponding algebraic description, but equality with the topological subcategory remains conjectural.