Quasi-isomorphism between sheaf-quantization and Floer curved algebras

Let $\bm L$ be a Lagrangian brane, let $CF_{\mathrm{SQ}}(\bm L,\bm L)$ be the colimit curved dga constructed from sheaf quantizations, and let $CF(\bm L,\bm L)$ be the corresponding curved Floer $A_\infty$-algebra. The curved algebra comparison conjecture. There exists a quasi-isomorphism

$$CF_{\mathrm{SQ}}(\bm L,\bm L)\simeq CF(\bm L,\bm L)$$

of curved $A_\infty$-algebras. This would identify the sheaf-theoretic and Floer-theoretic deformation algebras; the supplied text does not state a proof.