Conjecture on derived contraction algebras determining stable endomorphism dgas

Let $A$ be an algebra with idempotent $e$, let $M$ be the corresponding maximal Cohen–Macaulay module, and write

$$A/^{\mathbb{L}}AeA$$

for the derived quotient. Assume that $A/AeA$ is an Artinian local algebra. Derived contraction algebra conjecture. The quasi-isomorphism type of the derived quotient determines the quasi-isomorphism type of

$${\mathrm{\mathbb{R}}}\underline{\mathrm{End}}_{R}(M)$$

as a differential graded algebra over $k[\theta,\theta^{-1}]$. This would formalize the idea that the stable endomorphism dga is obtained from the derived quotient by adjoining the inverse of the periodicity element. The source presents this as a natural conjecture; no resolution is supplied.