Calaque–Căldăraru–Tu's derived blow-up L-infinity algebroid conjecture

Assume the setting of the main theorem, and let $C_{Z/X}^{\vee}$ be the dual of the relevant complex. Define the structure ring of the formal derived blow-up by

$$\mathcal{O}_{Z_{X}^{\infty}}:=\varprojlim_{n\to\infty}\operatorname{cofib}(R_{Z/X}^{n}\to R_{Z/X}^{0}).$$

L-infinity algebroid conjecture. There exists a minimal $L_{\infty}$-algebroid structure on $C_{Z/X}^{\vee}$ whose Chevalley–Eilenberg algebra is equivalent to $\mathcal{O}_{Z_{X}^{\infty}}$.

This conjecture relates the formal structure of derived blow-ups to $L_{\infty}$-algebroid structures, inspired by work of Calaque, Căldăraru and Tu. The supplied text gives no resolution.