Non-exact wrapped Fukaya category and deformed multiplicative preprojective algebra

Let $X_{\mathrm{res}}$ be the resolution of the $A_n$ surface singularity, let $D_r$ be the indicated divisor, and let $s$ be a formal parameter with coefficient field $\mathbb{C}((s))$. Set $q_i(s)=e^{s\lambda_i}$. Non-exact wrapped Fukaya equivalence conjecture. The perfect derived non-exact wrapped Fukaya category satisfies

$$D^{\pi}\mathcal{W}(X_{\mathrm{res}}\smallsetminus D_r)\simeq D^b(\Lambda^{q(s)}(\widetilde{A}_n)),$$

with $q_i(s)=e^{s\lambda_i}$. This would provide the missing categorical computation in the non-exact setting and extend the exact-case identification to deformed multiplicative preprojective algebras; the paper notes that foundational ingredients for the non-exact category remain unavailable.