Once immersed Lagrangians are admitted as objects of Fukaya categories, the twisted complexes are largely redundant. Joyce [41, conjecture 3.6] claims that by including immersed and singular Lagrangians with rank one local systems, then $D^{b}Fuk(X)$ is automatically idempotent closed, so there is no difference between $D^{b}Fuk(X)$ and $D^{\pi}Fuk(X)$. However, it is highly nonobvious why direct summands are Yoneda represented by geometric Lagrangian objects,⁶⁵⁶⁵ 65 There exist some wild speculations, such as incorporating coisotropic branes into the Fukaya category in order to have more geometric objects. so this claim is regarded by many experts as a weakness of Joyce’s proposal. For this reason, in our more restrictive proposal we stick with the more geometric $D^{b}Fuk(X)$ (including immersed and singular objects, but not formal idempotent summands) in favour of $D^{\pi}Fuk(X)$, and the idempotent closure problem does not falsify our program.