In the situation of Conjecture 3.2, the enlarged version of $D^{b}{\mathbin{\mathscr{F}}}(M)$ with objects $(L,E,b)$ for $L$ a possibly singular, compact, immersed, graded Lagrangian is idempotent complete. Hence $D^{\pi}{\mathbin{\mathscr{F}}}(M)\simeq D^{b}{\mathbin{\mathscr{F}}}(M),$ and we can take all objects of $D^{\pi}{\mathbin{\mathscr{F}}}(M)$ to be geometric, of the form $(L,E,b)$.