Infinite boundary depth conjecture for Maslov-zero Lagrangian tori

Let $L\subset M$ be a Maslov $0$ Lagrangian torus, and let $C^*(L,M)$ be its Floer complex with differential satisfying

$$\partial(C^*(L,M))=\{0\}.$$

Here $\tau(L)$ denotes the relevant boundary-depth invariant. Infinite boundary depth conjecture. Then

$$\tau(L)=\infty.$$

This conjecture would remove the exactness assumption from the preceding result and establish the key condition needed for the reconstruction problem for general SYZ fibrations.