Quantization problem for Lagrangian torus fibrations

Let $(X,L)$ be a polarized compact Kähler manifold, with $L$ a pre-quantum bundle, and let $\pi:X\rightarrow B$ be a Lagrangian torus fibration. Let $\Gamma_{X/B}(X,L)$ denote the space of distributional sections supported on Bohr–Sommerfeld fibers and covariantly constant along the polarization. Quantization problem. The two spaces of wave functions are canonically isomorphic:

$$\Gamma_{X/B}(X,L)\cong H^0(X,L).$$

This asks for independence of the resulting quantization from the choice of polarization. The source records proofs in important cases, including flag manifolds and sufficiently large tensor powers under a nondegeneracy hypothesis, but leaves the general statement open.