Generic sheaf quantizability of rotated holomorphic Lagrangians

Ascertain whether, for a holomorphic Lagrangian L in T^*C, the rotated Lagrangian L_θ := e^{2π i θ} · L is sheaf quantizable for generic θ ∈ S^1.

Background

After proposing an embedding of the Fukaya category into a sheaf-theoretic Tamarkin category, the author formulates a concrete consequence: that generic rotations of a holomorphic Lagrangian in T^*C admit sheaf quantizations. This would provide a sheaf-theoretic counterpart to unobstructedness phenomena (e.g., Solomon–Verbitsky) and extend the construction of sheaf quantizations beyond special cases.

The paper proves a version of this statement for spectral curves (existence of a dense set of angles admitting sheaf quantizations), but the general claim for arbitrary holomorphic Lagrangians remains conjectural.