Embedding of an infinitesimally wrapped Fukaya category into the equivariant Tamarkin category

Establish the existence of an infinitesimally wrapped Fukaya category of nonexact Lagrangians in the cotangent bundle T^*M and construct a natural embedding functor from Fuk(T^*M) into the equivariant Tamarkin-type sheaf category Sh_{τ>0}^{R^δ}(M × R_t).

Background

The paper develops spectral networks and sheaf quantization techniques for holomorphic Lagrangians in cotangent bundles, drawing connections between symplectic geometry (Fukaya categories) and sheaf-theoretic frameworks (Tamarkin categories). The conjecture proposes a categorical bridge: an embedding of an infinitesimally wrapped Fukaya category of nonexact Lagrangians into an equivariant Tamarkin-type sheaf category, which would underpin a sheaf-theoretic model for Fukaya theory in nonexact settings.

While related cases (e.g., integral Lagrangians) have been partially addressed in prior work, the general existence of such an embedding for nonexact Lagrangians remains conjectural and would unify the sheaf quantization approach with Fukaya categories in this broader context.