Compatibility of spectral networks and partially wrapped Fukaya categories with Stokes local systems

Demonstrate that the relation between spectral networks and partially wrapped Fukaya categories is compatible with the theory of Stokes local systems. Concretely, construct and verify an equivalence relating the non‑abelianization functor ΦW and the Yoneda module Y over the partially wrapped Fukaya category W through a functor to the category of Stokes local systems, ensuring the expected commutative diagram holds.

Background

The paper proposes a diagram linking the non‑abelianization functor ΦW, the Yoneda module Y over the partially wrapped Fukaya category W, and a functor to Stokes local systems à la Boalch. This would conceptually integrate spectral networks/Floer theory with Stokes phenomena.

While substantial evidence is developed (e.g., equivalences between F and ΦW in exact settings, and categorical identifications over wrapped/partially wrapped Fukaya categories), the general compatibility with Stokes local systems is not established. The conjectured compatibility would unify the analytic (Stokes) and symplectic‑categorical frameworks.