Non-commutative Hodge-theoretic interpretation of holomorphic Floer theory

Let $(M,\Omega_I)$ be holomorphic symplectic, set $\omega_u=\operatorname{Re}(u^{-1}\Omega_I)$ and $B_u=\operatorname{Im}(u^{-1}\Omega_I)$, and let $F(M,\omega_u,B_u)$ be the corresponding Fukaya category. Holomorphic Floer Betti-data conjecture. The Betti data for the non-commutative Hodge theory of $RW(M,\Omega_I)$ is induced by

$$DQ(M,\Omega_I)\simeq F(M,\omega_u,B_u)\otimes\mathbb{C}(!(u)\!).$$

Moreover, its Stokes data is induced by the holomorphic dependence of $F(M,\omega_u,B_u)$ on $u$ and is determined by the relevant counts of $J_u$-holomorphic curves. This is proposed as a reformulation of predictions associated with non-perturbative quantization and resurgence; the source gives no resolution.