Stringy category structure-constants conjecture

Let $R^k(\alpha)=\sum_{g=0}^{\infty}R^k_g\alpha^g$ be the formal power series whose coefficients are defined by counts of holomorphic maps from a genus-$g$ curve with $k$ boundary components, with boundary arcs mapped to the Lagrangian submanifolds and marked boundary points mapped to their intersection points. Stringy category conjecture. The elements $R^k(\alpha)$ form the structure constants of a stringy category. This claim is part of the proposed extension of Fukaya's construction using open holomorphic curves; the supplied text gives no resolution or further precise formulation.