The rationality conjecture for A-model structure constants of Calabi–Yau threefolds

Assume that $V$ has dimension $3$. Let $K_{i,j,k}(z)$ be the structure constants defining the A-model connection $\nabla_{AV}$ in the $z$-coordinates, and let $\Phi_0(z)$ be the generalized hypergeometric series.

Rationality conjecture. The function

$$\Phi_0^2(z)K_{i,j,k}(z)$$

is rational in the $z$-coordinates.

This predicts rationality of the normalized A-model structure constants in the Calabi–Yau threefold case, providing a bridge between the hypergeometric period and quantum-cohomological data; no resolution is given in the source.