Fermat-hypersurface superpotential conjecture

Let $V$ be the subspace spanned by the immersed-point generators $X_1,\ldots,X_{n+2}$, and write a deformation as $b=\sum_{i=1}^{n+2}x_iX_i$. Let $W$ be the mirror superpotential obtained from the immersed Lagrangian construction, and let $check{q}(q)$ denote the inverse mirror map for the Fermat hypersurface $tilde{X}$. Superpotential conjecture. The elements of $V$ should be weak bounding cocycles, and, after a change of coordinates in $(x_1,\ldots,x_{n+2})$, the superpotential should be equivalent to

$$W=\sum_{i=1}^{n+2}x_i^{n+2}+check{q}(q)x_1\cdots x_{n+2}.$$

In dimension one the weak unobstructedness and the equality of the generalized SYZ map with the mirror map are established; the conjecture proposes that these statements persist in general dimensions and gives an explicit form for the higher-dimensional mirror superpotential.