The Weinstein-domain identification conjecture for Lagrangian skeleta

Let $Z$ be the open Batyrev–Borisov complete intersection with skeleton

$$\Lambda=\Phi^{-1}(\eL_\Sigma)\cap(M_{S^1}\times S),$$

where $S=\partial\widetilde{C}_{0,\beta}\subset M_\R$ is the codimension-$r$ sphere introduced above, and let $(S,\Sigma)$ be the fanifold obtained by pulling back the stratification of $N_\R$ by $\Sigma$. Denote by $\mathbf{W}(S,\Sigma)$ the Weinstein domain constructed from this fanifold. Weinstein-domain identification conjecture. There exists an isomorphism of Weinstein domains

$$Z\cong\mathbf{W}(S,\Sigma).$$

This conjecture would identify the A-side complete intersection with the Weinstein domain produced by the general fanifold construction, clarifying the relationship between the specific skeleton of $Z$ and the broader gluing framework for mirror symmetry. The source provides no evidence of a resolution, so the conjecture remains open.