The moduli conjecture for strongly asymptotically conical special Lagrangian folds

Let $L$ be a strongly asymptotically conical special Lagrangian $m$-fold in $\mathbb C^m$ with cone $C$, and let $k$ be the number of ends of $C$ at infinity. Let $\mathcal M^s_L$ be the moduli space of strongly asymptotically conical special Lagrangian $m$-folds in $\mathbb C^m$ with cone $C$. Strongly asymptotically conical moduli conjecture. Near $L$, the space $\mathcal M^s_L$ is a smooth manifold of dimension $b^1(L)+k-1$. The paper presents this as an expected local moduli result because the relevant proofs were not yet complete.