Joyce's special Lagrangian invariant conjecture for Calabi–Yau 3-folds

Let $(M,J,\omega,\Omega)$ be an (almost) Calabi–Yau $3$-fold with compact underlying $6$-manifold $M$, complex structure $J$, Kähler form $\omega$, and holomorphic volume form $\Omega$. Let $D^b(F(M,\omega))$ denote the derived Fukaya category, and let $\tau$ be the Bridgeland-type stability condition determined by $\Omega$. Joyce's special Lagrangian invariant conjecture. There should exist invariants $K^\alpha(J)\in\mathbb Q$ for $\alpha\in H_3(M,\mathbb Z)$ counting special Lagrangian homology $3$-spheres $N\subset M$ with $[N]=\alpha$, as well as possibly other immersed or singular special Lagrangian $3$-folds. They should be independent of $\omega$ and of complex rescalings of $\Omega$, transform according to the triangulated-category extension of the stated wall-crossing formula under deformation of $J$, and agree under mirror symmetry with the corresponding invariants of $\tilde\tau$-semistable objects in $D^b(\operatorname{coh}(P))$ for a mirror Calabi–Yau $3$-fold $P$. The source further proposes analogous systems counting configurations and a possible extension to (almost) Calabi–Yau $m$-folds for $m\geq 2$. This is presented as an extension of the extended Donaldson–Thomas conjecture and is not resolved in the source.