Holomorphic extension conjecture for the stability-condition embedding

Let $\mathcal{MC}(m)^{\Gamma}_{\ast,s}$ be the open subspace of framed cubic differentials whose zeros are distinct. Let $\mathcal D$ be the associated $CY_3$ category, let $\mathrm{Stab}_0(\mathcal D)$ be the specified connected component of its stability manifold, and let $\mathcal Aut_0(\mathcal D)$ be the quotient of the automorphisms preserving that component by those acting trivially on it. The map $K$ is the holomorphic embedding from the connected component $\mathcal{MC}(m)^{\Gamma}_{1,\ast}$ into $\mathrm{Stab}_0(\mathcal D)/\mathcal Aut_0(\mathcal D)$ constructed in the preceding theorem. Holomorphic extension conjecture. The map $K$ can be holomorphically extended to $\mathcal{MC}(m)^{\Gamma}_{\ast,s}$ as a map $\widetilde{K}$, namely

$$\widetilde{K}: \mathcal{MC}(m)^{\Gamma}_{\ast,s}\to\mathrm{Stab}_0(\mathcal D)/\mathcal Aut_0(\mathcal D).$$

The conjecture proposes extending the stability-condition construction beyond the BPS-free generic base-point setting to the locus of framed differentials with distinct zeros. The source does not state whether this extension has been established.