Bridgeland stability conjecture for the double tilt of an abelian threefold

Let $X$ be an abelian threefold, let $B\in\operatorname{NS}_{\mathbb{R}}(X)$, and let $\omega\in\operatorname{NS}_{\mathbb{R}}(X)$ be an ample class. With $\mathcal{B}_{\omega,B}$ the tilt of $\operatorname{Coh}(X)$ at the $\mu_{\omega,B}$-torsion pair, define $\nu_{\omega,B}$ as above, let $\mathcal{T}'_{\omega,B}=\operatorname{HN}^{\nu}_{\omega,B}(0,+\infty]$ and $\mathcal{F}'_{\omega,B}=\operatorname{HN}^{\nu}_{\omega,B}(-\infty,0]$, and set $\mathcal{A}_{\omega,B}=\langle\mathcal{F}'_{\omega,B}[1],\mathcal{T}'_{\omega,B}\rangle\subset D^b(X)$. The central charge is $Z_{\omega,B}$. Bridgeland stability conjecture. The pair $(Z_{\omega,B},\mathcal{A}_{\omega,B})$ is a Bridgeland stability condition on $D^b(X)$. This is the original threefold stability conjecture of Bayer, Macrì, and Toda; it is equivalent, under the rationality and Noetherian hypotheses described in the source, to the Bogomolov–Gieseker type inequality in the next row.