Converse to the Bridgeland stability criterion for deformed Hermitian–Yang–Mills

Let $(X,\omega)$ be a Kähler $3$-fold and let $L\to X$ be a holomorphic line bundle. Assume that $L$ admits a solution of the deformed Hermitian–Yang–Mills equation with lifted angle $\hat{\theta}\in(\pi,\frac{3\pi}{2})$. Let $Z_V(L)$ and $\varphi_V(L)$ denote the central charge and slicing angle associated to every irreducible analytic subset $V\subset X$, and let $\mathbb H=\\{z\in\mathbb C:{\rm Im}(z)>0\\}$. Proposition~ asserts, in particular, the corresponding upper-half-plane and angle inequalities. Converse conjecture. The converse of Proposition~ holds. This updates a conjecture from Collins–Jacob–Yau; its small-radius limit for ample line bundles was proved by Collins and Székelyhidi, but the full converse remains unresolved in the supplied source.