Collins–Yau conjecture on dHYM solutions and Bridgeland stability

Let $X$ be the compact Kähler manifold under consideration, and let $L$ be a holomorphic line bundle on $X$. A metric solving the deformed Hermitian–Yang–Mills equation is a metric on $L$ satisfying that equation, and $D^b(\operatorname{Coh}(X))$ denotes the bounded derived category of coherent sheaves on $X$. Collins–Yau conjecture. $L$ admits a metric solving the deformed Hermitian–Yang–Mills equation if and only if $L$ is a Bridgeland stable object in

$$D^b(\operatorname{Coh}(X)).$$

This conjecture proposes an equivalence between the differential-geometric existence problem for the deformed Hermitian–Yang–Mills equation and Bridgeland stability for line bundles. Its resolution is not specified in the supplied source context.