Hazrat's shift-equivalence conjecture for Cuntz–Krieger and Leavitt path algebras

Let $A$ and $B$ be two finite essential matrices, and let $A$ and $B$ be shift equivalent (SE) when they are shift equivalent as nonnegative integer matrices. Denote by $\mathcal{O}_A$ and $\mathcal{O}_B$ the Cuntz–Krieger graph C*-algebras, with canonical gauge actions $\gamma^A$ and $\gamma^B$, and by $L_A$ and $L_B$ the associated Leavitt path algebras. The algebras $L_A$ and $L_B$ are graded Morita equivalent when they are Morita equivalent through equivalences preserving the grading.

Hazrat's conjecture. The following are equivalent:

1. $A$ and $B$ are SE.
2. $\mathcal{O}_A$ and $\mathcal{O}_B$ are stably isomorphic in a way preserving their gauge actions $\gamma^A$ and $\gamma^B$.
3. $L_A$ and $L_B$ are graded Morita equivalent.

This conjecture seeks a converse to Krieger's result that gauge-action-preserving stable isomorphism of the Cuntz–Krieger graph C*-algebras implies shift equivalence, while also asserting the corresponding equivalence with graded Morita equivalence of Leavitt path algebras. The supplied text does not state whether the conjecture has been resolved.