The Legendrian BMW algebra isomorphism conjecture

Let $\operatorname{BMW}^{\mathfrak{Leg}}_n$ be the Legendrian BMW algebra and let $\operatorname{BMW}^{\infty}_n$ be the specialized BMW algebra, with $\varphi\colon \operatorname{BMW}^{\mathfrak{Leg}}_n\rightarrow\operatorname{BMW}^{\infty}_n$ the algebra homomorphism induced by the map from Legendrian to framed tangles. When $\operatorname{BMW}^{\mathfrak{Leg}}_n$ is defined over $\mathbb{Z}(s)$, the Legendrian BMW isomorphism conjecture. The map $\varphi$ is an algebra isomorphism. This conjecture asserts that the Legendrian BMW algebra has no additional relations beyond those detected in the specialized framed BMW algebra; the supplied text gives no resolution, so its status remains open.