The initial-data-set rigidity conjecture for Euclidean prisms

Let $n\geq 3$, let $P^n$ be a Euclidean prism, $P_0\times[0,1]^{n-2}$, and let $(\Omega^n,g,k)$ be an initial data set admitting a degree-one map onto $P$. Assume that $(\Omega,g,k)$ satisfies the dominant energy condition, the boundary dominant energy condition, and that the dihedral angles of $\Omega$ are everywhere less than or equal to those of $P$. Initial-data-set rigidity conjecture. Then, on $\Omega$,

$$\mu-|J|_g=0.$$

This is proposed as a general version of a lemma intended to imply the spacetime positive mass theorem. The supplied text does not state whether the conjecture has been resolved.