Topology of tame contractible $n$-manifolds, $n=6,7$, with Positive BiRicci Curvature and Ricci lower bounds

We show that if an open smooth $6$-manifold $M^6$ is the interior of a compact, contractible manifold with boundary $X^6$, such that $π_3(X,\partial X)=0$, and $M$ supports a complete metric with uniform positive BiRicci curvature and Ricci curvature bounded below, then $M$ is diffeomorphic to $\mat