  For sequences of warped product metrics on a $3$-torus satisfying the scalar
curvature bound $R_j \geq -\frac{1}{j}$, uniform upper volume and diameter
bounds, and a uniform lower area bound on the smallest minimal surface, we find
a subsequence which converges in both the Gromov-Hausdorff and the
Sormani-Wenger Intrinsic Flat sense to a flat $3$-torus.
