It is well known that any metric with nonnegative scalar curvature on a torus is flat. Naturally, this leads one to wonder what the space of metrics with almost nonnegative scalar curvature looks like for the torus. Since scalar curvature is such a rough quantity, it’s a good guess that this space should exhibit quite a bit of flexibility. Indeed, this has been confirmed by recent work in the area. Therefore, in order to study this question fruitfully, one needs to carefully choose both the relevant hypotheses and topology. In this talk I will present joint work with Lizhi Chen in which we use Stern’s inequality to establish torus stability in the sense of Dong-Song for metrics with a lower Cheeger and metric bound.