  We show that for closed orientable manifolds the $k$-dimensional stable
systole admits a metric-independent volume bound if and only if there are
cohomology classes of degree $k$ that generate cohomology in top-degree.
Moreover, it turns out that in the nonorientable case such a bound does not
exist for stable systoles of dimension at least two.
  Additionally, we prove that the stable systolic constant depends only on the
image of the fundamental class in a suitable Eilenberg-Mac Lane space.
Consequently, the stable $k$-systolic constant is completely determined by the
multilinear intersection form on $k$-dimensional cohomology.
