  The Harder-Narasimhan types are a family of discrete isomorphism invariants
for representations of finite quivers. Previously (arXiv:2303.16075), we
evaluated their discriminating power in the context of persistence modules over
a finite poset, including multiparameter persistence modules (over a finite
grid). In particular, we introduced the skyscraper invariant and proved it was
strictly finer than the rank invariant. In order to study the stability of the
skyscraper invariant, we extend its definition from the finite to the infinite
setting and consider multiparameter persistence modules over $\mathbb Z ^n$ and
$\mathbb R^n$. We then establish an erosion-type stability result for this
version of the skyscraper invariant.
