  We consider a generalized Dirac operator on a compact stratified space with
an iterated cone-edge metric. Assuming a spectral Witt condition, we prove its
essential self-adjointness and identify its domain and the domain of its square
with weighted edge Sobolev spaces. This sharpens previous results where the
minimal domain is shown only to be a subset of an intersection of weighted edge
Sobolev spaces. Our argument does not rely on microlocal techniques and is very
explicit. The novelty of our approach is the use of an abstract functional
analytic notion of interpolation scales. Our results hold for the Gauss-Bonnet
and spin Dirac operators satisfying a spectral Witt condition.
