  We argue that the formation of Yu-Shiba-Rusinov excitations in proximitized
thin films is largely mediated by a type of Andreev-bound state named after de
Gennes and Saint James. This is shown by studying an experimentally motivated
model and computing the overlap of the wave functions of these two subgap
states. We find the overlap stays close to unity even as the system moves away
from weak coupling across the parity-changing quantum phase transition. Based
on this observation, we introduce a single-site model of the bound state
coupled to a quantum spin. The adequacy of this description is assessed by
reintroducing the coupling to the continuum as a weak perturbation and studying
its scaling flow using Anderson's poor man's scaling.
