present in much more general cases than the experimentally relevant strong-coupling limit.

We additionally perform numerical simulations of a nanowire/superconductor hybrid system in which a region of the nanowire is left uncovered by the superconductor. As we explicitly incorporate a superconducting layer with finite thickness, our numerical model accounts for both the strong proximity coupling and the strong dependence of the proximitized region on the geometry of the superconductor, two crucial aspects of the system that have been neglected in previous works. Consistent with our analytical model, we find a low-energy ABS by tuning the spin-orbit length to a resonant value with respect to the dot length $L$, with no topological phase transition occurring due to the strong proximity coupling. Crucially, we find that the presence of this ABS is insensitive to the thickness of the superconducting layer and the details of the proximity effect; as the properties of the proximitized region of the nanowire, and thus the topological phase transition, are highly dependent on these two quantities [@Reeg:2017_3; @Reeg:2018; @Reeg:2018_2], this result further demonstrates that the ABS is a property of the dot and unrelated to any properties of the superconducting region. Finally, we show that if the quantum 