Interpolation for Brill-Noether curves in $\mathbb{P}^4$

In this paper, we compute the number of general points through which a general Brill-Noether curve in $\mathbb{P}^4$ passes. We also prove an analogous theorem when some points are constrained to lie in a transverse hyperplane. As explained in arXiv:1809.05980, these results play an essential role in the first author's proof of the Maximal Rank Conjecture.