The hyperbolic cosmetic filling conjecture

Let $N$ be a cusped hyperbolic 3-manifold, and consider fillings of $N$ along distinct slopes that produce hyperbolic manifolds. A filling pair is cosmetic if the resulting manifolds are homeomorphic, either orientation-preservingly (true) or orientation-reversingly (reflective). Hyperbolic cosmetic filling conjecture. Cusped hyperbolic manifolds admit no cosmetic fillings, true or reflective, yielding hyperbolic manifolds. The conjecture is motivated by an earlier theorem in the source, but no resolution is supplied.