Cusp-shape norm conjecture for equal-volume Dehn fillings

Let $M$ be a $1$-cusped hyperbolic $3$-manifold with cusp shape $c_{1}$. Cusp-shape norm conjecture. If

$$\operatorname{vol} M(p,q)=\operatorname{vol} M(p',q')$$

for sufficiently large $|p|+|q|$, then

$$|p+c_1q|=|p'+c_1q'|.$$

The conjecture proposes that, asymptotically, equality of real volumes forces equality of the corresponding cusp-shape norms. The source presents it as a proposed explanation of the experimental relation between volume differences and the cusp shape; no resolution is given.