Rational linear independence conjecture for volumes of large Dehn fillings

Let $\mathcal{M}$ be a $1$-cusped hyperbolic $3$-manifold with non-quadratic cusp shapes. For $n>0$, choose $n$ distinct Dehn filling coefficients, all sufficiently large, and let the resulting filled manifolds be the corresponding Dehn fillings of $\mathcal{M}$. Rational linear independence conjecture. Their volumes are linearly independent over $\mathbb{Q}$.

A theorem in the paper proves the analogous statement for pseudo complex volumes under the same non-quadratic cusp-shape and sufficiently-large-coefficient hypotheses. The conjecture asks for the corresponding assertion for ordinary volumes.