Chen–Yang integrality conjecture for Turaev–Viro invariants of torus links

Let $T_{(m,n)}$ be the $(m,n)$-torus link in $S^3$, with $m<n$. Let $TV_r(S^3\setminus T_{(m,n)})$ be its Turaev–Viro invariant. Chen–Yang integrality conjecture. If $r$ is coprime to $n$, then $TV_r(S^3\setminus T_{(m,n)})$ is an integer independent of the choice of the roots of unity $q$.

The conjecture is suggested by numerical calculations for several torus-knot and torus-link complements and predicts both integrality and root-independence under the stated coprimality condition; it remains open.