Chen–Yang unknot detection conjecture for Turaev–Viro invariants

Let $K$ be a knot in $S^3$, and let $TV_r(K)$ denote the corresponding Turaev–Viro invariant, evaluated at the allowed roots of unity $q$. Chen–Yang unknot detection conjecture.

$$TV_r(K)=1\ \text{for all }r\text{ and }q\quad\Longleftrightarrow\quad K\text{ is the unknot}.$$

The conjecture is motivated by the calculation that the unknot has invariant equal to $1$ for every level and allowed root of unity; it asks whether the whole family detects the unknot and remains open.