The equivalence conjecture for the universal invariant of a knot

Let $K$ be a 0-framed knot. Consider the universal invariant $Z_\mathbb{D}(K)$, the coloured Jones polynomials $\{J_K^n(K)\}_{n\geq 2}$, and the Rozansky polynomials $\{P_K^n(K)\}_{n\geq 1}$.

Universal-invariant equivalence conjecture. The datum of the universal invariant $Z_\mathbb{D}(K)$ is equivalent to any of the three pieces of data in the preceding theorem.

The paper notes that $Z_\mathbb{D}(K)$ determines the universal $U_h(\mathfrak{sl}_2)$ invariant, and hence the other two data sets. The conjectural content is that no additional information is contained in $Z_\mathbb{D}(K)$.