The conjectural identification of the first Bar-Natan–van der Veen polynomial

Let $K$ be a 0-framed knot. The polynomial $\rho_K^{1,0}$ is a Bar-Natan–van der Veen polynomial, and $P_K^1$ is the first Rozansky polynomial.

First-polynomial identification conjecture.

$$\rho_K^{1,0}=P_K^1.$$

Computational tables support this equality. The source further explains that, for higher indices, the corresponding polynomials appear to differ because of the chosen central element in the construction.