Type-B hyper-polynomial conjecture

Let $K=K_{r,s}$ be a knot with $r,s\in\mathbf{Z}$, and let $b$ be a dominant weight for all $B_m$ with $m\ge n\ge2$. Type-B hyper-polynomial conjecture. There exists a polynomial $\mathcal{H}^{B}_{r,s}(b;q,t,u,a)$ with integral coefficients in positive powers of $a,q,t$ and powers $u^{\pm1}$ such that, for all $m\ge n$,

$$\mathcal{H}^{B}_{r,s}(b;q,t,u,a=-u^{m-1})=\widetilde{J\!D}^{B_m}_{r,s}(b;q,t,u).$$

Moreover,

$$\mathcal{H}^{B}_{r,s}(b;\sqrt q,1,u,a)=\mathcal{H}^{D}_{r,s}(b;q,t,a)=\mathcal{H}^{C}_{r,s}(b;q,t,u=1,a),$$

and the type-$B$ hyper-polynomial is invariant under the stated parameter transformation. These are proposed compatibilities among the $B,C,D$ theories; the source provides no proof of the general assertion.