Closure relation conjecture for dual polynomials of multi-indexed $(q$-)Racah systems

Let $R_i(z)$, for $i=0,1,-1$, be the polynomials defined by the determinant formula in equation (Ri2), together with the preceding definitions of their coefficients, and let $\check{X}(j)$ and $B^{\text{dual}}_{\mathcal{D},j}$ be the quantities appearing there. The closure relation is the relation denoted by equation (cr). Closure relation conjecture. The closure relation

$$\text{(cr)}$$

holds for the polynomials $R_i(z)$ defined by equations (Ri) and (Ri2). This conjecture asserts that the polynomials obtained from the multi-indexed $(q$-)Racah systems satisfy the same type of closure relation as the original systems, despite their generally higher degrees.