The $Q^{r}$ shift conjecture for symmetric pretzel-knot differences

Let $Q^r(c,r)$ denote the $r$th difference associated with a pretzel knot with odd parameters $a,b,c$, and let $[r]$ denote the symmetric representation with index $r$. Here $A$ and $q$ are the HOMFLY variables.

The $Q^r$ shift conjecture. For all odd integers $a,b,c$ and symmetric representations $[r]$,

$$Q^r(c,r)\,A^r q^{2r(r-1)}=Q^r(c+2,r).$$

The property is part of the paper's conjectured general properties and was verified there only for the stated finite computational ranges, so the general assertion remains open.