Integrality conjecture for reformulated colored Kauffman invariants of links

Let ${\cal L}$ be an unoriented link with $L$ components, colored by representations $R_1,\ldots,R_L$. Let $\hat h_{R_1,\ldots,R_L}(t,\nu)$ and $\hat g_{R_1,\ldots,R_L}(t,\nu)$ be the reformulated colored Kauffman invariants, and set $z=t-t^{-1}$. Kauffman integrality conjecture for links. There are integers $N^{c=0}_{R_1,\ldots,R_L;g,Q}$, $N^{c=1}_{R_1,\ldots,R_L;g,Q}$ and $N^{c=2}_{R_1,\ldots,R_L;g,Q}$ such that

$$\hat h_{R_1,\ldots,R_L}(t,\nu)\in z^{L-2}{\mathbb Z}[z^2,\nu^{\pm1}],\qquad \hat g_{R_1,\ldots,R_L}(t,\nu)\in z^{L-1}{\mathbb Z}[z,\nu^{\pm1}],$$

with

$$\hat h_{R_1,\ldots,R_L}(t,\nu)=z^{L-2}\sum_{g\geq0}\sum_{Q\in{\mathbb Z}}N^{c=0}_{R_1,\ldots,R_L;g,Q}z^{2g}\nu^Q,$$ $$\hat g_{R_1,\ldots,R_L}(t,\nu)=z^{L-1}\sum_{g\geq0}\sum_{Q\in{\mathbb Z}}\left(N^{c=1}_{R_1,\ldots,R_L;g,Q}z^{2g}\nu^Q+N^{c=2}_{R_1,\ldots,R_L;g,Q}z^{2g+1}\nu^Q\right).$$

This extends the knot-level Kauffman integrality prediction to unoriented links, where the reformulated invariants involve Kauffman invariants together with HOMFLY invariants for all choices of orientations.