Algebraicity conjecture for perturbative link invariants in Seifert spaces

Let $M$ be a Seifert space with orbifold Euler characteristic $\chi>0$, and let $a$ be the Seifert parameter occurring in the exponential variable. Let $L$ be a finite-degree extension of $\mathbb{Q}(e^{-\chi u_0/(2a)})$, and let $L_2\subseteq L$ be obtained from $L$ by the substitution $u_0\mapsto2u_0$.

Link-invariant algebraicity conjecture. All perturbative colored HOMFLY invariants of links in $M$ belong to $L$, and all perturbative colored Kauffman invariants of links in $M$ belong to $L_2$.

The conjecture would extend the algebraicity established for fiber knots to the missing basic knots and arbitrary links; the source explicitly presents this as an open proposal.