The Borel-resummed invariant conjecture for colored Jones asymptotics

Let $K$ be a knot, let $J_n(q)$ be its $n$-colored Jones polynomial, and let $F_K(x,q)$ be the two-variable invariant defined by Borel resummation of the colored Jones expansion. For a root of unity $\zeta$, write $q=\zeta e^{\hbar}$. The Borel-resummed invariant conjecture. For every color $n$, the asymptotic expansions of $(q^{n/2}-q^{-n/2})J_n(q)$ and $F_K(q^n,q)$ near every root of unity agree; equivalently,

$$(\zeta^{n/2}e^{n\hbar/2}-\zeta^{-n/2}e^{-n\hbar/2})J_n(\zeta e^{\hbar})\stackrel{\mathrm{perturbatively}}{=}F_K(\zeta^n e^{n\hbar},\zeta e^{\hbar}).$$

This proposes that $F_K(x,q)$ contains the asymptotic information of colored Jones polynomials at every root of unity. The source notes that this is compatible with the volume conjecture because the relevant limits are of different types: the limit defining $F_K$ is radial, whereas the volume-conjecture limit lies on the unit circle.