The characteristic equals deformation variety conjecture for knots

Let $K$ be a knot in $S^3$. Its deformation variety $D(K)$ is the image of the character variety of $\mathrm{SL}_2(\mathbb C)$ representations of the complement $M=S^3-\operatorname{nbd}(K)$ under restriction to the boundary torus, viewed in $(\mathbb C^\star)^2$ with coordinates $(L,M)$. The characteristic variety is the algebraic variety associated with the recursion relations of the colored Jones function. For an affine subvariety $V\subset\mathbb C^2$, write $V=V_0\sqcup V_1\sqcup V_2$ for its decomposition into pure-dimensional subvarieties, and call two subvarieties essentially equal when their one-dimensional parts agree up to the union of some lines $y=a$. The characteristic equals deformation variety conjecture. For every knot in $S^3$, the characteristic and deformation varieties are essentially equal. This conjecture proposes that the algebraic geometry encoded by the recursion relations of the colored Jones function agrees, up to the stated one-dimensional exceptional components, with the boundary character variety arising from the knot complement.