Strong Slope Conjecture for knots

Let $K$ be a knot, let $M_K$ be its exterior, and let $js_K$ be the set of Jones slopes obtained from the cluster points of $4n^{-2}d_+[J_K(n)]$. Let $jx_K$ be the cluster-point set of twice the normalized linear terms of the highest colored-Jones degrees. Strong Slope Conjecture. Let $a/b\in js_K$ be a Jones slope, with $b>0$ and $\gcd(a,b)=1$. Then there is an essential surface $S\subset M_K$ with $|\partial S|$ boundary components, each component of $\partial S$ having slope $a/b$, such that

$$\frac{\chi(S)}{|\partial S|b}\in jx_K.$$

This strengthens the Slope Conjecture by relating the Euler characteristic of the essential surface to the linear term of the colored Jones polynomial. It is presented as a conjecture, and no general resolution is given in the paper.