The slope conjecture on the linear degree terms of colored Jones polynomials

For a knot $K\subset S^3$, write the maximal and minimal degrees of its colored Jones function as quadratic quasi-polynomials

$$d_{\varepsilon}[J_K(n)]=a_K^\varepsilon(n)n^2+b_K^\varepsilon(n)n+c_K^\varepsilon(n),\qquad \varepsilon\in\{+,-\}.$$

A knot is called mono-sloped when each $a_K^\varepsilon(n)$ is constant. Slope conjecture. For every non-trivial knot $K\subset S^3$,

$$b_K^+(n)\leq 0\qquad\text{and}\qquad b_K^-(n)\geq 0.$$

The source notes that this conjecture was proposed in the cited work and that the unknot is excluded because $b_U^+(n)=1/2$ and $b_U^-(n)=-1/2$; its resolution status is not specified.