Polynomial defining the maximal-dimensional augmentation component for knots

Let $K\subset\mathbb{R}^3$ be a knot, let $HC_*(K)$ be its contact homology algebra, and let

$$V_K=\setn{(\epsilon(\lambda),\epsilon(\mu))}{\epsilon\text{ is an augmentation of }HC_*(K)}\subset(\mathbb{C}^*)^2.$$

Let $\overline{V_K}$ denote the closure of $V_K$. Polynomial-component conjecture. The maximum-dimensional component of $\overline{V_K}$ is the vanishing set of a polynomial for every knot $K\subset\mathbb{R}^3$. This asserts algebraicity of the maximal-dimensional augmentation component, a property relevant to the relationship between knot contact homology and polynomial knot invariants. The supplied text gives no resolution or further scope for this claim.