Equality of top HOMFLY–Khovanov–Rozansky polynomials in the knot case

Let $\beta$ be a braid whose closure $\hat\beta$ is a knot. Let $\mathcal{P}_{\operatorname{KR}}^{\operatorname{top}}(\beta;q,t)$ denote the equivariant top polynomial and let $\mathcal{P}_{{\operatorname{KR}};\mathbb{C}}^{\operatorname{top}}(\beta;q,t)$ denote its non-equivariant analogue. Assume that

$$\mathcal{P}_{{\operatorname{KR}};\mathbb{C}}^{\operatorname{top}}(\beta;q,t)\neq0.$$

Equality conjecture. Under these assumptions,

$$\mathcal{P}_{\operatorname{KR}}^{\operatorname{top}}(\beta;q,t)=\mathcal{P}_{{\operatorname{KR}};\mathbb{C}}^{\operatorname{top}}(\beta;q,t).$$

The surrounding discussion notes that the relevant top polynomial is known to be a link invariant when the closure is a knot, while the asserted equality between the equivariant and non-equivariant constructions is presented as conjectural. The supplied text gives no resolution of this claim.