Galashin–Lam conjecture on DAHA/EHA invariants and KR homology of algebraic links

Let $C$ be a convex monotone curve, let $L_C$ be its associated link, and let $\mathcal P^{\mathcal E}_C(a,q,t)$ and $\mathcal P^{\operatorname{KR}}_{L_C}(a,q,t)$ denote respectively the paper's EHA invariant and the Khovanov–Rozansky polynomial. Galashin–Lam's algebraic-link conjecture. If $L_C$ is algebraic, then

$$\mathcal P^{\mathcal E}_C(a,q,t)=(1-t)^{\operatorname{k}(C)-1}\mathcal P^{\operatorname{KR}}_{L_C}(a,q,t),$$

up to multiplication by an explicit monomial in $a,q^{1/2},t^{1/2}$. This specializes the paper's question about which ${\mathbb Z}$-convex curves satisfy the identity; the source gives no resolution.