The colored-link motivic–DAHA embedding conjecture

Let $\mathcal{R}=\mathbf{F}_q[[x,y]]\subset\Omega=\mathbf{F}_q[[\epsilon_j,\zeta_j]]$, and let $\widetilde{\mathcal R}=\mathbf{F}_q[[\widetilde x,\widetilde y]]$ be the sufficiently general deformation with $\widetilde x=\sum_{j=1}^{\tau}\pi_j\chi_j$ and $\widetilde y=y$. Suppose $\sigma=(c_1\ge\cdots\ge c_\kappa)$. Colored-link embedding conjecture. The standard modules for $\mathcal R$ can be identified with standard modules for $\widetilde{\mathcal R}$ whose componentwise spans satisfy $\mathcal O_i\widetilde M=\Omega_i$, and under this identification

$$\prod_{j=1}^{c_1-1}(1+aq^j)\,\mathcal H^{mot}_\sigma$$

is naturally embedded in the motivic superpolynomial $\widetilde{\mathcal H}$ of $\widetilde{\mathcal R}$.