Knot-quiver skein relation conjecture

Let $K$ be a knot with corresponding quiver $Q_K$. For each crossing of type $L_+$, let $K_{i,\tau}$, with $\tau\binom{}{}$ replaced by $\tau eq$? be the knot or link obtained by changing or smoothing the $i$-th crossing, where $\tau ewcommand{}{}$ is one of the resolutions $-$ and $0$. The corresponding quivers are denoted $Q_{K_{i,\tau}}$. Knot-quiver skein relation conjecture. For every resolution $i,\tau$, $Q_{K_{i,\tau}}$ is a subquiver of $Q_K$ in an appropriate framing, and $Q_K$ admits a block form composed from any two such resolutions. This conjectural lifting of the HOMFLY-PT skein relation would encode all symmetric-coloured HOMFLY-PT skein relations at the quiver level; its status is not resolved in the supplied text.