Non-determinacy of HOMFLY-PT homology for diagrams

We show that for any two knots $K_1$, $K_2$ in $\mathbb{R}^3$, there exist diagrams $D_1$ and $D_2$ that represent $K_1$ and $K_2$, respectively, such that the Khovanov--Rozansky triply graded homologies of $D_1$ and $D_2$ are isomorphic.

The methods expand on Abel's paper [Abe17].