The dimer-model conjecture for torus knots

A $(p,q)$ torus knot is the knot represented by the standard torus-knot construction with coprime positive integers $p$ and $q$. A dimer model is a combinatorial model whose underlying graph is bipartite and whose perfect matchings encode the relevant knot-theoretic data.

Torus-knot dimer-model conjecture. Every $(p,q)$ torus knot admits a dimer model.

The conjecture is proposed as a future direction motivated by the explicit computations in the paper and by the braid-group description of torus knots. The source does not give evidence that it has been proved or disproved.