Combinatorial computability of Legendrian contact homology for products of Legendrian knots

Legendrian knots are Legendrian submanifolds in the contactization of a one-dimensional base, and their Legendrian contact homology is encoded by a differential graded algebra generated by Reeb chords. For two such knots, consider their Legendrian product in the corresponding product contact manifold. Combinatorial computability conjecture. The Legendrian contact homology of the products of Legendrian knots can be computed combinatorially. Legendrian contact homology is generally defined by counts of rigid punctured holomorphic disks; a combinatorial computation would extend the known combinatorial descriptions for Legendrian knots to their products. The source gives no resolution of this conjecture.