Existence of nondestabilizable Legendrian knots with vanishing contact homology

A nondestabilizable Legendrian knot is a Legendrian knot that cannot be obtained from another Legendrian knot by stabilization. Its Legendrian contact homology is the homology associated with its contact-homology differential graded algebra. Existence conjecture. There exist nondestabilizable Legendrian knots with vanishing contact homology. The proposed evidence is conditional: the paper proves vanishing for a particular Legendrian knot and notes that, if this knot is nondestabilizable, it would give the first such example. Thus the claim remains open in the source.