Uniqueness conjecture for the elastic teardrop-heart

Let the figure-eight knot class be the knot class represented by the figure-eight knot, and let an elastic knot be understood in the sense of Gerlach–Reiter–von der Mosel. Elastic teardrop-heart conjecture. The elastic teardrop-heart obtained in Miura, Müller and Rupp is the unique elastic knot for the figure-eight knot class. The conjecture concerns a non-circular elastic knot motivated by experimental realizations; its resolution is not specified in the source.