Existence conjecture for stable closed leafed elasticae

For an integer $r\geq4$, a closed $r$-leafed elastica is a closed elastic curve consisting of $r$ leaves. A stable elastic knot for the unknot class is a curve that locally minimizes the bending energy within the closure of the unknot class. Stable leafed-elastica conjecture. There are integers $r\geq4$ such that a closed $r$-leafed elastica is a stable elastic knot for the unknot class. This conjecture proposes further stable elastic-knot candidates beyond the elastic propeller and is motivated in part by the experimental realization of a $4$-leafed elastica; the source does not specify whether it has been resolved.