Kusner–Sullivan's composite-knot energy conjecture

Let $[K_1]$ and $[K_2]$ be isotopy classes of knots, and let $[K_1\sharp K_2]$ be their composite isotopy class. For an isotopy class $[K]$, write $E^{(2)}_{\circ}([K])$ for the infimum of $E^{(2)}_{\circ}$ on that class; an $E^{(2)}_{\circ}$--minimizer is a knot in the class attaining this infimum. Kusner–Sullivan's conjecture. There are no $E^{(2)}_{\circ}$--minimizers in any isotopy class of a composite knot $[K_1\sharp K_2]$, and

$$E^{(2)}_{\circ}([K_1\sharp K_2])=E^{(2)}_{\circ}([K_1])+E^{(2)}_{\circ}([K_2]).$$

The conjecture arose from numerical experiments and the proposed pull-tight behavior of the two tangles in a composite knot. The source gives no resolution.