Nice-balance conjecture for balanced links

Let $L$ be a link that is balanced in the sense of the paper's balance criterion, and let a link be nicely balanced when its kink measure is represented by a kink tension function with the stated regularity. Nice-balance conjecture. Every balanced link is nicely balanced. In particular, the kink measure is supported over piecewise $C^2$ arcs of the link. This is presented as a rephrasing of the preceding regular-balance conjecture using the paper's main theorem.