Tree--necklace Gauss-load conjecture

Let $\Gamma$ be a tree-like or tree--necklace shadow, let $\operatorname{pt}(\Gamma)$ denote its Gauss load, and let $\operatorname{rot}(\Gamma)$ denote its rotation number. A reduced tangent-angle realization is obtained by deleting redundant full turns of monotonicity intervals, and a coorientation minimizes the conflict number when it minimizes the number of inflection conflicts.

Tree--necklace Gauss-load conjecture. For tree-like and tree--necklace shadows, the minimum Gauss load is obtained by a reduced tangent-angle realization of a coorientation minimizing the conflict number, after deleting all redundant full turns of monotonicity intervals. In particular, in these classes the only way to have $\operatorname{pt}(\Gamma)>|\operatorname{rot}(\Gamma)|$ should be that every reduced realization has a collection of Gauss folds whose images cover the whole circle.

Gauss load measures the least covering depth of the tangent circle by monotonicity intervals of the tangent angle. The conjecture connects this obstruction to the conflict-number minimization model, but the supplied text gives no resolution.