The vertical-ray conjecture for phase-lock areas

Let $\omega>0$. For $r\in\mathbb Z\setminus\{0\}$, let $L_r^+=L_r\cap\{A\geq0\}$ be the upper part of the phase-lock area, let $\Lambda_r=\{B=r\omega\}$ be its axis, and let $\mathcal P_r$ be the higher simple intersection. Define the vertical ray

$$S_r=\{r\omega\}\times[A(\mathcal P_r),+\infty)\subset\Lambda_r.$$

The vertical-ray conjecture.

$$L_r^+\cap\Lambda_r=S_r$$

for every $r\in\mathbb Z\setminus\{0\}$.

The source uses this conjecture to derive other geometric conjectures about phase-lock areas and constrictions; no proof or disproof is given in the supplied text.