The uniqueness conjecture for positive simple intersections

Let $\omega>0$. For $r\in\mathbb Z\setminus\{0\}$, let $L_r$ be the phase-lock area and let

$$\Lambda_r=\{B=r\omega\}$$

be its axis. A simple intersection is a point of $\partial L_r\cap\Lambda_r$ that is not a constriction.

The uniqueness conjecture. For every $r\in\mathbb Z\setminus\{0\}$, the simple intersection with positive ordinate is unique.

The source notes that the possible ordinates form a finite set of roots of a known polynomial, while the asserted uniqueness remains a conjecture.