Shifted nonintersection conjecture for phase-lock areas

For $r\in\mathbb N$, let $L_r$ denote the phase-lock area with rotation number $r$, and let

$$\Lambda_{r-2}=\{B=\omega(r-2)\}\subset\mathbb R^2.$$

Shifted nonintersection conjecture. The phase-lock area $L_r$ does not intersect the line $\Lambda_{r-2}$. The source notes that this conjecture follows from the preceding nonintersection conjecture under additional known geometric facts, but supplies no resolution evidence for the conjecture itself.