Constriction abscissa conjecture for phase-lock areas

Let $L_\rho$ be the phase-lock area with rotation number $\rho$, and call the separation points between consecutive bounded domains in its chain constrictions when they do not lie on the horizontal $B$-axis. Constriction abscissa conjecture. In every phase-lock area $L_\rho$, all constrictions lie on the line

$$\{B=\rho\omega\}.$$

This is described as a main open conjecture on the geometry of the phase-lock area portrait and is supported experimentally; a survey and related open problems are cited in the source.