The constriction-curve and phase-lock-area garland conjecture

Consider the three-dimensional parameter space $\mathbb R^2_{B,A}\times(\mathbb R_+)_{\omega}$. For $r\in\mathbb Z_{\neq0}$, the growth points of the phase-lock areas form the $r$-th growth curve, and the family of constrictions is a one-dimensional submanifold whose connected components are called constriction curves. Denote the three-dimensional phase-lock area with rotation number $r\in\mathbb Z$ by $\widehat L_r$. Constriction-curve and garland conjecture. Each constriction curve is bijectively projected onto $(\mathbb R_+)_{\omega}$, and each three-dimensional phase-lock area is a countable garland of domains, with any two adjacent domains separated either by the corresponding growth curve or by a constriction curve. The source presents this as an open problem about the global geometry of the family of phase-lock areas and constrictions.