Basic-list conjecture for disconnected large bifurcation supports

Let a generic two-parameter glocal family of vector fields have a disconnected large bifurcation support. The basic list consists of the six unavoidable generic one-parameter degeneracy classes $\mathrm{AH}$, $\mathrm{SN}$, $\mathrm{HC}$, $\mathrm{SC}$, $\mathrm{SL}$, and $\mathrm{PC}$. Basic-list conjecture. Exactly two degeneracies from this basic list occur, each corresponding to one connected component of the large bifurcation support; moreover, a non-synchronization condition holds for each degeneracy of class $\mathrm{PC}$. The source says these results are expected to be proved in forthcoming work, so the statement remains conjectural.