Sulci are localized furrows on the surface of soft materials that form by a compression-induced
instability. We unfold this instability by breaking its natural scale and translation invariance, and compute
a limiting bifurcation diagram for sulcfication showing that it is a scale-free, subcritical nonlinear
instability. In contrast with classical nucleation, sulcification is continuous, occurs in purely elastic
continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus
nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On
unloading, it quasistatically shrinks to a point with a lower critical strain, explained by breaking of scale
symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with no energy
barrier. Simple experiments confirm the existence of these two critical strains.