  We study the structural features and underlying principles of
multi-dislocation ground states of a crystalline spherical cap. In the
continuum limit where the ratio of crystal size to lattice spacing $W/a$
diverges, dislocations proliferate and ground states approach a characteristic
sequence of structures composed of radial grain boundaries ("neutral scars"),
extending radially from the boundary and terminating in the bulk. Employing a
combination of numerical simulations and asymptotic analysis of continuum
elasticity theory, we prove that an energetic hierarchy gives rise to a
structural hierarchy, whereby dislocation number and scar number diverge as
$a/W \to 0$ while scar length and dislocation number per scar become {\it
independent} of lattice spacing. We characterize a secondary transition
occurring as scar length grows, where the $n$-fold scar symmetry is broken and
ground states are characterized by polydisperse, forked-scar morphologies.
