  The mixed spherical models were recently found to violate long-held
assumptions about mean-field glassy dynamics. In particular, the threshold
energy, where most stationary points are marginal and that in the simpler pure
models attracts long-time dynamics, seems to lose significance. Here, we
compute the typical distribution of stationary points relative to each other in
mixed models with a replica symmetric complexity. We examine the stability of
nearby points, accounting for the presence of an isolated eigenvalue in their
spectrum due to their proximity. Despite finding rich structure not present in
the pure models, we find nothing that distinguishes the points that do attract
the dynamics. Instead, we find new geometric significance of the old threshold
energy, and invalidate pictures of the arrangement of most marginal inherent
states into a continuous manifold.
