  The density structure surrounding the iron core of a massive star when it
dies is known to have a major effect on whether or not the star explodes. Here
we repeat previous surveys of presupernova evolution with some important
corrections to code physics and four to ten times better mass resolution in
each star. The number of presupernova masses considered is also much larger.
Over 4,000 models are calculated in the range from 12 to 60 Msun with varying
mass loss rates. The core structure is not greatly affected by the increased
spatial resolution. The qualitative patterns of compactness measures and their
extrema are the same, but with the increased number of models, the scatter seen
in previous studies is replaced by several localized branches. More
physics-based analyses by Ertl et al. (2016) and M$\"u$eller et al. (2016) show
these branches with less scatter than the single parameter characterization of
O'Connor & Ott (2011). These branches are particularly apparent for stars in
the mass ranges 14 - 19 Msun and 22 - 24 Msun. The multi-valued solutions are a
consequence of interference between several carbon and oxygen burning shells
during the late stages of evolution. For a relevant range of masses, whether a
star explodes or not may reflect more the small, almost random differences in
its late evolution than its initial mass. The large number of models allow
statistically meaningful statements about the radius, luminosity, and effective
temperatures of presupernova stars, their core structures, and their remnant
mass distribution.
