  We study constructions of stable holomorphic vector bundles on Calabi-Yau
threefolds, especially those with exact anomaly cancellation which we call
extremal. By going through the known databases we find that such examples are
rare in general and can be ruled out for the spectral cover construction for
all elliptic threefolds. We then introduce a generalized version of
Hartshorne-Serre construction and use it to yield extremal bundles of general
ranks and study their geometry. In light of this probing the geometry of the
space of stable vector bundles, we revisit the DRY conjecture on stable
reflexive sheaves while focusing on the distribution of Chern numbers to use
both theoretical and statistical ideas to provide evidence for DRY.
