  The computational difficulty of six-dimensional neutrino radiation
hydrodynamics has spawned a variety of approximations, provoking a long history
of uncertainty in the core-collapse supernova explosion mechanism. Under the
auspices of the Terascale Supernova Initiative, we are honoring the physical
complexity of supernovae by meeting the computational challenge head-on,
undertaking the development of a new adaptive mesh refinement code for
self-gravitating, six-dimensional neutrino radiation magnetohydrodynamics. This
code--called {\em GenASiS,} for {\em Gen}eral {\em A}strophysical {\em
Si}mulation {\em S}ystem--is designed for modularity and extensibility of the
physics. Presently in use or under development are capabilities for Newtonian
self-gravity, Newtonian and special relativistic magnetohydrodynamics (with
`realistic' equation of state), and special relativistic energy- and
angle-dependent neutrino transport--including full treatment of the energy and
angle dependence of scattering and pair interactions.
