  The main theorem, I.a, is the existence for excellent Deligne-Mumford champ
of characteristic zero of a resolution functor independent of the resolution
process itself. Perceived wisdom was that this was impossible, but the
counterexamples overlooked the possibility of using weighted blow ups. The
fundamental local calculations take place in complete local rings, and are
elementary in nature, while being self contained and wholly independent of
Hironaka's methods and all derivatives thereof, i.e. existing technology.
Nevertheless Abramovich, Temkin, and Wlodarczyk, [ATW], have varied existing
technology to obtain an even shorter proof of principalisation, I.f, in the
geometric case. Excellent patching is more technical than varieties over a
field, and whence easier geometric arguments are pointed out when they exist.
