  A definition of partonic jet flavor that is both theoretically well-defined
and experimentally robust would have profound implications for measurements and
predictions especially for heavy flavor applications. Recently, a definition of
jet flavor was introduced as the net flavor flowing along the direction of the
Winner-Take-All axis of a jet which is soft safe to all orders, but not
collinear safe. Here, we exploit the lack of collinear safety and propose a
factorization theorem of perturbative flavor fragmentation functions that resum
collinear divergences and describe the evolution of flavor from the short
distance of jet production to the long distance at which hadronization occurs.
Collinear flavor evolution is governed by a small modification of the DGLAP
equations. We present a detailed all-orders analysis and identify exact
relations that must hold amongst the various anomalous dimensions by
probability conservation and the existence of fixed points of the
renormalization group flow. We explicitly validate the factorization theorem at
one-loop order, and demonstrate its consistency at two loops in particular
flavor channels. Starting at two-loops, constraints on phase space imposed by
flavor measurements potentially allow for non-trivial soft contributions, but
we demonstrate that they are scaleless and so explicitly vanish, ensuring that
soft particles are summed inclusively and all divergences are exclusively
collinear in nature. This factorization theorem opens the door to precision
calculations with identified flavor in the infrared.
