Current all-orders proofs of factorization of hard processes
are made by extracting the leading power behavior of Feynman graphs,
i.e., by extracting asymptotics strictly order-by-order in
perturbation theory. The resulting parton densities and
fragmentation functions include non-perturbative effects. I show
how there are missing elements in the proofs; these are related to
and exemplified by string and cluster models of hadronization. The
proofs rely on large rapidity differences between different parts of
graphs for the process; but in reality large rapidity gaps are
filled in.