  In a finite real reflection group, two factorizations of a Coxeter element
into an arbitrary number of reflections are shown to lie in the same orbit
under the Hurwitz action if and only if they use the same multiset of conjugacy
classes. The proof makes use of a surprising lemma, derived from a
classification of the minimal linear dependences (matroid circuits) in finite
root systems: any set of roots forming a minimal linear dependence with
positive coefficients has a disconnected graph of pairwise acuteness.
