  This paper shows that simplicial oriented geometries can be characterized as
groupoids with root systems having certain favorable properties, as conjectured
by the first author. The proof first translates Handa's characterization of
oriented matroids, as acycloids which remain acycloids under iterated
elementary contractions, into the language of groupoids with root systems, then
establishes favorable lattice theoretic properties of a generalization of a
construction which Brink and Howlett used in their study of normalizers of
parabolic subgroups of Coxeter groups and uses Bj\"orner-Edelman-Ziegler's
lattice theoretic characterization of simplicial oriented geometries amongst
oriented geometries.
