  This paper gives a description of the full space of Bridgeland stability
conditions on the bounded derived category of a contraction algebra associated
to a 3-fold flop. The main result is that the stability manifold is the
universal cover of a naturally associated hyperplane arrangement, which is
known to be simplicial, and in special cases is an ADE root system. There are
four main corollaries: (1) a short proof of faithfulness of pure braid group
actions in both algebraic and geometric settings, the first that avoid normal
forms, (2) a classification of tilting complexes in the derived category of a
contraction algebra, (3) contractibility of a certain stability space
associated to the flop, and (4) a new proof of the $K(\pi,1)$-theorem in
various finite settings, which includes ADE braid groups.
