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 Formula Presented-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 the 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 the stability space Formula Presented associated to the flop; and (4) a new proof of the Formula Presented-theorem in various finite settings, which includes ADE braid groups.
