We prove Toda's normalized quintic Gepner conjecture. On every smooth complex quintic threefold, we construct a numerical Bridgeland stability condition for which tensoring by the hyperplane bundle, followed by the spherical twist at the structure sheaf, increases phase by 2/5.

Let X be a smooth projective complex threefold with trivial canonical bundle. We construct numerical Bridgeland stability conditions with the exact ordinary and square-root-Todd central charges at every sufficiently large volume. One volume threshold works on an open set of real twists and ample directions. The resulting stability conditions have the support property on the full numerical Grothendieck group and stable point sheaves. Separately, on every smooth projective complex threefold we prove a strong tilt inequality above a volume threshold uniform in the object and twist along a fixed polarization.