Characterization of spherical objects by HN support

Determine whether the Harder–Narasimhan support always characterizes spherical objects in an arbitrary 2-Calabi–Yau category equipped with a generic stability condition.

Background

For a generic stability condition on a finite-type 2-Calabi–Yau category, every semistable spherical object is stable, so the Harder–Narasimhan factors of a spherical object are themselves spherical. This permits the definition of the HN support as a point of the associated simplicial complex. The paper proves instead that the ordered list of HN factors determines the spherical object, but does not establish that the support, which forgets ordering and multiplicities beyond its formal encoding, always does so.