  In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa
(GV) type formula for the generating series of stable pair invariants on
Calabi-Yau (CY) 4-folds. The purpose of this paper is to give an interpretation
of the above GV type formula in terms of wall-crossing phenomena in the derived
category. We introduce invariants counting LePotier's stable pairs on CY
4-folds, and show that they count certain stable objects in D0-D2-D8 bound
states in the derived category. We propose a conjectural wall-crossing formula
for the generating series of our invariants, which recovers the conjectural GV
type formula. Examples are computed for both compact and toric cases to support
our conjecture.
