A motivic integral identity for (-1) -shifted symplectic stacks

We prove a motivic integral identity relating the motivic Behrend function of a (-1) -shifted symplectic stack to that of its stack of graded points. This generalizes analogous identities for moduli stacks of objects in a 3-Calabix2013Yau category obtained by Kontsevichx2013Soibelman and Joycex2013Song, which are crucial in proving wall-crossing formulae for Donaldsonx2013Thomas invariants. We expect our identity to be useful in generalizing motivic Donaldsonx2013Thomas theory to general (-1) -shifted symplectic stacks.