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A motivic integral identity for
$(-1)$-shifted symplectic stacks
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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 
$3$-Calabi–Yau abelian categories obtained by Kontsevich and Soibelman, and Joyce and Song, which are crucial in proving wall-crossing formulae for Donaldson–Thomas invariants. We expect our identity to be useful in extending motivic Donaldson–Thomas theory to general 
$(-1)$-shifted symplectic stacks.
