  In this article, we study the index of log Calabi--Yau pairs $(X,B)$ of
coregularity 0. We show that $2\lambda(K_X+B)\sim 0$, where $\lambda$ is the
Weil index of $(X,B)$. This is in contrast to the case of klt Calabi--Yau
varieties, where the index can grow doubly exponentially with the dimension.
Our sharp bound on the index extends to the context of generalized log
Calabi--Yau pairs, semi-log canonical pairs, and isolated log canonical
singularities of coregularity 0. As a consequence, we show that the index of a
variety appearing in the Gross--Siebert program or in the Kontsevich--Soibelman
program is at most $2$. Finally, we discuss applications to Calabi--Yau
varieties endowed with a finite group action, including holomorphic symplectic
varieties endowed with a purely non-symplectic automorphism.
