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A strictification result is proved for isotropic distributions on derivedschemes equipped with negatively shifted homotopically closed $2$-forms. It isshown that any derived scheme over $\mathbb{C}$ equipped with a $-2$-shiftedsymplectic structure, and having a Hausdorff space of classical points, admitsa globally defined Lagrangian distribution as a dg$\mathbb{C}^{\infty}$-manifold.

Strictification and gluing of Lagrangian distributions on derived schemes with shifted symplectic forms