Quantisation of derived Poisson structures

We prove that every $0$-shifted Poisson structure on a derived Deligne--Mumford $n$-stack admits a curved $A_{\infty}$ quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes. Where the Kontsevich-Tamarkin approach to quantisation hinges on invariance of the Hochschild complex under affine transformations, we instead exploit the observation that it carries an involution, and that such involutive deformations of the complex of polyvectors are essentially unique.