We show that the celebrated operad of pre-Lie algebras is very rigid: it has no non-obvious degrees of freedom from either of the three points of view: deformations of maps to and from the three graces of operad theory, homotopy automorphisms, and operadic twisting. Examining the latter, it is possible to answer two questions of Markl from 2005, including a Lie-theoretic version of the Deligne conjecture.
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