Tamarkin's homotopy-type conjecture for natural Lie operations

Let ${\cal B}_{\it Lie}^*$ be the differential graded operad of natural operations on the Chevalley–Eilenberg complex of a Lie algebra with coefficients in itself, and let ${\cal L{\it ie\/}}$ be the operad governing Lie algebras. Tamarkin's conjecture. The operad ${\cal B}_{\it Lie}^*$ has the homotopy type of ${\cal L{\it ie\/}}$. This conjecture concerns the homotopy type of natural operations and would describe the Lie-operadic structure governing them; the paper presents its main result as a step toward this conjecture, but does not establish the full claim.