The Deligne-Drinfeld conjecture: the Grothendieck-Teichmuller Lie algebra is free on odd generators

Theorem 1.1: there are homogeneous $\sigma_{2k+1}\in W_{2k+1}$ such that $e_{2k+1}\mapsto\sigma_{2k+1}$ is a graded Lie isomorphism $\mathrm{Lie}_{\mathbb Q}\langle e_3,e_5,\dots\rangle\cong(W,\{\,,\})$, with $W$ closed under the Ihara bracket, and the induced map on weight completions is a continuous isomorphism. Via Willwacher's theorem this gives $H^0(\mathrm{GC}_2)\cong\mathrm{Lie}\langle e_3,e_5,\dots\rangle$. With Brown's theorem it identifies $\mathfrak{grt}_1$ with the motivic Lie algebra. Generators are not canonical, and no other graph-complex degrees are computed.

Theorem 1.1: there are homogeneous $\sigma_{2k+1}\in W_{2k+1}$ such that $e_{2k+1}\mapsto\sigma_{2k+1}$ is a graded Lie isomorphism $\mathrm{Lie}_{\mathbb Q}\langle e_3,e_5,\dots\rangle\cong(W,\{\,,\})$, with $W$ closed under the Ihara bracket, and the induced map on weight completions is a continuous isomorphism. Via Willwacher's theorem this gives $H^0(\mathrm{GC}_2)\cong\mathrm{Lie}\langle e_3,e_5,\dots\rangle$. With Brown's theorem it identifies $\mathfrak{grt}_1$ with the motivic Lie algebra. Generators are not canonical, and no other graph-complex degrees are computed.