Uniqueness in the Kashiwara-Vergne conjecture
  We prove that a universal symmetric solution of the Kashiwara-Vergne conjecture is unique up to order one. in the Appendix by the second author, this result is used to show that solutions of the Kashiwara-Vergne conjecture for quadratic Lie algebras existing in the literature are not universal. 
Anton Alekseev, Emanuela Petracci