Deligne–Drinfeld–Ihara, Alekseev–Torossian and Schneps–Raphael isomorphism conjecture

Let the four Lie algebras in the inclusions referred to in the source be graded by weight, and let the associated graded Lie algebras for the depth filtration be included as in the stated diagrams. Deligne–Drinfeld–Ihara, Alekseev–Torossian and Schneps–Raphael conjecture. The inclusions of weight-graded Lie algebras in the two diagrams are all isomorphisms in weights $W\geq 2$. This unifies several conjectures relating the double shuffle, Kashiwara–Vergne, linearized double shuffle and linearized Kashiwara–Vergne Lie algebras; the supplied text gives no resolution status.