We prove the Imbalance Conjecture: if every edge of a finite simple graph joins vertices of distinct degrees, then the multiset of all edge imbalances is graphic. Equivalently, every finite locally irregular graph is imbalance graphic. The proof uses a tail-deficiency form of the Erdős-Gallai criterion and a capacity estimate at a maximum-degree vertex.
A. A. Raoui (2026) studied this question.