Dimitrov's conjecture on the ordered Davenport constant and Loewy length

Let $p$ be a prime and let $G$ be a finite $p$-group. The Loewy length $\mathsf{L}(G)$ is the nilpotency index of the Jacobson radical of the group algebra $\mathbb{F}_p[G]$, and $\mathsf{D}_o(G)$ denotes the ordered Davenport constant of $G$. Dimitrov's conjecture.

$$\mathsf{D}_o(G)=\mathsf{L}(G).$$

The conjecture proposes an equality between a combinatorial invariant of finite $p$-groups and the Loewy length of their modular group algebras. The source gives no general resolution, although it studies the ordered Davenport constant for particular groups.