Traverso's truncation conjecture for p-divisible groups

Let $k$ be an algebraically closed field of characteristic $p>0$, and let $H$ be a $p$-divisible group over $k$ of codimension $c$ and dimension $d$. Let $n$ be the smallest positive integer such that $H$ is uniquely determined up to isomorphism by its truncation $H[p^n]$; equivalently, any $p$-divisible group over $k$ whose truncation of level $n$ is isomorphic to $H[p^n]$ is itself isomorphic to $H$.

Traverso's truncation conjecture. One has

$$n\leq\min\{c,d\}.$$

This conjecture predicts a sharp bound for the level of a truncation that determines a $p$-divisible group. The paper proves the bound for supersingular $p$-divisible groups, while the statement in the general case is not resolved here.