The Hodge–Tate weight conjecture for crystalline Breuil–Kisin modules

Assume $K=K_{{\mathrm{cyc}}}\cap K_\infty$. Let $\mathfrak M$ be a crystalline Breuil–Kisin module of rank $d$, let $\lambda:=\frac{\xi}{E([\pi^{\flat}])}$, and let $\widetilde A$ be the matrix of its tau-connection as in the preceding theorem. Let $r_1\leq r_2\leq\dots\leq r_d$ be the Hodge–Tate weights of the associated crystalline ${\mathbb Z}_p$-representation. The Hodge–Tate weight conjecture. The matrix

$$\prod_{i=1}^d(\lambda^{-1}\widetilde A+r_i d_q(E))$$

is $(p,[\pi^{\flat}])$-adic topologically nilpotent. This conjecture relates the Hodge–Tate weights of a crystalline representation to the associated crystalline Breuil–Kisin module. The source states that it can be implied by the Sen-operator conjecture, but gives no resolution for it.