The geometric Breuil–Mézard conjecture for crystalline special fibres

Let $\boldsymbol{\rho}$ range over residual representations and let $\boldsymbol{\lambda}$ range over regular tuples of labeled Hodge–Tate weights. For each Serre weight $\boldsymbol{k}$, let $Z_{\boldsymbol{k}}$ be a cycle in $\mathcal{X}_{d,\mathrm{red}}$, and let $n_{\boldsymbol{k}}^{\mathrm{crys}}(\boldsymbol{\lambda})$ denote the multiplicity of the Serre weight $\boldsymbol{k}$ in the reduction of the crystalline algebraic representation attached to $\boldsymbol{\lambda}$. The geometric Breuil–Mézard conjecture. There are cycles $Z_{\boldsymbol{k}}$ in $\mathcal{X}_{d,\mathrm{red}}$ such that, for every regular tuple of labeled Hodge–Tate weights $\boldsymbol{\lambda}$, the underlying cycle of the special fibre of $\mathcal{X}_d^{\mathrm{crys},\boldsymbol{\lambda}}$ is

$$\sum_{\boldsymbol{k}}n_{\boldsymbol{k}}^{\mathrm{crys}}(\boldsymbol{\lambda})\cdot Z_{\boldsymbol{k}}.$$

This is the stack-theoretic geometric refinement of the Breuil–Mézard conjecture: it predicts the cycles, and hence their multiplicities, uniformly across crystalline deformation conditions. The source does not state whether it is resolved.