Fayers' degree bound conjecture for cyclotomic Hecke algebra decomposition numbers

Let ${\boldsymbol\lambda},{\boldsymbol\mu}\in\mathscr{P}_{n}$. For the polynomials $d_{{\boldsymbol\lambda}{\boldsymbol\mu}}(q)$ and the defect $\mathop{\rm def}\nolimits_{}{{\boldsymbol\mu}}$ associated with multipartitions, let $\mathcal{K}_{n}$ denote the specified set of Kleshchev multipartitions. Fayers' conjecture.

$$\deg d_{{\boldsymbol\lambda}{\boldsymbol\mu}}(q)\leq\mathop{\rm def}\nolimits_{}{{\boldsymbol\mu}}.$$

Moreover,

$$\deg d_{{\boldsymbol\lambda}{\boldsymbol\mu}}(q)=\mathop{\rm def}\nolimits_{}{{\boldsymbol\mu}}$$

only if ${\boldsymbol\mu}\in\mathcal{K}_{n}$. The conjecture predicts a defect bound on canonical-basis or decomposition polynomials, with equality restricted to Kleshchev multipartitions; the source applies it to the study of cyclotomic Hecke and Weyl modules but provides no resolution status here.