Within-class collapsing conjecture for neural features

Consider the unconstrained feature model with $K$ classes, balanced class size $n$, classifier weights $\boldsymbol{w}_k$ and features $\boldsymbol{h}_{k,i}$, subject to $\\|\boldsymbol{w}_k\|=\|\boldsymbol{h}_{k,i}\|=1$. Let $(\boldsymbol{W}^*,\boldsymbol{H}^*)$ be a global solution and write $\boldsymbol{h}_k^*\doteq\sum_{i=1}^n\boldsymbol{h}_{k,i}^*$.

Within-class collapsing. All features within each class are identical: for each $k=1,\ldots,K$, $\boldsymbol{h}_{k,i}^*\equiv\boldsymbol{h}_k^*$ for every $i$.

This conjecture asserts the within-class feature collapse predicted by neural-collapse phenomena. Its resolution is not specified in the source.