Blockwise unimodality conjecture for Frobenius seaweed spectra

Let $A$ be any top or bottom block in a Frobenius seaweed of $\mathfrak{sl}(n)$ with $n\geq 2$. For each eigenvalue $i$, let $d_i$ be its multiplicity in the multiset of eigenvalues contributed by $A$. Blockwise unimodality conjecture. The sequence $\{d_i\}$ is unimodal about one half. The conjecture proposes a finer form of the observed unimodality of eigenspace dimensions for Frobenius seaweeds, with unimodality holding within each block. The source indicates that simulations support the claim, while a proof would require a refinement or different set of winding-down moves.