Conjecture on unimodality of minimal filling widths

Fix an activation degree $r$, a depth $h$, and input and output widths $d_0$ and $d_h$. Let $\bm d=(d_0,d_1,\ldots,d_h)$ be a minimal filling architecture. Unimodality conjecture. There is an index $i$ such that

$$d_0\leq d_1\leq\ldots\leq d_i$$

and

$$d_i\geq d_{i+1}\geq\ldots\geq d_h.$$

The claim formalizes the observed unimodal pattern of minimal filling architectures in the paper's computational examples; its resolution is not given in the supplied text.