Square-root growth conjecture for ranks of generic six-in-nine distributions

Let $H$ be a distribution with co-rank $s$ and rank $r$, so that its derived distribution satisfies $[H,H]=T$ and hence $s<r(r-1)/2$. Square-root growth conjecture. The minimal possible rank of $H$ grows as the square root of twice the co-rank; exceptions will remain very rare and may vanish entirely. This is a tentative prediction based on the listed ranks of semisimple $|2|$-graded parabolic geometries; the source does not establish a precise asymptotic statement or resolve whether exceptions eventually disappear.