Quantify the degree of dependency-length minimization across all Universal Dependencies treebanks

Natural-language sentences tend to place syntactically related words near each other, minimizing total dependency length. For a sentence with a projective dependency tree, the observed dependency length is $D_{\text{obs}} = \sum_{(h,d)} |pos(h)-pos(d)|$ summed over all head--dependent arcs. Let $D_{\text{rand}}$ be the mean of $D$ over random projective linearizations of the same unordered tree, and $D_{\min}$ the minimum over projective linearizations. Define the per-sentence optimality statistic $\Omega = (D_{\text{rand}} - D_{\text{obs}}) / (D_{\text{rand}} - D_{\min}) \in [0,1]$. QUESTION: over the treebanks of Universal Dependencies (UD) v2.x, (a) for what fraction of languages is $D_{\text{obs}}$ significantly below $D_{\text{rand}}$, (b) what is the cross-linguistic distribution (mean, spread, outliers) of the language-level mean $\bar\Omega$, and (c) does $\bar\Omega$ covary with independently coded word-order freedom or head-directionality?

Acceptance. FULLY RESOLVES: for a named UD v2.x release, report per-language $\bar\Omega$ and a permutation/randomization test of $D_{\text{obs}} < D_{\text{rand}}$ ($p<0.05$, $\geq 100$ random projective linearizations per sentence) covering $\geq 80$ languages; state the fraction with significant minimization and the mean/IQR of $\bar\Omega$; ship a reproducible script that parses CoNLL-U, computes $D_{\text{obs}}, D_{\text{rand}}, D_{\min}$ (Gildea-Temperley optimal-projective ordering), and reproduces the numbers from the public release. PARTIAL: the same on $\geq 20$ languages, or a faithful replication of the Futrell-37 result on current UD, or a genealogically/areally controlled test of covariation claim (c).