Does Zipf's meaning-frequency law (number of senses scaling as a power of frequency) hold cross-linguistically on open WordNets?

Zipf's meaning-frequency law states that the number of distinct meanings $m$ of a word scales with its corpus frequency $f$ as $m \sim f^{\delta}$, with the classic prediction $\delta \approx 1/2$. Operationalizing 'number of meanings' as the number of WordNet senses of a lemma and $f$ as its frequency in an open corpus, QUESTION: estimate $\delta$ for English (Princeton WordNet) and for several languages of the Open Multilingual Wordnet, test whether $\delta \approx 0.5$, and characterize cross-linguistic variation and the confound introduced by differing WordNet coverage/annotation depth.

Acceptance. FULLY RESOLVES: for English (Princeton WordNet) and $\geq 5$ Open Multilingual Wordnet languages, regress $\log m$ (senses per lemma) on $\log f$ (frequency from a named open corpus), estimate $\delta$ with a confidence interval, test it against $0.5$, and report cross-linguistic variation together with a sensitivity analysis for wordnet coverage/annotation depth and for the frequency source; ship a reproducible pipeline from the public WordNet/OMW and corpus data. PARTIAL: an English-only careful estimate with frequency-source sensitivity analysis, or an estimate on $\geq 3$ languages.