Zipf's Law of Abbreviation in a Logographic Script: Coding-Theoretic Bounds on Chinese Character Stroke Counts

Abstract

Zipf's law of abbreviation -- the tendency of frequent forms to be short -- is one of the best-supported regularities in language, and recent work has moved from demonstrating it to measuring how far lexicons are compressed relative to principled baselines. That programme has so far addressed word lengths in alphabetic and syllabic scripts. We transfer it to a logographic script, taking the stroke as the unit of articulatory cost and the Chinese character as the coded form. Combining a stroke-order database covering all 20,902 characters of the CJK basic block with two independent frequency corpora (258.9M and 193.3M tokens), we find that the mean character type costs 12.71 strokes but the mean character token in running text only 7.22. Using the dually normalised optimality score of Petrini et al. (2026), the simplified inventory reaches Omega = 0.668, with the replication corpus at 0.609 -- inside and just below the 62-67% band those authors report for word lengths across 20 languages and 8 scripts, suggesting a compression ceiling largely independent of script type and cost unit. A logographic script also makes absolute coding bounds computable, since strokes come from a closed five-element taxonomy: the exact 5-ary Huffman optimum is 4.34 strokes and the entropy bound 4.28, so the observed system is 1.66x above optimal coding. This gap is not slack but structure. The Kraft sum of 5^(-l_i) is 2.05 on the frequency list and 5.03 on the full inventory, so stroke strings are provably not uniquely decodable in one dimension; characters are disambiguated by the two-dimensional arrangement of strokes, not their sequence, and the forgone compression buys componential transparency. Finally, treating the mid-twentieth-century simplification reform as a controlled compression event, we find it raised optimality from 0.555 to 0.668, with savings concentrated in the 1,000 commonest characters.