A molecular clock for writing systems reveals the quantitative impact of imperial power on cultural evolution

Large language models process the world's writing systems with radical inequality. We constructed the Digital Script Representation Index (DSRI), a seven-axis measure of digital support, and applied it to the 300 writing systems of the Global Script Database (Fukui, 2026). Only 29 scripts (9.7%) are fully supported by contemporary digital infrastructure; among 158 living scripts, 60 (38.0%) lack complete support. Tokenizer efficiency varies by a factor of 31.7 across 45 scripts measured with parallel text. A serial mediation model -- imperial intervention to speaker population to web corpus to tokenizer efficiency -- is consistent with full mediation, with the direct effect of empire indistinguishable from zero (beta = -0.22, p = 0.39) and structural equation model fit indices indistinguishable from saturation at n = 45; the bias-corrected bootstrap CI grazes zero, and we treat the mediation as suggestive rather than confirmatory. Across four independent LLM families (Claude, GPT-4o, Grok, DeepSeek; 12,000 API calls), base-rate-deviation error patterns converge at Spearman rho = 0.85-0.98 (all p < 0.002). 172 script-feature items are answered identically wrong by all four models; over-attribution outnumbers under-recognition 3.9:1, and "used for religion" alone concentrates 43.6% of convergent errors (enrichment 4.1x). With religion excluded as a sensitivity check, the cross-architecture convergence is preserved (mean rho = 0.87 on nine features) and the over-attribution asymmetry persists at 1.77:1 (n = 97, binomial p = 0.008), indicating multi-channeled rather than single-channeled bias. The findings are consistent with an interpretation in which the structural inequalities historical empires inflicted on script communities persist in contemporary language models through the shared training corpus rather than through any individual model's design choices.

Of the approximately 4,500 Oracle Bone Inscription (OBI) characters discovered from the Shang dynasty, only about 1,600 have been deciphered. Many computational approaches compare OBI with glyphs from one historical period at a time. However, during the evolution of Chinese characters, significant structural or semantic changes often occur in uncertain dynasties. A single-period reference may be insufficient when relevant forms change substantially between observed eras. Therefore, we propose the Manifold-based Script Evolution Framework (MSEF), a framework that models the evolution series (OBI, Bronze, Seal, Clerical, Regular) of Chinese characters as the continual evolution of a manifold space. MSEF represents each character as an era-specific manifold point and learns continuous inter-era transition rules via Neural Ordinary Differential Equations. Both manifold space and transition dynamics can be trained end-to-end through character evolution pairs across any two eras.

Learning similarity metrics for glyphs and writing systems faces a fundamental challenge: while individual graphemes within invented alphabets can be reliably labeled, the historical relationships between different scripts remain uncertain and contested. We propose a two-stage framework that addresses this epistemological constraint. First, we train an encoder with contrastive loss on labeled invented alphabets, establishing a teacher model with robust discriminative features. Second, we extend to historically attested scripts through teacher-student distillation, where the student learns unsupervised representations guided by the teacher's knowledge but free to discover latent cross-script similarities. The asymmetric setup enables the student to learn deformation-invariant embeddings while inheriting discriminative structure from clean examples. Our approach bridges supervised contrastive learning and unsupervised discovery, enabling both hard boundaries between distinct systems and soft similarities reflecting potential historical influences. Experiments on diverse writing systems demonstrate effective few-shot glyph recognition and meaningful script clustering without requiring ground-truth evolutionary relationships.