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

Writing systems are cultural replicators whose evolution has never been studied quantitatively at global scale. We compile the Global Script Database (GSD): 300 writing and notation systems, 50 binary structural characters, and 259 phylogenetic edges spanning 5,400 years. Applying four methods -- phenetics, cladistics, Bayesian inference, and neural network clustering -- we find that scripts exhibit a detectable molecular clock. The best-fitting model (Mk+Gamma strict clock) yields a substitution rate of q = 0.226 substitutions/character/millennium (95% CI: 0.034-1.22; Delta BIC = -4.1 versus relaxed clock; Delta BIC = -1,364.7 versus Mk without rate variation). Political interventions break this clock: deviation from expected divergence times correlates with intervention intensity (Spearman rho = 0.556, p < 10^{-4}), and per-character rate analysis reveals that intervention selectively rewrites deep structural features rather than merely accelerating change (rate profile correlation rho = 0.320). We identify 30 major script replacement events and rank their destructive impact. A ceiling effect suppresses independent invention wherever writing already exists (Fisher's exact OR = 0.054, p < 10^{-6}), and colonial contact predicts script extinction (Cox HR = 5.25, p = 0.0006). The Spanish Empire extinguished the most scripts (6 of 12 contacted, 50%), followed by the Empire of Japan (3 of 9, 33.3%). Feature coding was validated by inter-rater reliability testing with two independent human coders (Cohen's kappa = 0.877; human-LLM kappa = 0.929; Fleiss' kappa = 0.911).