Measuring Statutory Semantic Inertia: A Noise-Calibrated Framework for Separating Legal Semantic Stability from Ordinary Semantic Drift

Legal certainty is often taken to require that statutory words keep their meaning while ordinary words drift. Diachronic word embeddingscan measure distributional change, but their scores are sensitive to frequency, corpus size, training noise, and copied text. This paper audits two publicrepositories that implement Procrustes-aligned cosine displacement D, top-k neighbour Jaccard similarity J, and a multiplicative “Legal Semantic Inertia”index. Only the README files were accessible; the reported per-word values name no corpus, and the same words receive different values in the tworepositories, so the values are treated as unverified. The contribution is a measurement design: a paired same-word statutory/general comparison, a split-halfnoise floor with frequency calibration, near-duplicate control for textual inheritance, and a corrected, reported-alongside composite. The design is validatedby executed experiments on controlled synthetic corpora with known graded semantic change (20 corpus draws; 100 simulated worlds). There, D separatedchanged from unchanged words with AUC 0.97 (J: 0.88), word rankings were highly reproducible (mean Spearman 0.97), frequency calibration removed a−0.73 rank correlation between D and log-frequency, and copied text produced a spurious “inertia” effect (∆D = +0.061) that deduplication removed. Thecomposite did not outperform D alone, J-based interval estimates were anti-conservative, and a per-word noise-floor threshold produced a 48% false-alarmrate. No experiment on real statutory or general-language corpora has been performed; the paper makes no empirical claim about law