ADRIAN WILLIAM SHARMAN
Undeciphered administrative scripts resist linguistic analysis but encode mathematical relationships between signs and numerals that survive independent of language. We introduce Subtractive Metrological Domain Profiling (MDP), a computational method that classifies signs in ancient administrative scripts by analysing their statistical co-occurrence with metrological numeral systems. The method requires no linguistic assumptions, no phonetic hypotheses, and no prior knowledge of sign meanings. We validate MDP on proto-cuneiform (c. 3350-3000 BCE), achieving 100% accuracy on a 28-sign test set drawn from 31,191 sign tokens across 6,819 Uruk IV/III tablets. The method correctly separates grain (capacity system), rations (bisexagesimal system), fields (area system), and all discrete commodities (sexagesimal system). To overcome proto-cuneiform's numeral polyvalency, we introduce a subtractive diagnostic layer that isolates system-specific fractional anchors. We apply MDP to Proto-Elamite (c. 3100-2900 BCE), classifying 79 signs covering 64% of a 14,716-record corpus, independently reproducing decades of manual epigraphy and revealing line-level syntax (CLASSIFIER to PERSONNEL to COMMODITY), bureaucratic seal specialisation, and compound determinative patterns. We extend the framework to the Indus Valley script (c. 2600-1900 BCE) using 2,543 inscriptions across 52 sites. We discover statistically robust semantic locks between specific signs and specific seal animals: sign G321 appears exclusively on hare seals (195.6x enrichment), sign G850 exclusively on anthropomorphic-figure seals (60.5x), sign G48 on elephant seals (35.6x), and sign G436 on rhinoceros seals (31.7x). These provide the first corpus-scale statistical evidence that Indus seal animals encode institutional or departmental identity, with each animal type carrying a unique sign vocabulary. Code and data: https://github.com/souldriver007/mdp-ancient-scripts