Metrological Domain Profiling: A Computational Method for Classifying Signs in Undeciphered Administrative Scripts, Validated on Proto-Cuneiform and Applied to Proto-Elamite and the Indus Valley Script

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