Excel in Clay II: The Meluhha Operating System — A Mathematical Reconstruction of the Indus Valley Non-Linguistic Cargo-Tag Database

This paper treats the Indus script corpus of the Harappan civilization (c. 2600–1900 BCE, 1,916 verified inscriptions) as a closed, non-linguistic administrative database. Enforcing a strict projection-before-meaning protocol, this audit demonstrates that the century-long failure of phonetic decipherment is an architectural error rather than an informational deficit. Through mathematical and structural analysis, the paper establishes a rigid five-field (P1–P5) cargo-tag operating system governing Bronze Age Indian Ocean logistics. Key original findings include: mathematical proof of sequence uniqueness reaching 98.31% at a mean length of 4.6 signs (structurally incompatible with natural language); the identification of tariff-locking conditional distributions linking faunal icons (e.g., Unicorn, Gaur) to permitted metrological weight tiers; the functional classification of terminal Sign 311/342 as a transaction COMMIT operator and Sign 142 as a deficit flag structurally analogous to the Sumerian lá-NI; and cross-border validation through the Gadd No. 1 seal, proving third-party logistics (3PL) routing between Meluhhan and Mesopotamian jurisdictions. Part of the "Projection Before Meaning" cross-corpus research program.