State-Notation Protocol — Linear A: Hagia Triada (HT) Corpus Mathematical-structural analysis of the administrative corpus from Hagia Triada (HT): KU-RO / KI-RO operators, fractional system, ration module, social hierarchy, linguistic identification and reconstruction of damaged tablets Including the ready-to-use algorithm LinearA_Lacuna_Solver (Python / Constraint Satisfaction)

Linear A remains one of the Aegean Bronze Age's principal unsolved accounting scripts. This paper presents the State-Notation Protocol—a deterministic, non-phonetic framework for analyzing and restoring the administrative corpus of Hagia Triada (HT, ~148 tablets). Moving beyond speculative phonetic assignments, the protocol treats Linear A tablets as closed balance systems governed by absolute conservation laws. By analyzing the operational interplay between the intake/summing operator (KU-RO) and the deficit/debt operator (KI-RO), we establish: (1) a verified binary-halving fractional system (1/2 to 1/16) combined with economic quanta (1/5, 1/12) that closes balance equations with zero residual error; (2) a physical ration module (μ_base = 0.1 measure ≈ 2.88 L of grain), allowing contact-free mapping of the Minoan social hierarchy based solely on consumption coefficients; (3) syntactic evidence via the enclitic -QE (“and”) and the deduction vector KI-RO (kura-) demonstrating an Anatolian/Luwian grammatical structure overlaid with international Semitic accounting ideologemes; and (4) an algorithmic Constraint Satisfaction solver (LinearA_Lacuna_Solver) in Python that mathematically reconstructs damaged tablet entries with 100% deterministic precision. The protocol shifts Linear A from an unsolved mystery into a fully described, mathematically solved administrative topology.