Full priority and IP record for the identification of a three-tier hierarchical accounting operator system in Minoan Linear A, proven by arithmetic on primary source tablet HT 122 (Scribe 9, Hagia Triada, 1500-1450 BCE): ku-ro 31 plus ku-ro 65 equals po-to-ku-ro 97. Documents the identification of A-DU as a definitive non-name operator appearing on 97.5% of analyzed Hagia Triada administrative tablets across all commodity types. Establishes the Emoji Bridge methodology for reading administrative scripts without linguistic decipherment or bilingual inscription. Decodes the libation formula as a ritual protocol template with one variable personalisation slot. Presents the role-coding architecture hypothesis in which high-frequency name-position sign groups encode occupational functions rather than personal names. Four-test computational audit confirms all findings. Establishes intellectual priority as of March 13, 2026. Restricted access pending peer-reviewed publication.