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Abstract
We introduce the Abdeslam Prime Ancestry Theorem (APAT), a deterministic framework for classifying numbers as prime or composite based on symbolic irreducibility. Unlike traditional definitions rooted in divisibility, APAT defines a number as prime if it cannot be constructed from any smaller prime through a structured symbolic form. Every composite is shown to possess at least one such symbolic ancestry, while every prime is irreducible under this model. APAT offers a complete and structurally grounded theory of primality with applications in symbolic number theory and computational certification.