Elementary Prime Counting: A Constructive Framework for Rational Decomposition

Classical mathematics privileges integers and values greater than unity as the primary objects of counting, relegating fractional structure and scale symmetry to secondary, representational roles. This bias, while historically practical, obscures a deeper multiplicative structure governed by prime generators. In this paper we introduce Elementary Prime Counting (EPC), a base-independent, prime-duality framework in which primes and their duals act as fundamental generators of scale. Integers emerge as asymmetric special cases, while fractions constitute the natural numerical form. By treating expansion and contraction symmetrically and rejecting decimal-point ontology, EPC restores the missing half of the number system and provides a foundational perspective on prime structure and rational numbers, within which classical con- structions appear as restricted projections.