M12c Operational Number Theory: HyperPrimes, Zeta Flow, and the Riemann Programme in the Hyper Core Framework

This monograph applies the Hyper Core framework developed in M12a and M12b to operational number theory, focusing on prime structure, arithmetic localisation, and spectral representations. Working entirely within the Hyper Core language, the monograph reformulates classical arithmetic objects as operational invariants on discrete lattices. It develops rank‑adapted arithmetic functions, local factor decompositions, and operational zeta‑type constructions that mirror classical Dirichlet and Euler structures without invoking external analytic assumptions. M12c establishes the operational setting required for later spectral and symmetric‑core analyses, making explicit how arithmetic phenomena emerge from Hyper Core invariants rather than from ad hoc number‑theoretic input. The purpose of this deposit is to document the number‑theoretic extension of the Hyper Core framework, explicitly dependent on M12a and M12b, and to establish its conceptual priority within the hyperoperation theory series.