FN04: Arithmetic Readout and Multiplicative Generation

The purpose of the present note is not to derive arithmetic from the Generative Comparability Principle developed in Paper–Π.Instead, it identifies a classical mathematical system that naturally realizes the same structural architecture. Prime factorization provides irreducible multiplicative generators. The logarithm converts multiplicative composition into additive depth, while exponentiation transforms additive depth back into multiplicative readout. The Euler product then reconstructs the global arithmetic structure from local irreducible generators. Accordingly, classical arithmetic supplies a mathematically exact example of the additive–multiplicative readout principle, Generator =⇒ Additive Depth =⇒ Exponential Readout =⇒ Global Reconstruction. This note therefore serves as an arithmetic companion to Paper–Π. Its purpose is interpretive rather than foundational. No claim is made that prime numbers generate physical geometry, that the Riemann zeta function determines the physical universe, or that arithmetic itself derives the Generative Comparability Principle. Instead, the note demonstrates that the structural architecture introduced in Paper–Π already appears naturally within classical number theory.