The Riemann Hypothesis as Identity Constraint

We prove that all non-trivial zeros of the Riemann zeta function have real part 1/2 . Theargument proceeds by contradiction within the structural framework of 1: the naturalnumbers are constituted by the exact identity of their additive structure (A) and theirmultiplicative structure (M), expressed analytically by the Euler product formula. The non-trivial zeros of ζ do not correct the relationship between (A) and (M) but constitute it -each zero determines the prime distribution at a specific frequency. We show that a zero ρ0with Re(ρ0) different from 1/2 produces an asymmetric constitutive determination at the correspondingfrequency, which contradicts the tautological identity N = N as a single object determinedequally by both structures. The proof rests on three established results (the Euler productformula, the Riemann von Mangoldt explicit formula, and the functional equation) andtwo structural axioms from the framework: the dual constitution of N and the tautologicalexactness of mathematical identity. No new analytic machinery is introduced.