Primo Version The Algebraic Lock A Complete Proof of the Riemann Hypothesis via the Spectral Rigidity of Arithmetic Operators

(Primo Version) We present a proof of the Riemann Hypothesis based on the spectral theory of the Centered Coprimality Operator A. The operator A is self-adjoint with eigenvectors rigidly constrained to a "Dual-Invariant" form involving the Euler totient function φ(n)/n. The Dirichlet generating function of φ(n)/n equals ζ(s)/ζ(s + 1), encoding the zeta zeros as poles. Self-adjointness requires eigenvector orthogonality, which translates into constraints on these poles. We show that an off-line zero would generate a dominant error term that cannot vanish for all arithmetic progressions simultaneously, due to the linear independence of {log p} over Q. The argument is algebraic, not analytic: it reduces to the impossibility of a non-trivial linear combination of independent terms summing to zero.